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SAT Math Practice Questions: Algebra

Question

x2-9x-3=-1

What is the solution set of the equation above?

A. {−4}
B. {0}
C. {3}
D. {3, 4}

Hint :

To solve a rational equation, first multiply both sides by the least common denominator (LCD) to clear the fractions.

Explanation

The given equation x2−9 x−3 =−1 is a rational equation because it contains a variable in a denominator. Solutions to a rational equation may be valid or extraneous, so solve for x and then check for extraneous solutions.

The only denominator in x2−9 x−3 =−1 is x − 3, so multiply both sides of the equation by x − 3 to clear the fraction.

x 2 - 9 x - 3 = - 1 Given equation
( x 2 - 9 ) ( x - 3 ) x - 3 = - 1 ( x - 3 ) Multiply both sides by (x − 3)
( x 2 - 9 ) ( x - 3 ) ⧸ x - 3 ⧸ = - 1 ( x - 3 ) Cancel factors to clear fraction
x 2 - 9 = - 1 ( x - 3 ) Simplify

To solve the resulting quadratic equation, rewrite it in standard form ax² + bx + c = 0 and then factor.

x2−9 =−1(x−3)
x2−9 =−x+3 Distribute −1 to (x − 3)
x2+x−12 =0 Add x and subtract 3 on both sides
(x+4)(x−3) =0 Factor

The expression (x + 4)(x − 3) is equal to 0 when either of its factors equals 0. Set each factor equal to 0 to solve for x.

x + 4 = 0 Set each factor equal to 0 x − 3 = 0
x = −4 Solve for x x = 3

Plug x = −4 and x = 3 into the given equation and simplify to check if they are valid or extraneous.

The solution x = −4 results in a true statement, so −4 is a valid solution.
The solution x = 3 results in a false statement, so 3 is an extraneous solution.

Therefore, the solution set of the given equation is {−4}.

Elimination strategy: It is possible to identify values of x where the given equation is undefined to eliminate Choices C and D.

(Choice B) 0 is not in the solution set, because 0 does not satisfy the given equation (see alternate method).

(Choice C) 3 is an extraneous solution, because the left side of the given equation x2−9 x−3 =−1 simplifies to the undefined fraction 00 when x = 3. Therefore, 3 is not in the solution set.

(Choice D) 3 and 4 may result from a combination of a sign error and the error described in Choice C.

Things to remember:

  • An equation that contains a variable in a denominator is a rational equation. To solve a rational equation, multiply both sides by the least common denominator (LCD) to clear the fractions.
  • Solutions to a radical equation may be valid or extraneous, so solve the equation and then plug the results into the given equation to check for extraneous solutions.
  • A rational equation is undefined when any variable denominator is equal to zero.

Alternate Method :

It is also possible to plug each possible solution from the choices into the given equation to determine the solution set. The choices include −4, 0, 3, and 4 as possible solutions.

Plug x = −4, x = 0, x = 3, and x = 4 into x2−9 x−3 =−1 to see which simplifies to a true statement.

Of the values from the choices, only −4 simplifies the equation to a true statement. Therefore, the solution set of the given equation is {−4}.

Note: When x = 3, the left side of the given equation x2−9 x−3 =−1 simplifies to the undefined fraction 00 .

Things to remember:

Any value that simplifies an equation to a true statement is a solution to the equation.

Question

If a − b = 3 and a + b = 4, what is the value of (a − b)(a2 − b2) ?

Hint :

Factor the expression (a2 − b2) as a difference of two squares.

Explanation

Notice that the given expression contains a difference of two squares (a2−b2) and a factor with a given value (a−b).

A difference of two squares of the form x2−y2 can be factored as (x+y)(x−y).

Factoring difference of squares illustration showing (x² − y²) = (x + y)(x − y)

The difference of two squares a2−b2 in the given expression can be factored as (a+b)(a−b), and both factors have given values. To evaluate (a−b)(a2−b2), first factor a2−b2 as a difference of two squares.

(a − b)(a2 − b2)Given expression
(a − b)(a + b)(a − b)Factor a2 − b2

Now plug in the given values for each of the factors (a−b) = 3 and (a+b) = 4.

(a − b)(a + b)(a − b)
(3)(4)(3)Substitute (a − b) = 3 and (a + b) = 4
36Multiply

The value of (a−b)(a2−b2) is 36.

Things to remember:

  • An expression of the form x2−y2 is a difference of two squares that can be factored as (x+y)(x−y).

Diagram demonstrating difference of two squares factoring pattern

  • If the value for an expression is given, it may be possible to rewrite a desired expression in terms of the given expression and plug in known values.

Question

The solutions to which inequality are represented by the shaded region of the graph?

A. y ≤ −2x − 4
B. y ≤ −4x − 2
C. y ≥ 2x − 4
D. y ≥ 4x − 2
Hint :

The graph of a linear inequality of the form y ≥ mx + b has shading above a boundary line.

The graph of a linear inequality of the form y ≤ mx + b has shading below a boundary line.

Explanation

The solutions represented by the given graph consist of all points in the shaded area and on the boundary line. Analyze the shading and the boundary line of the given graph and use a process of elimination.

The given graph is shaded above the line, so the inequality must be in the form y ≥ mx + b. Eliminate Choices A and B because they represent graphs with shading below the boundary line.

The boundary line of the given graph has a y-intercept of −4, so the boundary line equation in slope-intercept form must be y = mx − 4. Therefore, the inequality must be in the form y ≥ mx − 4.

Eliminate Choice D because it does not match this form.

Of the choices, only the inequality in Choice C has a graph with shading above the boundary line and a y-intercept of −4. By process of elimination, Choice C has the solutions represented by the shaded region.

Elimination strategy: The boundary line of the given graph has a positive slope. Therefore, it is possible to eliminate Choices A and B because each has a boundary line equation with a negative slope.

Things to remember:

  • The graph of a linear inequality of the form y > mx + b or y ≥ mx + b has shading above a boundary line.
  • The graph of a linear inequality of the form y < mx + b or y ≤ mx + b has shading below a boundary line.
  • The equation of the boundary line in slope intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Question

The bar graph shows the number of points scored by a football team in each of four games. For these four games, how much greater is the median number of points scored than the mean number of points scored?

Hint :

The mean of a data set is the sum of the values divided by the number of values.

The median is the middle of a data set when all values are ordered numerically.

Explanation

To find how much greater the median number of points is than the mean number of points, calculate each measure separately and then subtract the mean from the median.

First identify from the given bar graph that the numbers of points scored in the 4 games were 14, 9, 23, and 22.

Mean score

The mean of a data set is the sum of the values divided by the number of values.

The sum of the values is the sum of the numbers of points scored and the number of values is the number of games.

Plug the numbers of points (14, 9, 23, and 22) and the number of games (4) into the expression for the mean and simplify to calculate the mean score.

sum of points scorednumber of games Mean number of points
14+9+23+224 Plug in values
684 Add in numerator
17 Divide

The mean number of points is 17.

Median score

The median is the middle of a data set when all values are ordered numerically. For a data set with an even number of values, the median is the average of the middle two.

The numbers of points scored are 14, 9, 23, and 22. Order these values numerically and then calculate the average of the middle two to find the median number of points scored.

The median number of points is 18.

The mean is 17 points and the median is 18 points. Subtract 18 − 17 = 1 to see that the median is 1 point greater than the mean.

Things to remember:

  • The mean of a data set is the sum of the values divided by the number of values.
  • The median is the middle of a data set when all values are ordered numerically. For a data set with an even number of values, the median is the average of the middle two.

Question

The table above shows some values of x and their corresponding values of y, where d is a constant. If the relationship between x and y is linear, which of the following equations represents the relationship?

A. dx + 4y = 24
B. 4x + dy = 24
C. dx + 4y = 24d
D. 4x + dy = 24d

Hint :

Every pair of corresponding values of x and y must satisfy the equation that defines the relationship between x and y.

Explanation

In the given table, each row represents a pair of corresponding values of x and y. Every pair of corresponding values of x and y must satisfy the equation that defines the relationship between x and y.

Choose a pair of corresponding values from the table to plug into each equation from the choices to see which results in a true statement. For simpler calculations, plug in x = d and y = 20 and simplify.

The values x = d and y = 20 satisfy only the equation in Choice D. Therefore, the equation that represents the relationship between x and y is 4x + dy = 24d.

Note: If a pair of corresponding values satisfied more than one equation in the answer choices, it would be necessary to plug a second set of values into those equations.

(Choice A) dx + 4y = 24 may result from the combination of errors described in Choices B and C.

(Choice B) 4x + dy = 24 may result from disregarding the constant term when simplifying the equation.

(Choice C) dx + 4y = 24d may result from swapping the x- and y-values when plugging them into the choices.

Things to remember:
Every pair of corresponding values of x and y must satisfy the equation that defines the relationship between x and y.

It is also possible to use the values in the given table to write an equation that represents a linear relationship between x and y.

The slope of a line that represents a function is equal to the change in y divided by the corresponding change in x. A line has a constant slope, so the slope is the same between any two pairs of corresponding values.

The change in y is equal to the difference between any two y-values, and the change in x is equal to the difference between the corresponding values of x.

Each row in the given table represents a pair of corresponding values of x and y. Find the change in y and the corresponding change in x for any two rows and divide to calculate the slope m.

The slope is - 4 d . Notice that each choice is given in standard form Ax + By = C. The slope of an equation in standard form is - A B (proof), so compare to see that the desired equation must be of the form 4x + dy = C.

Now plug a pair of corresponding values from the table into 4x + dy = C and simplify to find the value of C. Choose (d, 20) for simpler calculations.

4x + dy = C
4(d) + d(20) = C Plug in x = d and y = 20
24d = C Simplify

The value of C is 24d. Substitute 24d for C in the equation 4x + dy = C.

4x + dy = C
4x + dy = 24d Plug in C = 24d

Therefore, the equation that represents the given relationship is 4x + dy = 24d.

Note: It is also possible to first determine the equation in slope-intercept form and then rearrange to standard form (see how).

Things to remember:

  • For a linear equation in standard form Ax + By = C, the slope is equal to - A B .
  • The (x, y) coordinates of every point on a line must satisfy any equation of the line.
Study Guide References :

Question

An equation of a circle in the xy-plane with radius 2 and center at (5, −4) is x2 + y2 + ax + by = c. What is the value of c ?

Hint :

The equation of a circle in standard form is (x − h)2 + (y − k)2 = r 2.

Explanation

The equation of a circle in standard form is (x − h)2 + (y − k)2 = r 2, where (h, k) is the center and r is the length of the radius.

The given circle has radius 2 and center at (5, −4), so plug in r = 2 and (h, k) = (5, −4) to get an equation of the circle in standard form.  Then rewrite the equation in the form x2 + y2 + ax + by = c to identify the value of c.

(x − h)2 + (y − k)2 = r 2 Standard form
(x − 5)2 + (y − (−4))2 = 22 Plug in (h, k) = (5, −4) and r = 2
(x − 5)2 + (y + 4)2 = 4 Simplify

Now expand the perfect squares (x − 5)2 and (y + 4)2 and then rearrange the equation to the form x2 + y2 + ax + by = c.

(x − 5)2 + (y + 4)2 = 4
x2 − 10x + 25 + y2 + 8y + 16 = 4 Expand (x − 5)2 and (y + 4)2
x2 + y2 − 10x + 8y + 41 = 4 Rearrange and combine constant terms on left
x2 + y2 − 10x + 8y = −37 Subtract 41 from both sides

Compare the resulting equation to the given equation to identify c.

Things to remember:

  • The equation of a circle in standard form is (x − h)2 + (y − k)2 = r 2, where (h, k) is the center and r is the length of the radius.

  • To expand (a + b)2, use the identity (a + b)2 = a2 + 2ab + b2 or rewrite the expression (a + b)2 as (a + b)(a + b) and multiply.

Question

The complete graph of the function g is shown in the xy-plane above. What is the y-intercept of the graph of y = g(x − 3) ?

A. (0, 0)
B. (0, 2)
C. (0, 3)
D. (0, 4)
Hint :

The y-intercept of a graph is the point where the graph crosses the y-axis.

Transform the given graph of g to get the graph of g(x − 3), and then find the y-intercept of the transformed graph.

Explanation

The function y = g(x − 3) is defined in terms of g(x), so it represents a transformation to the function g.

For any function f(x), the graph of y = f(x − h) + k is the graph of y = f(x) transformed by a horizontal shift of h units and a vertical shift of k units.

In y = g(x − 3), the number 3 is subtracted from the input x, so it represents a horizontal shift of 3 units to the right.

Therefore, the graph of y = g(x − 3) is the graph of y = g(x) shifted to the right 3 units. This means every point on the graph of g(x − 3) is 3 units to the right of every point on the graph of g(x).

Identify the point where the graph of y = g(x − 3) crosses the y-axis to determine the y-intercept.

The graph of y = g(x − 3) crosses the y-axis at 4, so its y-intercept is (0, 4).

(Choice A) (0, 0) is the y-intercept of the graph of g(x) − 3, instead of g(x − 3).

(Choice B) (0, 2) is the y-intercept of the graph of g(x + 3), instead of g(x − 3).

(Choice C) (0, 3) is the y-intercept of the graph of g(x), instead of g(x − 3).

Things to remember:

  • For any function f(x), the graph of y = f(x − h) + k is the graph of y = f(x) transformed by a horizontal shift of h units and a vertical shift of k units
  • The y-intercept of a graph is the point where the graph crosses the y-axis, and it has an x-value of 0.

Alternate Method :

The y-intercept of a graph is the point where the graph crosses the y-axis, and it has coordinates (0, y).

The question asks for the y-intercept of the graph of y = g(x − 3), but the given graph shows y = g(x). First plug x = 0 into y = g(x − 3).

y = g(x − 3)
y = g(0 − 3) Plug in x = 0
y = g(−3) Simplify

Therefore, the y-intercept of the graph of y = g(x − 3) has a y-value that is equal to the value of g(−3). The function notation g(−3) means the value of the function g when x is −3.

To identify the value of g(−3) from the given graph, find the y-value of the point where x = −3.

The value of g(−3) is 4. Therefore, the graph of g(x − 3) has y-intercept (0, 4).

Things to remember:

  • The y-intercept of a graph is the point where the graph crosses the y-axis, and it has an x-value of 0.
  • The function notation f(a) means the output (or value) of f(x) when the input is a.

Question

In a warehouse, there are 7 shelves of cardboard boxes and 8 shelves of plastic boxes. Each shelf of cardboard boxes has 12 boxes that weigh 25 pounds or more and 8 boxes that weigh less than 25 pounds. Each shelf of plastic boxes has 11 boxes that weigh 25 pounds or more and 9 boxes that weigh less than 25 pounds. A box from one of these shelves will be selected at random. What is the probability of selecting a plastic box, given that the box is 25 pounds or heavier?

Hint:

To find the probability of a desired event, use the following formula:

Explanation

The question asks for the probability of selecting a plastic box, given that the box is 25 pounds or heavier.

To find the probability of a desired event, use the following formula:

The total number of possible outcomes is the total number of boxes that are 25 pounds or heavier.
The number of desired outcomes is the number of those boxes that are plastic.

The total boxes that weigh 25 pounds or more is the sum of the numbers of plastic boxes and cardboard boxes that weigh 25 pounds or more.

It is given that there are 8 shelves with 11 plastic boxes on each shelf that weigh 25 pounds or more and that there are 7 shelves with 12 cardboard boxes on each shelf that weigh 25 pounds or more.

Multiply each number of shelves by the number of boxes on each shelf to see that there are 8 ∙ 11 = 88 plastic boxes and there are 7 ∙ 12 = 84 cardboard boxes that weigh 25 pounds or more.

Now simplify the probability.

P = 88 88 + 84
P = 88 172 Add in denominator
P = 22 43 Simplify: 88 172 = 4   ⋅   22 4   ⋅   43

The probability of selecting a plastic box, given that the box is 25 pounds or heavier, is 22 43

Things to remember:
To find the probability of a desired event, use the following formula:

Question

An object, launched from a height of 0 feet, reaches a maximum height of 576 feet 6 seconds after launch. A quadratic function can be used to model the height, in feet, of the object above the ground in terms of time, in seconds, after launch. Based on the model, what is the height, in feet, of the object, 2 seconds after launch?

A. 192
B. 320
C. 432
D. 560

Hint:

The maximum of a quadratic function occurs at the vertex of its parabola. The vertex form of a quadratic function is f(x) = a(x − h)2 + k.

Explanation

It is given that the height of an object in terms of time is modeled by a quadratic function. To find the height of the object 2 seconds after launch, first write an equation for height f(x) in terms of time x.

The object is launched from height 0 and reaches its maximum height of 576 feet at 6 seconds. The maximum of a quadratic function occurs at the vertex of its parabola, so the given model has vertex (6, 576).

The vertex form of a quadratic function is f(x) = a(x − h)2 + k, where (h, k) is the vertex and a is the scale factor. Plug (h, k) = (6, 576) into vertex form.

f(x) = a(x − h)2 + k Vertex form
f(x) = a(x − 6)2 + 576 Plug in (h, k) = (6, 576)

Now find the value of a. The object was launched from a height of 0 feet, so f(x) = 0 when x = 0. Plug these values into f(x) = a(x − 6)2 + 576 and solve to find that a = −16.

Plug a = −16 into the equation for height f(x) in terms of time x.

f(x) = a(x − 6)2 + 576
f(x) = −16(x − 6)2 + 576 Plug in a = −16

Therefore, an equation that defines the given model is f(x) = −16(x − 6)2 + 576.

The height after 2 seconds is equal to f(2), the value of the function f when the time x is 2. Plug x = 2 into f(x) and solve for f(2).

f(x) = −16(x − 6)2 + 576
f(2) = −16(2 − 6)2 + 576 Plug in x = 2
f(2) = −16(16) + 576 Subtract and apply exponent: (2 − 6)2 = (−4)2
f(2) = −256 + 576 Multiply
f(2) = 320 Simplify

Based on the model, the height of the object 2 seconds after launch is 320 feet.

(Choice A) 192 may result from mistaking the function that represents the given scenario to be linear (instead of quadratic).

(Choice C) 432 is the height of the object 3 seconds after launch, but the question asks for the height 2 seconds after launch.

(Choice D) 560 may result from disregarding the scale factor a when attempting to write an equation that represents the given scenario in vertex form.

Things to remember:

  • The maximum or minimum of a quadratic function occurs at the vertex of its parabola.
  • The vertex form of a quadratic function is f(x) = a(x − h)2 + k, where (h, k) is the vertex and a is the scale factor.

Question

The table shows three values of x and their corresponding values of y, where y = f(x) + 6 and f is a quadratic function. What is the y-coordinate of the y-intercept of the graph of y = f(x) in the xy-plane?

Hint :

For any function f(x), the graph of y = f(x − h) + k is the graph of y = f(x) transformed by a horizontal shift of h units and a vertical shift of k units.

The equation of a quadratic function in vertex form is y = a(x − h)2 + k, where (h, k) is the vertex of the parabola and a is the scale factor.

Explanation

The equation y=f(x)+6 is in terms of f(x), so it is the result of a transformation to the function f(x). The constant 6 is added to the output f(x) , so it represents a vertical shift 6 units up.

Graph showing vertical shift of y = f(x) + 6

Each row of the table represents an (x, y) point on the graph of y=f(x)+6. The question asks for the y-intercept of f(x), so apply the transformation to the given table to get a table of values for y=f(x).

Every point on the graph of y=f(x)+6 is 6 units above a point on the graph of y=f(x), so subtract 6 from each y-value to get a table that represents points on the graph of y=f(x).

Table showing f(x)+6 values and adjusted f(x) values after subtracting 6

It is given that f(x) is a quadratic function, so its graph is a parabola. A vertical axis of symmetry passes through the vertex and is located halfway between any two points on a parabola that have the same y-value.

Notice that two points from the table have the same y-value (4). Therefore, the point with an x-value halfway between 17 and 21 is the vertex (h, k). This point is in the table (19, −8).

Parabola with vertex at (19, −8) and symmetric points marked

Plug (h, k) = (19, −8) into the vertex form equation y=a(x−h)2+k to see that an equation for the graph of f(x) is y=a(x−19)2−8 . Plug in a different point from the table to solve for a. Choose (x, y) = (17, 4).

Plug a = 3 into y=a(x−19)2−8 to see that an equation for f(x) is y=3(x−19)2−8 . To find the y-coordinate of the y-intercept, plug in x = 0 and solve for y.

Note: It is also possible to use the given table of values to see that the equation of the transformed function is y=3(x−19)2−2 and has y-intercept 1,081. Then subtract 6 to get the y-coordinate of the y-intercept of f(x).

Things to remember:

  • For any function f(x), the graph of y=f(x−h)+k is the graph of y=f(x) transformed by a horizontal shift of h units and a vertical shift of k units.
  • A vertical axis of symmetry passes through the vertex (h, k) of a parabola and is located halfway between any two points on a parabola that have the same y-value.
  • The equation of a quadratic function in vertex form is y=a(x−h)2+k, where (h, k) is the vertex of the parabola and a is the scale factor.

Question

The table shows three values of x and their corresponding values of y, where y = f(x) + 6 and f is a quadratic function. What is the y-coordinate of the y-intercept of the graph of y = f(x) in the xy-plane?

A. −8
B. −4
C. 0
D. 4

Hint :

The function notation f(x) = 0 means the output (or value) of the function f is 0 when the input is x.

Explanation

The function notation f(x) = 0 means the output (or value) of the function f is 0 when the input is x.

Solutions to f(x) = 0 correspond to x-intercepts on the graph of the function f. The given graph of function f intersects the x-axis at (−8, 0), so f(−8) = 0.

Therefore, the value of x for which f(x) = 0 is −8.

(Choice B) −4 corresponds to the y-intercept (instead of the x-intercept), so this value corresponds to f(0), instead of solutions to f(x) = 0.

(Choice C) 0 is the value of f(x) when x = −8, but the question asks for the value of x for which f(x) = 0.

(Choice D) 4 may result from the combination of a sign error and the error described in Choice B. When x = 4, the function value f(x) is 6 (instead of 0).

Things to remember:

  • The function notation f(x) = 0 means the output (or value) of the function f is 0 when the input is x.
  • Solutions to f(x) = 0 correspond to x-intercepts on the graph of the function f.

Question

A small company classifies its employees according to how long they have been employed. Eight employees have worked at the company for less than 6 months and are classified in Group A. Nine employees have worked at the company for at least 6 months but no more than 12 months and are classified in Group B. Ten employees have worked at the company for more than 12 months and are classified in Group C. Which of the following could be the median amount of time, in months, that these 27 employees have worked at the company?

A. 5.5
B. 7
C. 12.5
D. 16

Hint :

The median of a data set is the middle of the set when all values are ordered numerically.

Explanation

The median of a data set is the middle of the set when all values are ordered numerically. When the number of values is odd, the median is the middle value.

The number of months each employee has worked at the company is unknown, but the range of months for each group is given. First consider the groups from least to greatest according to the ranges of months worked.

It is given that there are 27 employees, so the median number of months must be the number worked by the 14th employee (proof).

Starting with the first range, add the number of employees in each successive group to find the group that contains the 14th employee and identify the range of months that employee has worked.

The 14th employee was in Group B, so the 14th employee worked at least 6 months and no more than 12 months.

Of the choices, only Choice B falls within this range. Therefore, the median number of months could be 7.

(Choices A, C, and D) These choices are not possible numbers of months because they do not fall within the range worked by the 14th employee (at least 6 months and no more than 12 months).

Things to remember:
The median of a data set is the middle of the set when it is ordered numerically. When the total number of values is odd, the median is the middle value. When it is even, the median is the average of the middle two values.

Question

In a tall office building, an express elevator descends from a height of 300 feet to 20 feet at a constant rate of 8 feet per second. What type of function best models the relationship between the height of the descending elevator and time?

A. Increasing linear
B. Decreasing linear
C. Increasing exponential
D. Decreasing exponential

Hint :

A function is linear if the same number is added to each value to get the next.  A function is exponential if the same number is multiplied by each value to get the next.

Explanation

A function is linear if the same number is added to each value to get the next (the difference is constant).
A function is exponential if the same number is multiplied by each value to get the next (the ratio is constant).

It is given that the elevator descends 8 feet per second, so the same number (−8) is added every second. Therefore, the function is linear.

As the number of seconds increases, the height of the elevator decreases. Therefore, the function is decreasing.

The function that best models the relationship between the height of the elevator and time is decreasing linear.

(Choice A) "Increasing linear" is incorrect because as time increases, the height of the elevator decreases.

(Choice C) "Increasing exponential" may result from the combination of errors described in Choices A and D.

(Choice D) "Decreasing exponential" is incorrect because the same number is added (−8) for each constant change in time. A relationship is exponential if the same number is multiplied for each constant change in time.

Things to remember:

A relationship between two variables is:

  • linear if the same number is added to each value to get the next value (the difference between consecutive values is constant).
  • exponential if the same number is multiplied by each value to get the next value (the ratio of consecutive values is constant).

Question

Angle P has a measure of  7 π 12  radians.  If the measure of angle Q is  3 π 4  radians greater than the measure of angle P, what is the measure of angle Q, in degrees?

A. 30
B. 105
C. 135
D. 240

Hint :

The angle measure of a complete circle is 360°, or 2π radians.

For any angle, the ratio of its degree measure to 360° must equal the ratio of its radian measure to 2π radians.

Explanation

An angle can be measured in radians or degrees. A complete circle contains 2π radians, or 360°.

Diagram illustrating angle measures in radians and degrees, showing a full circle with 2π radians and 360°

It is given that the measure of angle Q is 3 π 4 radians greater than that of angle P, and that the measure of angle P is 7 π 12 radians. Add to find the radian measure of angle Q.

To add fractions, first rewrite them with a common denominator.

Step-by-step addition of radian measures: 7π/12 + 3π/4 using common denominator 12

The radian measure of angle Q is 16 π 12 radians. Let d be the equivalent degree measure and set up a proportion.

For any angle, the ratio of the degree measure to 360° must equal the ratio of the radian measure to 2π radians. Plug in the given radian measures and then solve the proportion.

Proportion setup: d/360 = (16π/12)/(2π) for converting radians to degrees

Now solve for d.

Proportion setup: d/360 = (16π/12)/(2π) for converting radians to degrees

The measure of angle Q is 240 degrees.

Note: It is also possible to first find the degree measure for each angle, and then add 105 and 135 to find that the degree measure of angle Q is 240.

(Choice A) 30 may result from finding the degree measure that is 3π4 radians less than (instead of greater than) the measure of angle P.

(Choice B) 105 is the degree measure that is equivalent to 7π12 radians, but angle Q is 3π4 radians greater than 7π12 radians.

(Choice C) 135 is the degree measure that is equivalent to 3π4 radians, but angle Q is 3π4 radians greater than 7π12 radians.

Things to remember:

The ratio of the degree measure of an angle to 360° must be equal to the ratio of the radian measure of the same angle to 2π radians.

To convert from radians to degrees, it is also possible to multiply by a conversion factor that cancels the old unit and replaces it with the new unit.

A conversion factor is a fraction that is equivalent to 1, so it changes only the units and not the quantity. Use a fraction with the new unit in the numerator and the old unit in the denominator.

Final calculation using conversion factor: (16π/12) × (180/π) = 240 degrees

The radian measure of angle Q is 16 π 12 (see main explanation). To convert from radians to degrees, multiply by a fraction with degrees in the numerator and the equivalent number of radians in the denominator.

The conversion is 360° = 2π radians, so the conversion factor is 360 ° 2 π radians . Cancel radians and simplify to find that 16 π 12 radians is equivalent to 240 degrees.

Final calculation using conversion factor: (16π/12) × (180/π) = 240 degrees

The measure of angle Q is 240 degrees.

Note: It is possible to use an equivalent conversion 180° = π radians when converting between degrees and radians.

Things to remember:

  • To convert from one unit to another, multiply by a conversion factor that cancels the old unit and replaces it with the new unit.
  • The conversion between degrees and radians is 360° = 2π radians or 180° = π radians.

Question

13 20 y - 11 20 x = 10 13 - 13 20 y

11 10 x + 13 10 = ry + 33 10

In the system of equations shown, r is a constant. If the system has no solution, what is the value of r?

Hint :

A system of linear equations has no solution if the same expression of x and y is equal to two different numbers.

Explanation

It is given that the system has no solution, so its graph must consist of lines that do not intersect. Therefore, the lines must be parallel. Parallel lines have the same slope but different y-intercepts.

Graphical representation of two parallel lines (no intersection)

Rewrite the given system of linear equations in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Isolate the y-term in the first equation.

First equation rewritten isolating y-term

Rewrite the second equation to align like terms, then compare the two equations to identify the slopes and y-intercepts.

Second equation rewritten and slopes compared

Set the slopes equal and solve for r to find the value of r that makes the slopes the same.

Set slopes equal
Multiply both sides by r
Multiply both sides by 2611 , the reciprocal of 1126
Simplify

For the y-intercepts to be different and the slopes to be the same, the value of r must be 2610.

Note: It is possible to plug r = 26 10 into the second equation to verify that the y-intercepts are different (graph).

Things to remember:

  • A system of linear equations has no solution if its graph consists of two parallel lines because parallel lines never intersect.
  • Parallel lines have the same slope but different y-intercepts.

Alternate Method :

A system has no solution if the same expression of x and y is equal to two different numbers.

Same expression equals two different numbers scenario

Rewrite the given system of linear equations in standard form so that the constant terms are isolated.

System rewritten in standard form isolating constant terms

Now each equation is written in standard form. Notice that −1120x is a multiple of −1110x. Multiply the first equation by 2 so that the x-terms are the same −1110x and −1110x.

First equation multiplied to match x-terms

The x-terms are the same (−1110x and −1110x) and the constant terms are different (2013≠−2), so identify the value of r that makes the y-terms the same.

Final step identifying r for no-solution condition

Therefore, the value of r must be 2610 for the system to have no solution.

Things to remember:
A system has no solution if the same expression of x and y is equal to two different numbers.

Question

In triangle LMN, the measure of angle  L  is 30°, the length of  LM ¯  is 10 units and the length of  LN ¯  is 8 units. What is the area, in square units, of triangle  LMN ?

Hint :

The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex.

Explanation

The formula for the area of a triangle is A= 12 bh , where b is the length of the base and h is the height.

Draw triangle LMN and label it with the given information. Let LM ¯ with a given length of 10 be the base of the triangle and notice the height of the triangle is unknown.

Triangle LMN with base LM labeled 10 and height unknown

The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex.

Draw a line segment from vertex N down and perpendicular to base LM ¯ . Label the new point of intersection P. The length of NP ¯ is the height of triangle LMN.

Triangle LMN with perpendicular height NP drawn from vertex N to base LM

Triangle LNP is a right triangle with a given angle of 30°, so it is a 30°-60°-90° triangle.

In a 30°-60°-90° triangle, the hypotenuse is twice the length of the shorter leg. Compare the side lengths of the general triangle to triangle LNP to see that hypotenuse LN must be twice the height NP.

30-60-90 triangle showing LN as hypotenuse and NP as shorter leg

The length of the hypotenuse is 8, so set 2x equal to 8 and divide by 2 to find the length of the shorter leg x.

2x = 8 Length of hypotenuse of special right triangle
x = 4 Divide by 2 on both sides

The length of the shorter leg is 4, so the height of triangle LMN is 4. Plug the length of the base (10) and the height (4) into the formula for the area of a triangle and simplify.

Area calculation for triangle LMN using base 10 and height 4

The area of triangle LMN, in square units, is 20 .

Things to remember:

  • The formula for the area of a triangle is A= 12 bh , where b is the length of the base and h is the height.
  • A 30°-60°-90° triangle has the following ratio of side lengths:

30-60-90 triangle side ratio diagram

  • The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex.

Question

The table above shows a number of species of simians classified by type and conservation status. What is the ratio of vulnerable New World monkeys to endangered New World monkeys?

A. 21 : 22
B. 22 : 21
C. 27 : 28
D.28 : 27

Hint :

Identify the number of monkeys from the table that are in each category.

Explanation

A ratio is a comparison of numbers. To find the ratio of vulnerable New World monkeys to endangered New World monkeys, identify the number of each from the table.

Identify the intersection of the Vulnerable column and the New World row.
Identify the intersection of the Endangered column and the New World row.

The choices are given in odds form, so the ratio of vulnerable New World monkeys to endangered New World monkeys is 22 : 21.

(Choice A) 21 : 22 may result from mistakenly swapping the order of the numbers in the desired ratio.

(Choice C) 27 : 28 may result from the errors described in Choices A and D.

(Choice D) 28 : 27 may result from mistakenly identifying the numbers in the Old World row (instead of the New World row).

Things to remember:
A ratio is a comparison of numbers. It is possible to express a ratio in the following forms:

Question

y = −x 2 + 4x + p
y = −6

In the system of equations shown, p is a constant. For which value of p does the system have exactly one distinct real solution?

Hint :

A solution to a system of equations is a point of intersection (x, y) in the xy-plane.  In the given system, y = −6 represents a horizontal line and y = −x 2 + 4x + p represents a parabola.

Explanation

A solution to a system of equations is a point of intersection (x, y) in the xy-plane.  In the given system, y = −6 represents a horizontal line and y = −x 2 + 4x + p represents a parabola.

A parabola intersects a horizontal line at 0, 1, or 2 points.  If a parabola intersects a horizontal line at a single point, then that point must be the vertex of the parabola (proof).

To find the value of p, first find the coordinates of the vertex of the parabola.  Use the vertex formula for an equation in standard form y = ax 2 + bx + c to find the x-coordinate of the vertex.

Compare the equation of the parabola y = −x 2 + 4x + p to standard form y = ax 2 + bx + c to see that a = −1 and b = 4. Plug these values into the vertex formula and simplify.

x = - b 2 a x-coordinate of vertex
x = - 4 2 - 1 Plug in a = −1 and b = 4
x=2 Simplify

The x-coordinate of the vertex is 2.  The parabola intersects the line y = −6 when the y-coordinate of the vertex is equal to −6.

Therefore, the given system of equations has exactly one distinct real solution when the vertex of the parabola is (2, −6).  Plug (x, y) = (2, −6) into the equation y = −x 2 + 4x + p and solve for p.

y = −x2 + 4x + p Given equation
−6 = −(2)2 + 4(2) + p Plug in (x, y) = (2, −6)
−6 = −4 + 8 + p Apply exponent and multiply
−6 = 4 + p Combine constant terms
−10 = p Subtract 4 from both sides

Things to remember:

  • A solution to a system of equations is a point where the graphs of the equations intersect in the xy-plane.
  • If a horizontal line intersects a parabola at only one point, it must intersect at the vertex of the parabola.
  • The vertex formula defines the x-coordinate of the vertex of a parabola with a quadratic equation in standard form y = ax 2 + bx + c:

It is also possible to use the substitution method to create a single quadratic equation in terms of x , then use the discriminant to determine what value of p results in one distinct real solution.

It is given that y = − 6 , so substitute −6 for y in the first equation y = − x 2 + 4 x + p and rewrite it in standard form y = a x 2 + b x + c .

y = − x 2 + 4 x + p Given first equation
− 6 = − x 2 + 4 x + p Plug in y = − 6
0 = − x 2 + 4 x + p + 6 Add 6 on both sides

A quadratic equation in standard form 0 = a x 2 + b x + c has exactly one solution when the discriminant b 2 − 4 a c is equal to 0 . The discriminant is the expression under the square root in the quadratic formula.

Quadratic formula illustrating the discriminant b² - 4ac

Compare the equation 0 = − x 2 + 4 x + p + 6 to standard form to identify the values of a , b , and c .
Note: It is given that p is a constant, so p + 6 is also a constant.

Identifying coefficients a = −1, b = 4, c = p + 6 from the quadratic equation

Plug these values into the discriminant b 2 − 4 a c and simplify.

b2 − 4ac Discriminant
42 − 4(−1)(p + 6) Plug in a = − 1 , b = 4 , and c = p + 6
16 + 4 ( p + 6 ) Apply the exponent and simplify
16 + 4 p + 24 Distribute 4 to ( p + 6 )
40 + 4 p Combine like terms

The discriminant is 40 + 4 p , so the system has exactly one solution when 40 + 4 p = 0 . Set the discriminant equal to 0 and solve for p .

40 + 4 p = 0 Set discriminant equal to 0
4 p = − 40 Subtract 40 from both sides
p = − 10 Divide by 4 on both sides

Things to remember:

  • To find the number of solutions to a linear and quadratic system, use the substitution method to create a single equation in terms of only x .
  • A quadratic equation in standard form has exactly one solution when the discriminant b 2 − 4 a c is equal to 0.

Question

The circle shown has center O, diameters AD‾ , BE‾ , and CF‾ , and the length of BO‾ is 9. If the length of minor arc AB⌢ is kπ, what is the value of k?

Hint :
The length of an arc divided by the circumference of the circle must equal the measure of its intercepting central angle divided by the measure of the entire circle.

Explanation

Ratios of the part to the whole are equivalent between the length of a circular arc and the measure of its intercepting central angle.

The length of an arc (part) divided by the circumference of the entire circle (whole) must equal the measure of its intercepting central angle (part) divided by the measure of the entire circle (whole), forming the following proportion:

The formula for the circumference of a circle is C=2πr , where r is the length of the radius. The angle measure on the given figure is in degrees, so use 360° for the measure of a whole circle (instead of 2π radians).

The central angle that intercepts AB⌢ is ∠AOB , so write the proportion as follows:

To find the measure of ∠AOB , first identify that ∠BOC and ∠EOF are a pair of vertical angles. When two lines intersect, the vertical angles formed by those lines are congruent.

Therefore, ∠BOC also has a measure of 50°. Now notice that ∠BOC forms a straight line AD‾ when combined with ∠AOB and ∠COD .

The measure of ∠AOB is 40°. Notice that BO‾ is a radius of the circle and has a given length of 9. Plug r=9 and m∠AOB=40 into the proportion, and then solve for the length of AB⌢ .

The length of AB⌢ is 2π, so the value of k is 2.

Things to remember:

  • Ratios of the part to the whole are equivalent between the area of a circular sector and the measure of its intercepting central angle. The following proportion relates circular sectors and central angles of a circle:
  • The formula for the circumference of a circle is C=2πr , where r is the length of the radius.

Question

Russell's toy box contains 15 solid-colored blocks: 6 red blocks, 4 blue blocks, and 5 purple blocks.  There is also a single number printed on each block.  Each number from 1 through 6 is printed on a red block, each number from 1 through 4 is printed on a blue block, and each number from 1 through 5 is printed on a purple block.  If Russell chooses a block at random from his toy box, what is the probability that the block will be purple or will have a 3 printed on it?

Hint :
To find the probability of a desired event, use the following formula:

Explanation

An item with one quality OR another quality has at least one of the qualities.  To find the probability of a desired event, divide the number of desired outcomes by the total number of possible outcomes.

The number of desired outcomes is the number of blocks that are purple OR printed with a 3.
The number of possible outcomes is the total number of blocks in the toy box.

It is given that there are 15 total blocks in the toy box: 6 red blocks printed with 1 through 6, 4 blue blocks printed with 1 through 4, and 5 purple blocks printed with 1 through 5.

There are 5 purple blocks, and there are 3 blocks printed with a 3.  Add 3 and 5, then subtract 1 for the 1 block that is both purple and printed with a 3 to see that there 7 blocks that are purple or printed with a 3.

Note:  There is 1 block that is both purple and printed with a 3, so it is necessary to subtract 1 from the sum of the 5 purple blocks and 3 blocks printed with a 3 to avoid double-counting.

Of the 15 total blocks, there are 7 blocks that are purple or printed with a 3.

The probability that Russell chooses a block that is purple or printed with a 3 is 7 15

Things to remember:

  • To find the probability of a desired event, use the following formula:
  • An item that has one quality OR another quality has at least one of the qualities (possibly both).
The SAT Reading and Writing section measures how well you can read, analyze, and refine written content. Work through exam-like questions covering comprehension, grammar, vocabulary, and rhetorical skills, with clear explanations to help you strengthen your accuracy and confidence.
SAT Reading and Writing Practice Questions: Reading Comprehension

Passage

By drawing water into a chamber in its large claw and then snapping the claw shut, a pistol shrimp can produce bubbles that, when popped, create a powerful shockwave that stuns nearby prey. However, these shockwaves do not harm the shrimp themselves, which hide in burrows, waiting to stun fish and other crustaceans. To explain this phenomenon, scientist Alexandra Kingston and colleagues studied pistol shrimp and noted that these shrimp have an orbital hood, a helmet-like exoskeleton covering their brain. Finding the feature unique to snapping shrimp, Kingston hypothesized that they are protected from shockwave trauma by their orbital hoods, leaving them unaffected by the damaging sound.

Question

Which finding, if true, would most directly undermine Kingston's hypothesis?

A. Pistol shrimp with orbital hoods left intact quickly return to their burrows after they snap their large claw without catching any prey.
B. Pistol shrimp whose orbital hoods were surgically removed are less disoriented than their prey after snapping because they are protected by their burrows.
C. Pistol shrimp that have had their orbital hoods surgically removed are unaffected by the powerful shockwaves that stun the prey.
D. Pistol shrimp that have had their orbital hoods left intact change the frequency and volume of their snaps depending on the type of prey.

Explanation

Determine what the hypothesis claims. Then, check the answers to select the finding that undermines (contradicts) Kingston's hypothesis.

The hypothesis proposes that pistol shrimp are protected from the shockwaves they create by their orbital hoods. Showing that pistol shrimp were protected even when their hoods were removed would demonstrate that the hood doesn't offer shockwave protection—it must come from something else.

One finding suggests that the orbital hoods don't protect shrimp and contradicts the hypothesis: Pistol shrimp that have had their orbital hoods surgically removed are unaffected by the powerful shockwaves that stun the prey.

(Choice A) After snapping to stun their prey, hooded pistol shrimp quickly returned to their burrows, which indicates that the shockwave didn't affect them, supporting rather than undermining the hypothesis.

(Choice B) The text describes pistol shrimp being unaffected by their shockwaves but doesn't state that the shrimp are less disoriented by their shockwaves when they are hiding in burrows.

(Choice D) The shrimp changing their snaps depending on the prey they spot wouldn't explain whether their orbital hoods protect shrimp from shockwaves.

Things to remember:
Information that undermines a theory will contradict what the hypothesis claims.

Passage

The Cretaceous period ended 66 million years ago, presumably when an asteroid hit the Earth, causing the extinction of dinosaurs. Paleontologists Kyle Atkins-Weltman and Eric Snively examined three bones of what they thought was a juvenile specimen of a caenagnathid—an already known species of dinosaur from this time period—in order to assess its maturity and found their specimen was an adult dinosaur from a completely different species. Atkins-Weltman and Snively claim that there could be even more dinosaur species that have yet to be discovered—potentially even through re-examination and reclassification of fossils already in museum collections.

Question

Which finding, if true, would most directly weaken Atkins-Weltman's and Snively's claim?

A. Additional caenagnathid bones are examined by other paleontologists who state that some of these bones have not been correctly classified.
B. Paleontologists reexamine a large number of previously catalogued dinosaur bones only to find that all of the species have been identified correctly.
C. Paleontologists agree that dinosaur species were in decline during the Cretaceous period despite the discovery of Atkins-Weltman and Snively.
D. Paleontologists determine that another method of identifying dinosaur species is more accurate than analyzing fossilized bones.

Explanation

Choice B is correct. Atkins-Weltman and Snively asserted that more dinosaur species could be discovered by looking closely at fossils in museums and changing the classification if they are incorrect. One way to weaken this assertion would be to analyze the categorized fossils, only to discover that they have been classified correctly.

Passage

During the Golden Age of Mexican Cinema, between 1930 and 1960, the Mexican film industry all but dominated Latin American cinema due to the industry's high production levels, quality, and economic success when people like Fernando de Fuentes, Emilio Fernández Romo, Joaquín Pardavé, and Dolores del Río participated in the creation of movies in various ways. However, the number of films these individuals participated in could have extended well beyond this time period as most of them began working before 1930 and continued to work well after 1960; it's feasible, therefore, that ______

Question

Which choice most effectively uses data from the table to complete the text?

A. Dolores del Río acted in significantly fewer films than did Emilio Fernández Romo, who is credited with 33 acting performances.
B. Joaquín Pardavé's 28 writing credits include only film scripts he wrote between 1942 and 1955.
C. Dolores del Río acted in well over 27 films and Fernando de Fuentes produced more than 37.
D. Fernando de Fuentes actually directed only 8 films and wrote scripts for 37.

Explanation

Determine what the text claims and choose an answer with information that logically completes the claim.

The text claims that the total number of film credits for each person listed in the table could have been higher than shown because their careers included years outside the Golden Age.

Therefore, it is feasible (reasonable; likely) that these individuals could have participated in more films than those listed in the table. The answer that supports this idea with data from the table states that it's feasible Dolores del Río acted in well over 27 films and Fernando de Fuentes produced more than 37.

(Choice A) This answer compares how many films Dolores del Río and Emilio Fernández Romo acted in over the course of their lives. However, because the table only indicates how many films each acted in during the Golden Age, it's not possible to know whether Dolores acted in significantly fewer than Emilio.

(Choice B) This answer focuses on the writing of Joaquín Pardavé from 1942 to 1955, but the text's claim deals with years beyond the period from 1930 to 1960.

(Choice D) This answer inaccurately cites data from the table, as Fernando de Fuentes directed 37 and wrote 42 films during the period, not 8 and 37 films, respectively.

Things to remember:
Although some of the choices might contain accurate information from the table, only the correct answer will support the text's claim.

Passage

The following text is adapted from Henry Wadsworth Longfellow's 1879 poem "The Cross of Snow."

In the long, sleepless watches of the night,

A gentle face — the face of one long dead —

Looks at me from the wall, where round its head

The night-lamp casts a halo of pale light.

Here in this room she died; and soul more white

Never through martyrdom of fire was led

To its [rest]; nor can in books be read

The legend of a life more [blessed].

Question

What is the main idea of the text?

A. The speaker is remembering a beloved's life after seeing her image.
B. The speaker is too saddened to focus on a beloved's features.
C. The speaker is agitated and imagines the ghost of a beloved in the room.
D. The speaker is restless and concerned about a beloved's reputation.

Explanation

Paraphrase the ideas in the poem's lines. Then summarize the ideas of the poem's sentences and choose the answer with an idea like your summary.

Paraphrased Lines
S1 At night when I can't sleep
the gentle face of a woman who died long ago
gazes at me from the wall, and around her head
is a halo of light created by the lamp.
S2 She died in this room, with a soul purer
than any other holy person who has died;
no books tell the story
of a more blessed person.
Summary The speaker describes an image of a woman and is reminded of her life.

One answer includes an idea like the summary statement: The speaker is remembering a beloved's life after seeing her image.

(Choice B) The speaker does focus on the woman's features, saying she had a “gentle face” and appears to have a halo around her head. The speaker's emotions are not described in the poem.

(Choice C) The speaker describes a deceased woman, but the poem doesn't describe the speaker's state of mind or suggest that the woman is a ghost.

(Choice D) The speaker describes a “sleepless” night and isn't resting, but there is no indication that the speaker is concerned about the reputation of a good woman characterized by a “gentle face” and holiness.

Things to remember:
Paraphrase the lines of the poem to determine its main idea.

Passage

Stephanie Jenouvrier of the Woods Hole Oceanographic Institution studied how ______ According to her 2021 research, emperor penguin chicks had an increased chance of drowning when they found fewer solid surfaces on which to rest after swimming.

Question

Which choice completes the text so that it conforms to the conventions of Standard English?

A. do emperor penguins depend on sea ice.
B. do emperor penguins depend on sea ice?
C. emperor penguins depend on sea ice?
D. emperor penguins depend on sea ice.

Explanation

Look at the sentence structure before the blank to determine whether a question or statement is needed to complete the sentence.

Question structure: Helping verb + noun + verb + dependent clause?
Ex. Did Karlton research how whales sleep?
Statement structure: Noun + verb + dependent clause.
Ex. Karlton researched how whales sleep.

“How” sometimes begins a question, but when it follows a statement, it begins a dependent clause that should place the noun before the verb.

Two sentence diagrams: Question (Did + noun + verb?) vs. Statement (Noun + verb.)

Because there is no helping verb before the noun “Stephanie Jenouvrier,” the sentence is a statement, and what follows “how” is a dependent clause that completes the statement. Therefore, the correct answer will place the noun before the verb and end with a period: emperor penguins depend on sea ice.

(Choice A) Placing the noun “emperor penguins” between the helping verb “do” and the verb “depend” is the structure for a question, not a statement.

(Choice B) A question can't complete a sentence that begins as a statement.

(Choice C) The sentence begins with a statement, and having the noun “emperor penguins” before the verb “depend” is the structure for a statement, so a period, not a question mark, is needed.

Things to remember:
When “how” follows a statement, it begins a dependent clause that will place the subject before the verb; the sentence will end with a period.

Passage

With more than 2,000 acts, the music festival South By ______ or SXSW, as the annual event is more frequently called—has grown in scope and size every year since 1987. SXSW attracts people from all over the US to Austin, Texas, for a weeklong celebration of creativity in music.

Question

Which choice completes the text so that it conforms to the conventions of Standard English?

A. Southwest—
B. Southwest:
C. Southwest,
D. Southwest

Explanation

Rule: A mid-sentence interruption should have the same punctuation—either two commas, two dashes, or a pair of parentheses—before and after it.

Each answer choice uses different punctuation, so look at the punctuation already in the sentence and determine what additional punctuation is required, if any.

Three pairs of punctuation: commas, dashes, parentheses

The nonessential information about what the festival is commonly called is not required for the sentence to make sense or to be grammatically correct. Therefore, this information, placed between the subject and the verb, is a mid-sentence interruption that should be set apart from the sentence with matching punctuation before and after it.

The sentence includes a dash AFTER the mid-sentence interruption. Therefore, a dash should also be placed BEFORE the interrupting phrase to set it apart from the rest of the sentence, making Southwest— correct.

(Choice B) A colon before the interruption would not match the dash after the interruption, and colons are never used in pairs to set apart a mid-sentence interruption.

(Choice C) Although a comma follows “SXSW,” this information is part of the interruption between the subject and main verb. Therefore, a comma after “Southwest” isn't required and wouldn't match the dash used after “called” to set apart the interruption.

(Choice D) The mid-sentence interruption should be separated by the same punctuation before and after it—this answer lacks the dash needed to match the second dash following the phrase.

Things to remember:
Use the same punctuation before and after a mid-sentence interruption.

Passage

Originally from the West African country of Sierra Leone, Michaela DePrince _____ in the 2011 ballet documentary First Position and performed professionally with the Harlem Dance Theater when she joined the Dutch National Ballet Company in 2013 at the age of 18, becoming the company's only dancer of African origin at the time.

Question

Which choice completes the text so that it conforms to the conventions of Standard English?

A. had already appeared
B. was already appearing
C. already appeared
D. already appears

Explanation

Rule: Use past perfect tense to show an action completed before another action or point in the past.

To choose the correct verb, look for clues in the sentence—like dates, other verbs, and time-order words—to determine the sequence of events.

Timeline: 2011 documentary → 2013 joined Dutch National Ballet

The past tense verbs “performed” and “joined” are clues that the action referred to in the blank also occurred in the past, and the time-order words “already” and “when” indicate a sequence of events: DePrince's documentary appearance happened in 2011, before she joined the Dutch National Ballet in 2013.

Therefore, because both actions happened in the past but the documentary appearance happened earlier in the past, the correct answer is the past perfect tense, had already appeared.

(Choice B) “Was already appearing” inaccurately suggests that the documentary, which was completed in 2011, was still being filmed when DePrince joined the ballet company in 2013.

(Choice C) The past tense (“appeared”) is incorrect because it doesn't specify when the action happened in relation to other past events. The word “already” indicates the action was completed before something else, so the past perfect tense (“had appeared”) is required to fit the specific sequence.

(Choice D) “Appears” is present tense, but the documentary was made in the past, in 2011.

Things to remember:
Use past perfect tense to show that one past action or event happened before another.

Question

A cardboard tube is in the shape of a circular cylinder that is open at both ends.  The height of the tube is 14 inches and its diameter is 8 inches.  What is the surface area, in square inches, of the tube?

A. 32π
B. 112π
C. 144π
D. 224π

Hint :

A circular cylinder that is open at both ends has a net that is a rectangle.

Explanation

To calculate the surface area of a three-dimensional figure, consider its net (the 2-dimensional shape of each surface). A circular cylinder that is open at both ends has a net that is a rectangle.

The formula for the area of a rectangle is A = l w . The rectangle has length l that is equal to the height h of the cylinder. The width w of the rectangle is equal to the circumference πd of the cylinder, where d is the diameter.

Rectangular net representation of an open cylinder

First use the given information about the cylinder to find the length and width of its rectangular net. The cylinder has a given height of 14 inches, so l = 14 .

The given diameter of the cylinder is 8 inches, so plug d = 8 into the circumference formula πd to find that w = 8 π .

Diagram showing cylinder dimensions used for surface area calculation

Now calculate the area of the rectangle. Plug l = 14 and w = 8 π into the area formula and simplify.

A = l w Area of a rectangle
A = ( 14 ) ( 8 π ) Plug in l = 14 and w = 8 π
A = 112 π Multiply

The surface area of the tube is 112 π square inches.

Note: It is also possible to use circumference formula 2 πr with radius r = 4 to see that the width is 8 π .

(Choice B) 32 π is equal to the combined area of the top and bottom surfaces of a closed cylinder with diameter 8.

(Choice C) 144 π is equal to the surface area of a cylinder with a diameter of 8 that is closed (instead of open) at both ends.

(Choice D) 224 π may result from using an incorrect formula for the circumference of the cylinder.

Things to remember:

  • The surface area of a three-dimensional figure is equal to the combined area of each shape in its net.
  • The net of a three-dimensional figure contains the two-dimensional shape of each surface in the figure.
  • A circular cylinder that is open at both ends has a net that is a rectangle.
  • The formula for the area of a rectangle is A = l w .
  • The circumference of a circle with diameter d is equal to πd .

Question

When triglycerides (RCO2CH2CH(O2CR′)CH2CO2R″) are mixed with methanol (CH3OH) in the presence of a catalyst, the reaction produces biofuels, a mixture of fatty acid methyl esters (CH3(CH2)nCOOCH3) and glycerin (C3H8O3):

Reaction diagram showing triglycerides reacting with methanol to form biofuel and glycerin

Scientists performed an experiment to determine the composition of the biofuel created from raw rice bran oil. Figure 1 shows the relationship between the transmittance of light in percent and wavenumber in 1cm , or cm−1.

Graph showing transmittance versus wavenumber for rice bran oil biofuel

Figure 1

Experiment

To determine the effect of oxygen in air on biofuel at 3 different temperatures, scientists assembled the apparatus shown in Figure 2. First, they connected a measuring cell, composed of a gold working electrode and a reference electrode in deionized water, to a computer. Then, they placed a reaction vessel sealed with a 2-holed stopper into a heating block. Next, they placed an incoming air inlet tube into 1 hole of the 2-hole stopper and a tube, used to connect the reaction vessel to the measuring cell, in the other hole.

Experimental setup consisting of a reaction vessel, heating block, electrodes, and inlet tubes

Figure 2

At each temperature, the scientists performed the following 3 steps:

  1. A small volume of biofuel was placed in the clean, empty reaction vessel, which was then sealed with the 2-holed stopper.
  2. The reaction vessel was heated to the desired temperature, and after 1 min the air inlet was opened to a rate of 10 L/hr.
  3. The open circuit potential (OCP), in mV, measured between the gold working electrode and the reference electrode, was continuously monitored for up to 50 hr of reaction time or until the biofuel degraded.

The results are shown in Figure 3.

Graph showing open circuit potential (OCP) over time for biofuel at different temperatures

Figure 3

1. This work, "Biodiesel," is a derivative of "Biodiesel from "Morelos" Rice: Synthesis, Oxidative Stability, and Corrosivity" by Zuñiga-Díaz J, Reyes-Dorantes E, Quinto-Hernandez A, Porcayo-Calderon J, Gonzalez-Rodriguez J.G, and Martinez-Gomez L, published under creative commons by Journal of Chemistry. This work, "Biodiesel," is licensed by UWorld.

What is the starting OCP value of the biofuel samples expressed in volts (V)?

A. 0.0050 V
B. 0.050 V
C. 0.50 V
D. 5.0 V

Explanation

Graph showing OCP values of biofuel samples from Figure 3

OCP value of the biofuel samples is shown in Figure 3. Examine Figure 3 to determine the starting OCP values for the biofuel samples, then convert the units to volts (V).

According to Figure 3, the starting OCP value (at time 0) was 50 mV.

Metric conversion illustration showing millivolts to volts conversion

Prior Knowledge: In metric conversion for every 1 volt (V), there are 1,000 millivolts (mV), so divide the value in mV by 1,000 or move the decimal point three places to the left to convert into V.

Therefore, the starting OCP value of the biofuel samples expressed in volts is 0.050 V.

(Choice A) 0.0050 V is equal to 5.0 mV, not 50 mV.

(Choices C and D) To convert mV to V, move the decimal point three places to the left, not one or two places.

Things to remember:
When converting from a smaller metric unit to a larger metric unit, the decimal point is moved to the left.

Question

When triglycerides (RCO2CH2CH(O2CR′)CH2CO2R″) are mixed with methanol (CH3OH) in the presence of a catalyst, the reaction produces biofuels, a mixture of fatty acid methyl esters (CH3(CH2)nCOOCH3) and glycerin (C3H8O3):

Reaction diagram showing triglycerides reacting with methanol to form biofuel and glycerin

Scientists performed an experiment to determine the composition of the biofuel created from raw rice bran oil. Figure 1 shows the relationship between the transmittance of light in percent and wavenumber in 1 cm , or cm−1.

Graph showing transmittance versus wavenumber for rice bran oil biofuel

Figure 1

Experiment

To determine the effect of oxygen in air on biofuel at 3 different temperatures, scientists assembled the apparatus shown in Figure 2. First, they connected a measuring cell, composed of a gold working electrode and a reference electrode in deionized water, to a computer. Then, they placed a reaction vessel sealed with a 2-holed stopper into a heating block. Next, they placed an incoming air inlet tube into 1 hole of the 2-hole stopper and a tube, used to connect the reaction vessel to the measuring cell, in the other hole.

Experimental setup consisting of a reaction vessel, heating block, electrodes, and inlet tubes

Figure 2

At each temperature, the scientists performed the following 3 steps:

  1. A small volume of biofuel was placed in the clean, empty reaction vessel, which was then sealed with the 2-holed stopper.
  2. The reaction vessel was heated to the desired temperature, and after 1 min the air inlet was opened to a rate of 10 L/hr.
  3. The open circuit potential (OCP), in mV, measured between the gold working electrode and the reference electrode, was continuously monitored for up to 50 hr of reaction time or until the biofuel degraded.

The results are shown in Figure 3.

Graph showing open circuit potential (OCP) over time for biofuel at different temperatures

Figure 3

1. This work, "Biodiesel," is a derivative of "Biodiesel from "Morelos" Rice: Synthesis, Oxidative Stability, and Corrosivity" by Zuñiga-Díaz J, Reyes-Dorantes E, Quinto-Hernandez A, Porcayo-Calderon J, Gonzalez-Rodriguez J.G, and Martinez-Gomez L, published under creative commons by Journal of Chemistry. This work, "Biodiesel," is licensed by UWorld.

According to Figure 1, of the following wavenumbers, which one has the lowest percent transmittance?

A. 722 cm−1
B. 1,069 cm−1
C. 1,436 cm−1
D. 3,007 cm−1

Explanation

Spectral graph showing transmittance values for different wavenumbers

Analyze Figure 1 to determine which of the wavenumbers listed in the answer choices has the lowest percent transmittance.

Figure 1 shows:

  • 722 cm−1 has approximately 86% transmittance.
  • 1,069 cm−1 has approximately 75% transmittance.
  • 1,436 cm−1 has approximately 84% transmittance.
  • 3,007 cm−1 has approximately 95% transmittance.

Therefore, wavenumber 1,069 cm−1 has the lowest percent transmittance.

(Choices A, C, and D) The wavenumbers in these answer choices all have a percent transmittance that is larger than the percent transmittance relating to wavenumber 1,069 cm−1. Therefore, these wavenumbers do not have the lowest percent transmittance.

Things to remember:
When answering questions about the lowest or highest value in a data set, start by looking at the answer choices to narrow down the number of points to analyze.

Passage

Bar graph of E. coli growth rate (OD600/h) vs. silver nitrate concentration (µM). Three strains: CR (wild-type, blue), C₁R₁ (orange), C₁R₂ (green). At 0 µM all ~0.45. At 20 µM: CR ~0.25, C₁R₁ ~0.38, C₁R₂ ~0.42. At 40 µM: CR ~0.05, C₁R₁ ~0.22, C₁R₂ ~0.32.

In a study on mutations in genes cusS and rho—genes that are involved in the bacteria E. coli’s response to environmental stressors—researchers examined the resistance of several strains of E. coli to varying concentrations of silver nitrate, a naturally antibacterial substance. Populations in the study included a wild-type strain with no mutations and two strains with the same mutation in cusS (C1) and differing mutations in rho (R1 and R2). The strains were identified as CR, C1R1, and C1R2, respectively. Together with previous findings that the C1 cusS mutation confers increased resistance to silver nitrate, data in the graph of growth rates suggest that ______

Question

Which completion of the text is best supported by data in the graph?

A. the R2 rho mutation is more effective on its own against silver nitrate than the C1 cusS mutation.
B. the cusS gene provides resistance to high concentrations of silver nitrate, while the rho gene provides resistance regardless of concentration.
C. the R2 mutation in rho may increase the effectiveness of the C1 cusS mutation when concentrations of silver nitrate are high.
D. E. coli's resistance to silver nitrate is highest when rho has both the R1 mutation and the R2 mutation.

Explanation

Find information in the text that connects to the data in the graph. Then, choose the answer that draws a logical conclusion from the data.

Line graph: Growth rate (OD600/h) vs. AgNO₃ (µM). CR (wild-type, blue) drops fastest. C₁R₁ (orange) drops slower. C₁R₂ (green) stays highest.

The text introduces three strains of bacteria, which correspond to the three lines in the graph. Each strain has different mutations. The C1R2 strain maintains a relatively high growth rate across the whole graph, while the growth rates of the other two strains drop sharply as the concentration of silver nitrate increases.

The text’s last sentence indicates that the C1 mutation has previously been found to help E. coli resist silver nitrate. Two strains contain the C1 mutation, but the one that also has the R2 mutation performs better than the other at high concentrations of silver nitrate.

Because the R2 mutation is the difference between those two strains, it’s reasonable to conclude that the R2 mutation in rho may increase the effectiveness of the C1 cusS mutation when concentrations of silver nitrate are high.

(Choice A) The graph doesn’t show any strains with the R2 mutation alone or the C1 mutation alone, so it’s not possible to conclude that one is more effective than the other on its own.

(Choice B) The graph shows strains with certain mutations in the genes cusS and rho, but there isn’t enough information to conclude anything about the individual genes on their own.

(Choice D) None of the strains have two rho mutations in the same gene.

Things to remember:
The answer must be supported by data in the graph.

Passage

Two beakers: left = cloudy water + pure TiO₂ under visible light → still cloudy. Right = clear water + Cu-TiO₂ under same visible light → crystal clear.

Titanium dioxide (TiO2) offers promise as a material for water purification: when TiO2 absorbs light, it acts as a catalyst for a reaction that eliminates pollutants. One disadvantage of TiO2, however, has to do with how different types of light (visible and full-spectrum) affect the photocatalytic process. With pure TiO2, the process is triggered only by full-spectrum light, not visible light, a fact that limits the material’s efficiency. Pelagia-Irene Gouma and her team devised a copper additive to expand the range of light that enables TiO2 to purify water. They tested the copper-enhanced TiO2 under both visible and full-spectrum light and concluded that the copper additive has the potential to improve TiO2-based materials’ efficiency in eliminating waterborne pollutants.

Question

Which choice best describes data from the graph that support Gouma and her team's conclusion?

A. Both the pure TiO2 and the copper-enhanced TiO2 eliminated more than 60% of pollutants when exposed to full-spectrum light for 240 minutes.
B. The copper-enhanced TiO2 eliminated a higher percentage of pollutants under visible light alone than pure TiO2 eliminated even under full-spectrum light.
C. Copper-enhanced TiO2 exposed to full-spectrum light eliminated approximately 75% of pollutants after 240 minutes, while pure TiO2 exposed to full-spectrum light eliminated approximately 25% of pollutants after 240 minutes.
D. There was a notable difference between the percentage of pollutants eliminated by copper-enhanced TiO2 when exposed to visible light only and when exposed to full-spectrum light.

Explanation

Summarize the text and identify the team’s conclusion. Then, analyze the graph to find data that support this conclusion and choose the answer that contains this data.

The text discusses TiO2 as a catalyst for water purification, claiming that TiO2 is inefficient because it works only under full-spectrum light. The final sentence states the researchers’ conclusion that adding copper to TiO2 may improve TiO2’s efficiency.

Bar graph: % pollutants removed in 240 min. Visible light: Pure TiO₂ = 20%, Cu-TiO₂ = 65%. Full-spectrum: Pure TiO₂ = 75%, Cu-TiO₂ = 95%.

The graph shows the performance of both copper-enhanced TiO2 and pure TiO2 under two different lighting conditions. Each bar represents the percentage of pollutants eliminated in 240 minutes, so a higher bar indicates more pollutants eliminated and therefore better efficiency.

The bars representing copper-enhanced TiO2 in each lighting condition are both higher than either of the bars for pure TiO2, indicating that copper-enhanced TiO2 was more efficient even under less favorable lighting conditions (visible only) than pure TiO2 was in favorable conditions (full-spectrum). Thus, the correct answer states that the copper-enhanced TiO2 eliminated a higher percentage of pollutants under visible light alone than pure TiO2 eliminated even under full-spectrum light.

(Choice A) This statement is accurate, but it doesn’t show that copper-enhanced TiO2 was more efficient than pure TiO2.

(Choice C) This choice is inaccurate based on the graph. Copper-enhanced TiO2 eliminated 95% of pollutants under full-spectrum light, while pure TiO2 eliminated 75%.

(Choice D) This choice refers only to copper-enhanced TiO2, so it doesn’t indicate increased efficiency compared with pure TiO2.

Things to remember:
The answer must contain accurate data AND support the team’s conclusion.

Passage

Two beakers: left = cloudy water + pure TiO₂ under visible light → still cloudy. Right = clear water + Cu-TiO₂ under same visible light → crystal clear.

During the Golden Age of Mexican Cinema, between 1930 and 1960, the Mexican film industry all but dominated Latin American cinema due to the industry's high production levels, quality, and economic success when people like Fernando de Fuentes, Emilio Fernández Romo, Joaquín Pardavé, and Dolores del Río participated in the creation of movies in various ways. However, the number of films these individuals participated in could have extended well beyond this time period as most of them began working before 1930 and continued to work well after 1960; it's feasible, therefore, that ______

Question

Which choice most effectively uses data from the table to complete the text?

A. Dolores del Río acted in significantly fewer films than did Emilio Fernández Romo, who is credited with 33 acting performances.
B. Joaquín Pardavé's 28 writing credits include only film scripts he wrote between 1942 and 1955.
C. Dolores del Río acted in well over 27 films and Fernando de Fuentes produced more than 37.
D. Fernando de Fuentes actually directed only 8 films and wrote scripts for 37.

Explanation

Determine what the text claims and choose an answer with information that logically completes the claim.

The text claims that the total number of film credits for each person listed in the table could have been higher than shown because their careers included years outside the Golden Age.

Table: Golden-Age Mexican Cinema (1930–1960). Dolores del Río: 27 acting credits (1911–1978 career). Fernando de Fuentes: 37 directing, 42 writing (1903–1969 career). Emilio Fernández Romo: 48 acting (1925–1986 career). Joaquín Pardavé: 31 writing (1942–1955).

Therefore, it is feasible (reasonable; likely) that these individuals could have participated in more films than those listed in the table. The answer that supports this idea with data from the table states that it’s feasible Dolores del Río acted in well over 27 films and Fernando de Fuentes produced more than 37.

(Choice A) This answer compares how many films Dolores del Río and Emilio Fernández Romo acted in over the course of their lives. However, because the table only indicates how many films each acted in during the Golden Age, it’s not possible to know whether Dolores acted in significantly fewer than Emilio.

(Choice B) This answer focuses on the writing of Joaquín Pardavé from 1942 to 1955, but the text’s claim deals with years beyond the period from 1930 to 1960.

(Choice D) This answer inaccurately cites data from the table, as Fernando de Fuentes directed 37 and wrote 42 films during the period, not 8 and 37 films, respectively.

Things to remember:
Although some of the choices might contain accurate information from the table, only the correct answer will support the text’s claim.

Passage

The following text is from Chandreyee Lahiri's 2021 short story "Dumba Chora." Sutapa describes her past to her new husband, Shekhar.

"Before our marriage…there was someone else." She turned to face him purposefully, pinning him with an unusually hard stare. Shekhar turned away, towards the darkened jungle, more to break that unsettling look than for anything else.

Question

As used in the text, what does the phrase "pinning him with" most nearly mean?

A. Holding him under
B. Freeing him from
C. Supporting him in
D. Guarding him with

Explanation

To determine the meaning of a phrase, read the context around the phrase for clues that indicate what the phrase means.

“Before our marriage…there was someone else.” She turned to face him purposefully, pinning him with an unusually hard stare. Shekhar turned away, towards the darkened jungle, more to break that unsettling look than for anything else.

The context indicates that Sutapa's “hard stare” made Shekhar feel so uncomfortable he had to look away to “break” the hold of her gaze; therefore, as used in the text, the phrase “pinning him with” most nearly means holding him under.

(Choice B) Shekhar felt forced to look away from Sutapa to “break” her stare. It isn't logical to say she was “freeing him from” her own stare if he had to turn away to free himself.

(Choice C) Sutapa's “unsettling look” made Shekhar feel uncomfortable rather than supported.

(Choice D) A person might guard or protect someone who is vulnerable by watching him intently, but the context indicates Sutapa is telling Shekhar something difficult for him to hear, not trying to protect him.

Things to remember:
Look for context clues surrounding a phrase to determine what it means in the text.

Passage

John Penders and his research associates hypothesized that a lack of gastrointestinal (GI) bacteria caused increased production of antibodies in response to certain diseases. To test the validity of this hypothesis, a second team of researchers designed a series of experiments using mice, some with GI bacteria and some without, in which both groups were exposed to a protein that triggers the immune system to mimic the onset of disease.

Question

Which finding from the experiments on mice, if true, would most strongly support Penders and his colleagues' hypothesis?

A. The mice without GI bacteria took significantly less time to react to the protein than the mice with GI did.
B. The mice without GI bacteria slept significantly more after the protein was introduced than the mice with GI did.
C. The mice without GI bacteria ate significantly less food after exposure to the protein than the mice with GI did.
D. The mice without GI bacteria produced significantly more antibodies in response to the protein than the mice with GI did.

Explanation

Summarize the hypothesis of Penders and his colleagues. Then, determine which statement supports the hypothesis.

According to the text, Penders and his associates hypothesized that when exposed to certain diseases, individuals without GI bacteria would have a stronger immune response and create more antibodies than those with GI bacteria.

For the experiment, mice were exposed to a protein that caused their immune systems to produce antibodies, just like they would if exposed to a disease. Therefore, the finding that would best support the hypothesis states that the mice without GI bacteria produced significantly more antibodies in response to the protein than the mice with GI did.

(Choices A, B, and C) None of these answers mention the production of antibodies, which is what the researchers were investigating.

  • Choice A: Although this idea seems logical, the text doesn't mention reaction time as a factor in determining whether GI bacteria impact immune response.
  • Choices B and C: It might be reasonable that animals fighting off a disease might sleep more or eat less food; however, there is no discussion in the text about either the energy levels or the food consumption of the mice when exposed to the protein.

Things to remember:
The best statement to support the validity of a hypothesis will contain information related to the text's discussion.

Passage

The following text is adapted from Hilda Conkling’s 1920 poem “Hills.”

The hills are going somewhere;
They have been on the way a long time.
They are like camels in a line
But they move more slowly.
Sometimes at sunset they carry silks,
But most of the time silver birch trees,
Heavy rocks, heavy trees, gold leaves
On heavy branches till they are aching...
Birches like silver bars they can hardly lift
With grass so thick about their feet to hinder...
They have not gone far
In the time I’ve watched them...

Question

Which choice best describes the overall structure of the text?

A. It discusses how the hills change from sunrise to sunset.
B. It compares the hills' features to treasures carried by pack animals.
C. It describes the appearance of hills, then of a valley.
D. It includes contrasting imagery of ancient rocks and young trees.

Explanation

A text's structure is the way its overall content is organized, and the SAT answer choices often reference this content's meaning.

Paraphrase the poem’s lines and consider what is discussed throughout the entire text. Then choose the answer that restates what is expressed about the subject.

Lines Paraphrase
1–2 The hills are taking a while to go somewhere.
3–4 The hills look like camels but move slower than these pack animals.
5–9 Sometimes they carry “silks,” but usually they carry heavier things like rocks and birch trees that are like “silver bars” with “gold leaves on heavy branches.”
10–12 The hills’ thick grass makes it hard for them to move, so they haven’t gone far while I’ve been watching.

The paraphrase, especially of lines 5–9, suggests that hills carry heavy items such as rocks and trees, just as camels carry valuable items like “silks,” “gold leaves,” and “silver bars.” In other words, regarding the poem’s structure, it compares the hills’ features to treasures carried by pack animals.

(Choice A) Sunset is mentioned in the poem, but sunrise is not; therefore, there is no discussion of how the hills change from the morning to the evening.

(Choice C) Although hills are described in the poem, valleys are not.

(Choice D) Line 7 describes rocks and then trees as “heavy,” but there is no mention of their ages. Also, information given in a single line of the poem doesn’t represent the overall structure of the text.

Things to remember:
A poem’s structure is determined by its content throughout the poem, so any answer with details not included in the poem or not representative of the poem as a whole is incorrect.

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Join over students who use UWorld to prepare for the SAT. Their results speak for themselves, consistent, structured practice leads to measurable score gains every time.
The explanations are better than any other resources around, which has taken my score from 1310 to 1500+.
Riley S.
The SAT QBank helps me learn and has a step-by-step explanation for everything. It gives real questions based on the test, and shows me what I should work on, along with the percentage of what I got wrong and what I got right. UWorld is the best!!!
Srihan A.
It has a large question bank with questions very similar to those given by the College Board. They provide great answer explanations and review features. Further, they provide a benchmark to analyze your own performance.Overall, it is a superb way to practice for the SAT!
Inian N.
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Save Big, Score High!

Access 1700+ SAT practice questions with answers anytime, anywhere, then watch your confidence and score soar.

What's Included
SAT QBank Starting at $99
Buy Now
SAT Prep Course Starting at $299
Buy Now
1700+ SAT-Level Practice Questions
Hone your skills with questions modeled directly after the official SAT. Each problem comes with an in-depth, visual explanation to clarify the answer and the strategy.
Custom SAT Practice Test Generator
Build practice tests focused on YOUR weak topics. Create timed mock exams or quick topic quizzes. Study your way, not someone else's way.
Progress Tracking Dashboard
See exactly which topics you're nailing and which need more work. Track your progress across all SAT practice tests and quizzes so you know where to focus.
Pick Your SAT Study Topics
Stop wasting time on content you already know. Choose specific SAT topics to practice and build a study plan that actually makes sense for you.
Smart SAT Study Planner
Tell us your schedule and we'll create a personalized SAT study plan that fits your life. Stay on track without the stress of figuring out what to study next.
Score-Predicting Full-Length SAT Mock Exam*
Take a complete practice exam under real testing conditions and get an estimated SAT score. See where you stand before test day.
Expert-Led SAT Video Lessons
In-house SAT tutors and educators break down tough concepts with clear animations and step-by-step explanations. Finally, understand the topics that confuse you.
SAT Study Guide Set (Print + Digital Book)
Our comprehensive SAT prep book set, available in both print and digital formats, provides focused content review. It's perfectly aligned with the videos and practice questions.
400+ Check-for-Understanding Questions
After each SAT lesson, use these foundational questions to confirm you understand the core concepts before tackling more difficult, exam-style problems. Build your confidence.
300+ Unique Practice Questions in Printed Book
The printed SAT guide includes an additional set of unique, exam-level practice questions not found online, complete with detailed, illustrated solutions for extra practice.

Access 1700+ SAT practice questions with answers anytime, anywhere, then watch your confidence and score soar.

SAT QBank Starting at $99
Buy Now
See Whats's Included
  • 1700+ SAT-Level Practice Questions
    Hone your skills with questions modeled directly after the official SAT. Each problem comes with an in-depth, visual explanation to clarify the answer and the strategy.
  • Custom SAT Practice Test Generator
    Build practice tests focused on YOUR weak topics. Create timed mock exams or quick topic quizzes. Study your way, not someone else's way.
  • Progress Tracking Dashboard
    See exactly which topics you're nailing and which need more work. Track your progress across all SAT practice tests and quizzes so you know where to focus.
  • Pick Your SAT Study Topics
    Stop wasting time on content you already know. Choose specific SAT topics to practice and build a study plan that actually makes sense for you.
  • Smart SAT Study Planner
    Tell us your schedule and we'll create a personalized SAT study plan that fits your life. Stay on track without the stress of figuring out what to study next.
Save Big, Score High!
SAT Prep Course Starting at $299
Buy Now
See Whats's Included
  • 1700+ SAT-Level Practice Questions
    Hone your skills with questions modeled directly after the official SAT. Each problem comes with an in-depth, visual explanation to clarify the answer and the strategy.
  • Custom SAT Practice Test Generator
    Build practice tests focused on YOUR weak topics. Create timed mock exams or quick topic quizzes. Study your way, not someone else's way.
  • Progress Tracking Dashboard
    See exactly which topics you're nailing and which need more work. Track your progress across all SAT practice tests and quizzes so you know where to focus.
  • Pick Your SAT Study Topics
    Stop wasting time on content you already know. Choose specific SAT topics to practice and build a study plan that actually makes sense for you.
  • Smart SAT Study Planner
    Tell us your schedule and we'll create a personalized SAT study plan that fits your life. Stay on track without the stress of figuring out what to study next.
  • Score-Predicting Full-Length SAT Mock Exam*
    Take a complete practice exam under real testing conditions and get an estimated SAT score. See where you stand before test day.
  • Expert-Led SAT Video Lessons
    In-house SAT tutors and educators break down tough concepts with clear animations and step-by-step explanations. Finally, understand the topics that confuse you.
  • SAT Study Guide Set (Print + Digital Book)
    Our comprehensive SAT prep book set, available in both print and digital formats, provides focused content review. It's perfectly aligned with the videos and practice questions.
  • 400+ Check-for-Understanding Questions
    After each SAT lesson, use these foundational questions to confirm you understand the core concepts before tackling more difficult, exam-style problems. Build your confidence.
  • 300+ Unique Practice Questions in Printed Book
    The printed SAT guide includes an additional set of unique, exam-level practice questions not found online, complete with detailed, illustrated solutions for extra practice.

Start your free trial with free SAT practice questions,
perfect for a quick topic review or a full deep dive into the entire exam.

Save Big, Score High!

Find out for yourself why students all over the country are using UWorld for their college prep. Sign up today and start down the path that leads to your dream school.

What's Included
ACT QBank Starting at $99
Buy Now
ACT Prep Course Starting at $299
Buy Now
2500+ ACT-Style Practice Questions
Access a massive bank of 2500+ practice questions that mimic the ACT's format, timing, and difficulty. Understand the 'why' behind every answer with detailed, illustrated solutions.
Custom ACT Practice Test Generator
Design your own ACT practice sessions. Focus on the sections or question types giving you trouble, from Science graphs to Rhetorical Skills. Build timed mock tests or short quizzes.
Progress Tracking Dashboard
Visually track your performance across every ACT section. The dashboard highlights your mastery level, showing you where you're excelling and where you need to review.
Pick Your ACT Study Topics
Maximize your study time by focusing on what matters. Choose specific ACT sections (Math, Reading, English) or even sub-topics to drill down and improve your composite score.
Smart ACT Study Planner
Let us build your ACT prep schedule. Just provide your availability and test date, and we'll create a step-by-step study plan that adapts to your life and keeps you moving forward.
Score-Predicting Full-Length ACT Mock Exam*
Experience a realistic, full-length ACT simulation. Complete all four sections under official timed conditions and receive a predicted composite score to gauge your readiness.
Expert-Led ACT Video Lessons*
Watch video lessons from top ACT educators. They break down challenging concepts from all four sections, using clear visuals and easy-to-follow test-taking strategies.
ACT Study Guide Set (Print + Digital Books)*
Our complete ACT study guide set, in print and digital, provides in-depth content review. Use it with the video lessons for a fully integrated and organized study system.
Check-for-Understanding Questions*
Solidify your knowledge with concept-check questions after each video lesson. Ensure you've grasped the fundamentals before moving on to challenging, fast-paced ACT practice.
Unique Practice Questions in Printed Book*
Find bonus, book-only ACT practice questions in your printed study guide. These extra problems (not available online) mimic the test and include full visual explanations.

Start your free trial with a free ACT practice questions,
whether you want a quick topic review or a deep dive into the whole test.

Find out for yourself why students all over the country are using UWorld for their college prep. Sign up today and start down the path that leads to your dream school.

ACT QBank Starting at $99
Buy Now
As low as $9/mo with Affirm
See What’s Included
  • 2500+ ACT-Style Practice Questions
    Access a massive bank of 2500+ practice questions that mimic the ACT's format, timing, and difficulty. Understand the 'why' behind every answer with detailed, illustrated solutions.
  • Custom ACT Practice Test Generator
    Design your own ACT practice sessions. Focus on the sections or question types giving you trouble, from Science graphs to Rhetorical Skills. Build timed mock tests or short quizzes.
  • Progress Tracking Dashboard
    Visually track your performance across every ACT section. The dashboard highlights your mastery level, showing you where you're excelling and where you need to review.
  • Pick Your ACT Study Topics
    Maximize your study time by focusing on what matters. Choose specific ACT sections (Math, Reading, English) or even sub-topics to drill down and improve your composite score.
  • Smart ACT Study Planner
    Let us build your ACT prep schedule. Just provide your availability and test date, and we'll create a step-by-step study plan that adapts to your life and keeps you moving forward.
  • Score-Predicting Full-Length ACT Mock Exam*
    Experience a realistic, full-length ACT simulation. Complete all four sections under official timed conditions and receive a predicted composite score to gauge your readiness.
Save Big, Score High!
ACT Prep Course Starting at $299
Buy Now
See What’s Included
  • 2500+ ACT-Style Practice Questions
    Access a massive bank of 2500+ practice questions that mimic the ACT's format, timing, and difficulty. Understand the 'why' behind every answer with detailed, illustrated solutions.
  • Custom ACT Practice Test Generator
    Design your own ACT practice sessions. Focus on the sections or question types giving you trouble, from Science graphs to Rhetorical Skills. Build timed mock tests or short quizzes.
  • Progress Tracking Dashboard
    Visually track your performance across every ACT section. The dashboard highlights your mastery level, showing you where you're excelling and where you need to review.
  • Pick Your ACT Study Topics
    Maximize your study time by focusing on what matters. Choose specific ACT sections (Math, Reading, English) or even sub-topics to drill down and improve your composite score.
  • Smart ACT Study Planner
    Let us build your ACT prep schedule. Just provide your availability and test date, and we'll create a step-by-step study plan that adapts to your life and keeps you moving forward.
  • Score-Predicting Full-Length ACT Mock Exam*
    Experience a realistic, full-length ACT simulation. Complete all four sections under official timed conditions and receive a predicted composite score to gauge your readiness.
  • Expert-Led ACT Video Lessons*
    Watch video lessons from top ACT educators. They break down challenging concepts from all four sections, using clear visuals and easy-to-follow test-taking strategies.
  • ACT Study Guide Set (Print + Digital Books)*
    Our complete ACT study guide set, in print and digital, provides in-depth content review. Use it with the video lessons for a fully integrated and organized study system.
  • Check-for-Understanding Questions*
    Solidify your knowledge with concept-check questions after each video lesson. Ensure you've grasped the fundamentals before moving on to challenging, fast-paced ACT practice.
  • Unique Practice Questions in Printed Book*
    Find bonus, book-only ACT practice questions in your printed study guide. These extra problems (not available online) mimic the test and include full visual explanations.
Save Big, Score High!

Flexible SAT & ACT prep with full QBank access, realistic tests, and smart tools like custom quizzes, study planner, and performance tracking to help you improve faster and score higher.

What’s Included in the SAT + ACT Bundle
SAT + ACT
QBank Bundle Starting at $199
Buy Now
SAT + ACT Prep
Course Bundle Starting at $549
Buy Now
4200+ Combined SAT + ACT Practice Questions
Master both exams with a comprehensive database of 4200+ questions. Practice items mirror the style of both the SAT and ACT, with clear, visual explanations for every single one.
Custom Practice Test Generator
Adapt your study plan for both tests. Generate targeted practice exams for the SAT, the ACT, or specific sections from both. It's the most flexible way to prep for both test days.
Progress Tracking Dashboard
Monitor your readiness for each exam in its own unique dashboard. The analytics break down your progress for the SAT and ACT separately, so you can intelligently divide your study time.
Pick Your Study Topics (SAT & ACT)
Optimize your prep by tackling SAT and ACT topics individually. Whether it's ACT English or SAT Math, you choose what to study, ensuring no time is wasted on concepts you already know.
Smart Study Planner
Tell us your schedule and test dates, and our planner will create a balanced study plan that allocates time for preparing for each test.
Score-Predicting Full-Length Mock Exams*
Gauge your readiness with score-predicting mock exams for both the SAT and ACT. See your estimated score for each test and identify key areas for improvement on each one.
Expert-Led ACT & SAT Video Lessons*
Master content for both exams. Our expert educators use clear visuals and step-by-step strategies to break down the toughest concepts on the ACT and SAT.
Complete ACT + SAT Study Guide Sets (Print + Digital)*
Get our comprehensive print and digital study guides for both the ACT and SAT. These books align perfectly with the video lessons for a fully integrated and organized study system.
Concept-Check Questions (for both exams)*
Reinforce your learning after each video lesson. These foundational questions for both ACT and SAT ensure you grasp the core concepts before tackling more difficult, exam-level practice.
Exclusive Book-Only Practice Questions*
Discover hundreds of unique, bonus practice questions for both the ACT and SAT found only in the printed study guides. These extra problems (not available online) include detailed visual explanations.

Flexible SAT & ACT prep with full QBank access, realistic tests, and smart tools like custom quizzes, study planner, and performance tracking to help you improve faster and score higher.

SAT + ACT QBank Bundle Starting at $199
Buy Now
See What’s Included
  • 4200+ Combined SAT + ACT Practice Questions
    Master both exams with a comprehensive database of 4200+ questions. Practice items mirror the style of both the SAT and ACT, with clear, visual explanations for every single one.
  • Custom Practice Test Generator
    Adapt your study plan for both tests. Generate targeted practice exams for the SAT, the ACT, or specific sections from both. It's the most flexible way to prep for both test days.
  • Progress Tracking Dashboard
    Monitor your readiness for each exam in its own unique dashboard. The analytics break down your progress for the SAT and ACT separately, so you can intelligently divide your study time.
  • Pick Your Study Topics (SAT & ACT)
    Optimize your prep by tackling SAT and ACT topics individually. Whether it's ACT English or SAT Math, you choose what to study, ensuring no time is wasted on concepts you already know.
  • Smart Study Planner
    Tell us your schedule and test dates, and our planner will create a balanced study plan that allocates time for preparing for each test.
  • Score-Predicting Full-Length Mock Exams*
    Gauge your readiness with score-predicting mock exams for both the SAT and ACT. See your estimated score for each test and identify key areas for improvement on each one.
Save Big, Score High!
SAT + ACT Prep Course Bundle Starting at $549
Buy Now
See What’s Included
  • 4200+ Combined SAT + ACT Practice Questions
    Master both exams with a comprehensive database of 4200+ questions. Practice items mirror the style of both the SAT and ACT, with clear, visual explanations for every single one.
  • Custom Practice Test Generator
    Adapt your study plan for both tests. Generate targeted practice exams for the SAT, the ACT, or specific sections from both. It's the most flexible way to prep for both test days.
  • Progress Tracking Dashboard
    Monitor your readiness for each exam in its own unique dashboard. The analytics break down your progress for the SAT and ACT separately, so you can intelligently divide your study time.
  • Pick Your Study Topics (SAT & ACT)
    Optimize your prep by tackling SAT and ACT topics individually. Whether it's ACT English or SAT Math, you choose what to study, ensuring no time is wasted on concepts you already know.
  • Smart Study Planner
    Tell us your schedule and test dates, and our planner will create a balanced study plan that allocates time for preparing for each test.
  • Score-Predicting Full-Length Mock Exams*
    Gauge your readiness with score-predicting mock exams for both the SAT and ACT. See your estimated score for each test and identify key areas for improvement on each one.
  • Expert-Led ACT & SAT Video Lessons*
    Master content for both exams. Our expert educators use clear visuals and step-by-step strategies to break down the toughest concepts on the ACT and SAT.
  • Complete ACT + SAT Study Guide Sets (Print + Digital)*
    Get our comprehensive print and digital study guides for both the ACT and SAT. These books align perfectly with the video lessons for a fully integrated and organized study system.
  • Concept-Check Questions (for both exams)*
    Reinforce your learning after each video lesson. These foundational questions for both ACT and SAT ensure you grasp the core concepts before tackling more difficult, exam-level practice.
  • Exclusive Book-Only Practice Questions*
    Discover hundreds of unique, bonus practice questions for both the ACT and SAT found only in the printed study guides. These extra problems (not available online) include detailed visual explanations.

Kick off your prep with a free trial!
Explore the SAT QBank and ACT QBank, whether you want a quick review or a full exam deep dive.

7-Day SAT Free Trial
7-Day ACT Free Trial
Subscription FAQs
Not All Qbanks Are Created Equal

Why Students Choose UWorld for SAT Practice Questions & Tests

Feature UWorld Other Providers
Digital SAT Realism
 Closely mirrors the real digital SAT’s style, logic, and pacing Practice can feel more generic and less true to the real exam
Question Bank Depth
 1,650+ exam-style questions support targeted, sustained practice Smaller banks can limit repetition, range, and focused practice
Answer Explanations
 Detailed explanations help you truly learn and master material vs memorization Explanations may be shorter, less visual, or less helpful for deeper review
Custom Practice Sets
 Build custom quizzes by topic and difficulty for focused practice. Standard quizzes make it hard to isolate and drill subjects needing the most work.
Performance Analytics
 Analytics clearly show which topics are strong and which need more attention, making progress easier to act on. Score tracking may be less specific and less actionable when students are trying to improve strategically.
Smart Study Tools
 Flashcards, notebook tools and built-in study support help reinforce learning Other options might offer practice questions without review and retention tools.
Mobile Access
 Mobile app sync makes it easy to practice and review across devices. Mobile access is not always seamless or convenient for studying on the go.
Self-Study Fit
 Designed for students who want targeted practice with built-in smart tools. Some options might be less effective for students preparing on their own.
Digital SAT Realism
UWorld

Closely mirrors the real digital SAT’s style, logic, and pacing

Other Providers

Practice can feel more generic and less true to the real exam

Question Bank Depth
UWorld

1,650+ exam-style questions support targeted, sustained practice

Other Providers

Smaller banks can limit repetition, range, and focused practice

Answer Explanations
UWorld

Detailed explanations help you truly learn and master material vs memorization

Other Providers

Explanations may be shorter, less visual, or less helpful for deeper review

Custom Practice Sets
UWorld

Build custom quizzes by topic and difficulty for focused practice.

Other Providers

Standard quizzes make it hard to isolate and drill subjects needing the most work.

Performance Analytics
UWorld

Analytics clearly show which topics are strong and which need more attention, making progress easier to act on.

Other Providers

Score tracking may be less specific and less actionable when students are trying to improve strategically.

Smart Study Tools
UWorld

Flashcards, notebook tools and built-in study support help reinforce learning

Other Providers

Other options might offer practice questions without review and retention tools.

Mobile Access
UWorld

Mobile app sync makes it easy to practice and review across devices.

Other Providers

Mobile access is not always seamless or convenient for studying on the go.

Self-Study Fit
UWorld

Designed for students who want targeted practice with built-in smart tools.

Other Providers

Some options might be less effective for students preparing on their own.

Frequently Asked Questions (FAQs)

SAT Question Bank

UWorld takes a fundamentally different approach to SAT prep that prioritizes active learning, conceptual mastery, and the specific demands of the Digital SAT over basic question-drilling.

What Makes UWorld Different:

  • Instructional Depth & Strategy: While free resources often focus on just the correct option, UWorld’s experts write detailed rationales for every single choice. We explain the underlying logic for the right answer and more importantly, why the distractors are wrong, helping you identify and avoid traps.
  • “Explanation-First” Philosophy: Every question is a learning opportunity. Our explanations don’t just tell you the answer; they teach you the fastest strategies and the core concepts required to solve similar problems on test day.
  • Retention-Focused Technology: Our platform goes beyond simple practice. We offer sophisticated performance tracking, customizable flashcards with spaced repetition, and a custom test generator designed to mimic the actual exam interface.

How We Compare:

  • UWorld vs. Khan Academy: Khan Academy provides a solid foundational baseline, but UWorld is designed to take you further. We provide deeper conceptual explanations and questions that more closely align with the highest-difficulty modules of the Digital SAT.
  • UWorld vs. Free College Board Tools: While free tools are great for gauging your starting point, they often lack the robust study tools and detailed feedback loops necessary for significant score improvement. UWorld provides the “why” behind every miss to ensure you don’t repeat mistakes.

The Bottom Line: We don’t just give you practice questions; we give you the tools to understand the logic behind the test. UWorld is an investment in a higher score and, ultimately, better college admissions opportunities.

Our questions are purpose designed and written to be at or slightly above the difficulty of the actual digital SAT exam.  Our in-house educators write these questions to closely mimic the actual SAT in terms of question style, logic, and interface.

  • Realistic Interface: Our platform is purpose-designed to replicate the Bluebook™ interface, so the actual exam feels just like another practice session.
  • Adaptive Simulation: Create customized quizzes that mimic the adaptive nature of the digital SAT. The Bottom Line: Practicing with UWorld makes the real exam feel familiar, easier, and far less stressful.

Students often say that UWorld’s questions are so realistic that exam day feels like just another practice session within the QBank.

The UWorld SAT QBank provides everything you need for targeted, effective practice.

  • 1,650+ Practice Questions: A massive library of exam-level questions you won’t find anywhere else.
  • Detailed Explanations: Step-by-step breakdowns for every correct and incorrect answer choice.
  • Performance Analytics: A dashboard to track your strengths, weaknesses, and predicted score range.
  • Smart Study Tools: Access to customizable flashcards, a My Notebook feature, and a mobile app for studying on the go. The Bottom Line: The QBank equips you with an extensive question pool and retention-focused tools to maximize your score.

UWorld gives you the tools and resources for effective SAT prep and our QBank will have you confident and ready for test day.

There’s no magic number but what we’ve seen work best for students is consistent and focused review. UWorld’s QBank is perfect for that because it includes a powerful SAT performance dashboard that serves as both a diagnostic and targeted study resource to highlight weak spots which are more important ot target than sheer volume.

Getting the most out of our QBank:

  • Targeted Practice: Focus on deeply reviewing the explanations of 20-30 targeted questions a day rather than mindlessly answering 200.
  • Quality Over Quantity: The key is to understand the why behind every mistake using our step-by-step breakdowns.

The Bottom Line: Let your performance analytics guide you; you are ready when you consistently score well in your weakest areas.

Our SAT practice questions are written by a dedicated team of in-house expert educators and top-tier scorers. Every question, potential answer and subsequent explanation undergoes rigorous review to ensure it mirrors the difficulty and “vibe” of the actual Digital SAT.

  • Expert Educators: Content is crafted by experienced professionals who deeply understand the test mechanics.
  • Top-Tier Scorers: Questions are designed by individuals who have mastered the exam themselves. The Bottom Line: UWorld’s questions are written by SAT experts to provide the most authentic practice experience possible.
Unlike some resources you’ll find online, UWorld doesn’t use AI, freelancers or other tools to generate questions because the quality of both question and explanation is our highest priority.

Yes. We offer a free trial that gives you access to a selection of our realistic SAT practice questions and, most importantly, our detailed answer explanations. UWorld makes it easy to start your dream score journey today with: 

  • No Commitment: Start your free trial without needing to enter a credit card.

  • Experience the Difference: See for yourself why students say our explanations are the “best” and how they help you understand the why behind every mistake. The Bottom Line: Try our free trial to explore our platform and see how our explanation-first approach can boost your score.

Once you try our questions and see the value of our explanations, you’ll quickly understand why our QBank products are seen as the gold standard for test prep.

Yes. This QBank is arguably the most effective tool for students needing a last minute crash course because it stops you from wasting time on material you already know. Here’s how our product optimizes your studying:

  • Performance Analytics: Find your biggest weaknesses and focus 100% of your remaining time there instead of randomly doing questions.

  • Rapid Improvement: Many students see significant score jumps in just a few weeks by focusing on deeply reviewing the explanations of 20-30 targeted questions a day.

Bottom Line: UWorld is highly effective for last-minute prep because it allows you to study smarter and target exactly what you need to improve.

Studying smarter, not just longer, through focused review of our detailed rationales is the fastest way to raise your score. Whether you have months, weeks or just days before your exam, targeting your weakest areas will always see you improve.

UWorld’s SAT QBank helps you improve your performance by: 

  • Identifying Weak Spots: Use the performance dashboard to pinpoint your exact weaknesses (e.g., Quadratics or Transitions).

  • Generating Custom Quizzes: Create targeted quizzes to focus specifically on those skills. 

The key is focused review. Don’t just answer questions; spend time on the detailed explanations for every question you get wrong.

Our questions are designed to be at or slightly above the difficulty of the actual digital SAT. In fact many of the students who use this product compare exam day to another QBank practice session because of both the quality of the questions and realistic interface.

The advantage of practicing with our questions is that each answer, right or wrong, comes with a detailed explanation so regardless of whether you get a question right or wrong, you’re gaining valuable information in how to approach the test and use critical thinking and reasoning to find the right answers.

Our QBank gives you the tools to simulate adaptive practice and get comfortable with the test’s structure.

  • Customizable Difficulty: You can build a quiz of “Medium” difficulty questions, then follow it with a quiz of “Hard” questions.
  • Realistic Interface: Combined with our timed mode that perfectly matches the Bluebook exam interface, you get a highly realistic environment.

The Bottom Line: UWorld allows you to master the pacing and difficulty changes you will face on the actual digital SAT.

This QBank is ideal for self-studiers who want to focus on targeted practice. It gives you our entire 1,650+ question library and all our smart study tools (analytics, flashcards, notebook) to find and fix your weaknesses on your own. 

The Course includes everything in the QBank, plus 100+ short, expert-led video lessons that teach you every single concept from the ground up, along with a guided study plan and prep book.

Bottom line: If you just need to practice and review, get the QBank. If you need to learn the core content and practice, the Course is the better fit. Check out our free trial to explore what’s the right fit for you.

Yes, absolutely. UWorld’s comprehensive SAT practice tests are fully available for both major sections of the new Digital SAT, giving you the flexibility to dive into whichever areas you need to work on the most. Preparing for both domains comprehensively is essential for maximizing your score. By utilizing our dual-section approach, you benefit from:

  • Targeted Math Practice: Thorough coverage of core math domains including algebra, problem-solving, and data analysis to sharpen your quantitative skills.
  • Relevant Reading & Writing Content: A vast question bank featuring the short passages and specific question types perfectly aligned with the new Digital SAT format.
  • Test-Day Readiness: Practicing both sections consistently helps you build the necessary mental endurance, perfect your timing, and develop the strategic focus needed to stay sharp across the full length of the test.

Absolutely! There is completely no limit to how many customized quizzes you can generate on our platform. This provides a massive advantage, especially once you have already exhausted the limited number of official College Board® practice tests. If you find yourself struggling with a specific skill, our platform adapts to your learning needs. With unlimited quiz generation, you can expect:

  • Targeted Repetition: Create as many focused quizzes as you need on hyper-specific topics, such as geometry or grammar rules, until you achieve complete mastery.
  • Immediate Feedback: Every single quiz provides instant, detailed explanations so you can learn from your mistakes immediately and avoid repeating them.
  • Rapid Improvement: Generate a fresh quiz immediately after reviewing your errors to reinforce the concepts you just learned.
  • Routine Consistency: Try taking a quick 10-question daily quiz; you will be amazed at how fast your skills improve through regular, bite-sized practice.

UWorld’s SAT practice tests provide a significantly more interactive, data-driven, and personalized learning experience than standard College Board® practice exams. While the College Board is an essential resource, it only offers a limited set of official tests and static answer keys. UWorld bridges this gap by combining official-level realism with advanced tools. Our platform elevates your prep by offering:

  • Unlimited Customization: Create an unlimited number of digital SAT practice tests tailored to your specific study needs.
  • In-Depth Explanations: Receive instant scoring and view highly detailed, step-by-step explanations for every single concept and answer choice (both correct and incorrect).
  • Advanced Data Insights: Your test bank is fully synced to a dynamic performance dashboard that instantly highlights your strongest subjects and pinpoints exactly what you need to work on more.
  • The Best of Both Worlds: You get the authentic feel of the real exam combined with the actionable data insights necessary to strategically boost your score.

Your SAT mock exam and practice test results should serve as the ultimate roadmap for your entire study plan. Rather than just looking at the final score, you can leverage your results to create a highly efficient, targeted preparation strategy. To get the most out of your results, follow this proven cycle:

  • Analyze the Data: After completing a full-length mock exam, dive into your performance metrics to identify and target your weakest areas.
  • Drill Specific Skills: Switch over to UWorld’s customizable practice tests to drill those exact weak points, whether that is problem-solving in Math or syntax in Reading & Writing.
  • Continuous Refinement: Engage in a continuous cycle of testing, reviewing explanations, and focusing your efforts. This ensures you are always improving the exact areas that carry the most weight for your final score.

The full-length SAT mock exam and the customizable practice tests serve two distinct but equally important purposes in your preparation journey. Understanding the difference ensures you use both tools at the right time.

  • The Mock Exam: This is a complete, score-predicting experience that meticulously replicates the entire Digital SAT. It perfectly mirrors the timing, format, and question difficulty of the real thing, making it the ideal tool for simulating actual test-day conditions.
  • Customizable Practice Tests: In contrast, these put you in complete control of your daily prep. You can hand-pick the subjects, micro-topics, or question difficulty levels you want to include.
  • Strategic Focus: The customizable tests make it incredibly easy to zero in on specific problem areas, like algebra or grammar, allowing you to strengthen your weaknesses without wasting valuable time on concepts you have already mastered.

UWorld’s full-length Digital SAT mock exam is widely recognized for its high level of accuracy in score prediction. It has been painstakingly designed by educational experts to match the real test in structural integrity, overall difficulty, and strict timing constraints. Because of this dedication to realism, you can expect highly reliable results. The accuracy of our mock exams is driven by:

  • Authentic Module Structure: Each section utilizes adaptive-style modules that seamlessly simulate the real Digital SAT, ensuring your results closely reflect how you’d perform on the actual test day.
  • Proven Precision: Most students discover that their final UWorld mock exam score falls within a very narrow margin of a few points of their actual SAT result, particularly if they don’t do any additional studying between the mock and the real test.
  • Actionable Analytics: The test’s built-in analytics not only give you a realistic score prediction but also clearly pinpoint exactly where to focus your remaining study time, whether you need to improve math logic, reading comprehension, or writing precision.

Timing your mock exams correctly is a crucial part of a successful SAT preparation strategy. We recommend spacing your full-length tests out to accurately gauge your progress over time. For the best results, follow this testing timeline:

  • Establish a Baseline: Take your first score-predicting mock exam early in your prep. This initial attempt serves as your baseline SAT mock test, clearly highlighting where you currently stand and exposing which subject areas require the most intensive work.
  • Targeted Practice: After your baseline test, spend time reviewing your results and utilizing custom SAT practice tests that focus heavily on your identified weaker topics.
  • Mid-Point Check-In: Take another full-length mock exam (using an official SAT practice test or another UWorld mock) midway through your study plan to accurately measure your progress and readjust your study strategy if necessary.

Once you complete your full-length SAT mock exam, you won’t just get a simple number. You will receive a comprehensive, highly detailed performance breakdown designed to guide your future study sessions. This personalized analysis is incredibly robust and includes:

  • Comprehensive Scoring: A clear view of your overall projected score, individual section scores, and hyper-specific subscores broken down by skill area.
  • Actionable Next Steps: Insightful data that helps you identify your most valuable next steps for improvement.
  • Targeted Direction: Clear indications on whether you need to prioritize more practice with algebraic expressions, focus on specific grammar corrections, or work on your reading comprehension timing.

Yes, absolutely! UWorld’s SAT Math sample test content is carefully and rigorously designed to match the format, question style, and exact difficulty level of the actual Digital SAT. We pride ourselves on the authenticity of our materials. By utilizing these practice questions, you will benefit from:

  • True-to-Test Logic: Each sample SAT Math test question perfectly reflects the reasoning, logic, and core concepts found on the real exam.
  • Pattern Recognition: Practicing with these questions teaches students how to correctly interpret tricky question wording, identify recurring patterns, and apply math concepts efficiently.
  • Confidence Building: Consistent exposure to highly accurate material builds immense test-day confidence and ensures that your preparation feels exactly like the real test environment.

Absolutely. We believe that practice is only effective if you can learn from your mistakes. That is why every single SAT Math sample question in our database comes paired with a step-by-step solution and a highly detailed explanation. Reviewing these explanations is a core part of the UWorld method. Our explanations are designed to provide:

  • Deep Understanding: Students can review the sample questions and answers to fully comprehend why a specific answer is correct, rather than just memorizing what the answer is.
  • Strategic Advantage: Each explanation actively helps students identify the best and fastest solving strategies for future questions.
  • Concept Recall: Explanations prompt students to recall key formulas and highlight ways to avoid falling for common test-maker traps and mistakes.
  • Interactive Learning: These comprehensive answer guides make studying interactive, deeply meaningful, and incredibly easy to follow.

UWorld’s extensive library of SAT Math example problems comprehensively covers all the major math domains that are tested on the official SAT. We leave no stone unturned to ensure you are ready for any question type. Our practice materials include:

  • Algebra: Extensive practice with linear equations, complex inequalities, and systems of equations.
  • Data Analysis: Real-world word problems and data interpretation involving ratios, percentages, and probabilities.
  • Advanced Math: Higher-level questions covering quadratic, polynomial, and exponential functions.
  • Geometry & Trigonometry: Detailed problems focused on calculating angles, navigating coordinate geometry, and applying measurement formulas.
  • Skill Enhancement: Together, these sample problems help students dramatically strengthen their conceptual understanding, sharpen their problem-solving speed, and significantly boost their overall test performance.

Yes. UWorld’s vast repository of practice materials includes content that aligns with both SAT II Math sample tests, which are commonly known as SAT Math Level 1 and SAT Math Level 2 sample tests. While these specific test formats represent older Subject Tests, the rigorous content remains incredibly valuable for deep, comprehensive math practice. Our materials cover:

  • Level 1 Concepts: Thorough practice spanning foundational algebra, standard geometry, and comprehensive data analysis.
  • Level 2 Concepts: Challenging, higher-level topics including advanced trigonometry, complex functions, and in-depth coordinate geometry.
  • Complete Preparation: Both levels of these SAT Math 2 sample tests are readily available online, ensuring that ambitious students are thoroughly over-prepared for all possible types of math questions they may encounter.

UWorld’s sample SAT Math tests firmly stand out from the competition due to their uncompromising realism and our industry-leading, detailed explanations. Generic worksheets or free PDFs simply cannot offer the same level of preparation. When you choose UWorld, you are choosing a premium study experience characterized by:

  • Perfect Mimicry: Unlike standard generic materials, our SAT Math example questions are painstakingly crafted to mimic the official SAT structure and phrasing exactly.
  • Cognitive Training: With our detailed rationales, students don’t just passively practice; they actively learn how to think exactly like the test maker.
  • Trusted Quality: This dedication to quality and conceptual deep-dives is exactly why UWorld is trusted and highly recommended by students, parents, and professional educators nationwide for SAT preparation.

Yes, completely. All of the SAT Reading and Writing sample questions available on UWorld follow the brand new Digital SAT format to the letter. The days of incredibly long reading passages are over, and our materials reflect that exact shift. When utilizing our English practice tools, you will find:

  • Short-Form Content: Each question is specifically linked to a distinct short passage or a brief informational text, exactly mirroring the official test’s structure.
  • Diverse Question Types: You can thoroughly explore various SAT sample reading questions, sample SAT writing questions, and grammar-in-context prompts.
  • Targeted Preparation: Our platform allows you to create highly customized exercise sets on UWorld’s adaptive system, ensuring your preparation is targeted, relevant, and aligned with the modern test.

Absolutely. We prioritize comprehension over simply checking a box. Every single SAT English sample question includes a rich, step-by-step answer explanation. These explanations walk you through the logical reasoning behind every single answer choice, explaining exactly why the right answer is right, and why the wrong choices are incorrect. The benefits of this approach include:

  • Skill Strengthening: These detailed breakdowns help students aggressively strengthen their grammar rules, context-based vocabulary, and overall reading comprehension skills.
  • Continuous Learning: Parents and educators love that every single question, whether answered right or wrong, turns into a valuable learning moment, rather than just an arbitrary score on a screen.
  • Pattern Recognition: Over time, reading these explanations helps students naturally recognize the traps test-makers frequently use in the Reading & Writing section.

When you use UWorld, you will never run out of high-quality practice material. Students have immediate access to hundreds of meticulously crafted SAT Reading and Writing sample questions. Beyond the sheer volume of questions, the platform offers powerful tools to utilize them effectively:

  • Unlimited Quizzes: You have the ability to build unlimited custom quizzes from this massive question bank.
  • Targeted Focus: You can choose to isolate your practice to specific areas, such as reading comprehension, strict grammar rules, or complex vocabulary-in-context questions.
  • Progress Tracking: The system meticulously tracks your progress along the way, visually highlighting your growth.
  • Efficient Studying: This vast volume and customization ensure every student focuses their time and energy exactly where improvement is needed most.

The Reading section of the SAT is notorious for testing how well you understand the nuances of a text, not just the surface-level facts. Our sample SAT reading questions and reading comprehension samples feature carefully constructed, short, evidence-based passages. These are designed to push your analytical skills to the next level. Engaging with these questions helps improve your comprehension by:

  • Testing Nuance: The questions rigorously test your understanding of authorial tone, complex arguments, and implied meaning.
  • Skill Building via Explanations: Reviewing our detailed explanations helps students learn how to quickly identify main ideas, infer hidden meanings, and properly evaluate textual evidence.
  • Long-Term Success: Mastering these exact analytical skills improves not just your immediate SAT scores, but significantly prepares you for college-level reading success in the future.

The SAT Writing section requires a firm grasp of standard English conventions, and our sample questions cover every single rule you will encounter on test day. Our SAT writing sample questions rigorously test essential grammar and usage skills. You will find comprehensive coverage of the following topics:

  • Punctuation & Structure: Mastering proper comma usage, semicolons, and overall sentence structure boundaries.
  • Verbs: Identifying correct verb tense, mood, and strict subject-verb agreement.
  • Modifiers & Parallelism: Fixing dangling modifiers and ensuring sentence elements remain perfectly parallel.
  • Expression of Ideas: Refining word choice, maintaining concise phrasing, and selecting the most logical transitions between sentences.
  • Contextual Learning: Each sample SAT English question explains these grammar rules using real-context examples, helping students learn naturally through application instead of memorizing dry rules in isolation.

The internet is full of test prep material, but much of it is unreliable. Many SAT sample English questions found floating around on Google searches, Quora threads, or Reddit forums may be wildly outdated, poorly written, or factually inaccurate. UWorld provides a safe, reliable, and premium alternative. Our Reading and Writing materials stand above the rest because:

  • Expert Craftsmanship: UWorld’s sample SAT Reading and Writing questions are written exclusively by highly experienced, expert educators.
  • Rigorous Review: Every question is meticulously reviewed for factual accuracy, appropriate difficulty scaling, and strict alignment with the latest Digital SAT format.
  • Verified Explanations: Each and every question includes beautifully detailed, verified explanations.
  • Trustworthy Prep: Students can rest easy knowing they are always preparing with the most trusted, highest-quality material available, without second-guessing their resources.

Setting a clear goal is the first step to achieving a great score. The SAT Reading and Writing section is scored on a scale from 200–800. While a “good” score depends entirely on the specific universities you are applying to, there are general benchmarks you can aim for. When setting your goals, consider the following:

  • Competitive Benchmarks: Highly competitive college applicants very often aim for a Reading and Writing score landing comfortably between 600 and 750.
  • Consistent Practice: Reaching this high tier requires dedication. Regularly reviewing SAT English sample questions (covering English conventions, reading comprehension, and writing expression) is key.
  • In-Depth Review: Combining consistent practice with our in-depth explanations can and will steadily improve your overall textual understanding and elevate your test-taking performance to hit your target numbers.
Learn From Actual SAT Experts

Meet UWorld's SAT Teachers

Real teachers. Real SAT questions. Our instructors carefully craft every SAT multiple choice practice question to look and feel just like the real exam, so you can study smarter and stress less.
Suzanne Dilday

Suzanne Dilday
Curriculum Manager

Experience 27 years teaching high school English, including 16 years for AP® English Language
Specialty Advanced rhetorical analysis, argumentative writing, and college-level literary skills
Other Facts Creates study materials for the SAT and ACT exams
View my Linkedin Profile
Peter Kenny

Peter Kenny
Content Developer

Experience 37 years teaching high school English, including 23 years for AP English Literature
Specialty In-depth knowledge of literature, language, and skills needed for academic success
Other Facts Has a Bachelor of Arts in English and a master’s in Humanities; creates study materials for the SAT and ACT exams
View my Linkedin Profile
Melanie White

Melanie White
Senior Content Developer

Experience 25+ years tutoring students for the SAT and ACT®, and 10 years as an SAT essay grader for the College Board®
Specialty High-school English, GED classes, and college-level composition classes
Other Facts Has a Bachelor of Arts in English with a specialization in Creative Writing and a Master of Arts in English as a Second Language
Anne Hellerman

Anne Hellerman
Senior Content Developer

Experience 13 years tutoring high-school students in English and math
Specialty SAT and ACT preparation, testing strategies, and a focus on helping students strengthen their academic foundation
Other Facts Creates study materials for both the SAT and ACT exams
Jessica Meyer

Jessica Meyer
Senior Content Developer

Experience 22 years in math education — classrooms and educational tech startups
Specialty Pedagogy and addressing students’ needs in math through traditional and innovative solutions
Other Facts Has a Bachelor of Science in Applied Mathematical Sciences and a Master of Arts in Mathematics
Joan Lester

Joan Lester
Senior Content Developer

Experience 10 years in engineering, and 12 years teaching high-school math
Specialty Technical and instructional disciplines by applying math to the SAT and ACT in preparation for future technical studies
Other Facts Has a Bachelor of Science in Mechanical Engineering and Master of Science in Engineering
View my Linkedin Profile
Stevenson Lauren

Lauren Stevenson
Senior Content Developer

Experience 20 years in math education, ranging from Algebra I to AP Calculus, and curriculum writing at both district and state levels
Specialty Pedagogy with real-world testing standards to prepare students for the SAT, ACT, AP Calculus, and AP Statistics
Other Facts Has a master's in Education and has completed doctoral coursework
Rebecca Plourde

Rebecca Plourde
Senior Content Developer

Experience 10+ years in SAT/ACT math content development, and 4 years teaching underperforming students
Specialty Adaptable and diverse math teaching methods that help students across skill levels
Other Facts Has a dual degree in Philosophy and Mathematics
View my Linkedin Profile
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Awards & Recognition

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Parent and Teacher Choice Award
2022 EdTech Awards Cool Tool Finalist
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Official SAT Practice Tests

Download official full-length practice tests written by the same team that writes the real SAT. Use alongside UWorld for comprehensive preparation. For the most authentic adaptive experience, take tests in Bluebook — College Board's official digital testing app.
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Key SAT Math Equations and Formulas

See essential formulas that do not appear on the official SAT Math reference sheet
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Core Grammar Rules

All the core SAT grammar rules you need to know
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Top 100 Vocabulary Words

Get a PDF of the top 100 SAT vocabulary words you need to know
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4 Strategies to Solve the Toughest Math Problems

Learn proven techniques for solving the toughest SAT math problems
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Roots, Prefixes and Suffixes

Use our guide to quickly breakdown words and their meaning
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SAT Reading: 7 Strategies to Maximize Time

Learn time management and strategies to approach SAT® reading with 7 simple ways.
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Improving Your SAT Math Score

Key studying and time management tips for a higher score
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Best SAT Practice Tests and Questions

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Frequently Asked Questions

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Example scenarion: An individual purchases a 180-day Qbank subscription and generates a few test blocks equal to 20% of the questions in the Qbank. After 45 days, he/she requests a refund. Because the elapsed duration is greater than the percentage of questions used, the refund amount will be based on a subscription converted to the closest duration (60 days) by deducting the applicable 60-day subscription fee from the refund. In the same scenario, if the individual had used 85% of the questions, the refund would be 15% of the subscription fee paid.

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Upon a successful transaction, you will be sent a confirmation email receipt.

A renewal is an extension of time to continue accessing an active subscription, and it will not start the subscription over, provide a reset, or grant access to additional questions that were not previously accessible. Because a renewal is an extension to an already active subscription, it is effective from the existing expiration date, not from the date of purchase, and cannot be deferred in any way to start at a later date/time.

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Recommended
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SAT Prep Course
Select Your Plan
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$299
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Score Booster Plan
90 Day Access
$349
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Most Popular
Deep Learning Plan
180 Day Access + One-Time Reset
$399
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Dream Score Plan
360 Day Access + One-Time Reset
$449
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