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SAT Math Practice Test 1: Algebra
Question
The functionf (x) is defined as 17 less than 6 times a numberx. Ify = f (x) is graphed in the xy-plane, what is the best interpretation of they-intercept?
| A. When the number is 0, \(f(x)=\dfrac{17}{6}\). | |
| B. When the number is 0, \(f(x)\)= −17 | |
| C. When \(f(x)\) = 0, the number is \(\dfrac{17}{6}\). | |
| D. When \(f(x)\) = 0, the number is -17. |
The y-intercept of a graph is the point where the line intersects the y-axis, so it has coordinates (0, y).
First write an equation for f(x), then evaluate f(0).
Explanation
The y-intercept of a graph is the point where the line crosses the y-axis, so it has coordinates (0, y). This point corresponds to the function notation f(0), which is the output (or value) of the linear function f when the input is 0.
To find the best interpretation of the y-intercept, first use the given information to write an equation for the function f. It is given that the function f(x) is defined as 17 less than 6 times a number x.
The function is f(x) = 6x − 17. To evaluate f(0), plug x = 0 into the function f and simplify.
| f(x) = 6x − 17 | Linear function f |
| f(0) = 6(0) − 17 | Plug in x = 0 |
| f(0) = −17 | Multiply |
The value of f(0) is −17. Therefore, the best interpretation of the y-intercept in the given choices is when the number is 0, f(x) = −17 (graph).
Note: It is also possible to compare the function f(x) = 6x − 17 to slope-intercept form f(x) = mx + b to see that the value of the y-coordinate of the y-intercept is −17.
(Choice A) "When the number is 0, " is a misinterpretation of the x-intercept, but the question asked for the y-intercept.
(Choice C) "When f(x) = 0, the number is " is an interpretation of the x-intercept, not the y-intercept.
(Choice D) "When f(x) = 0, the number is −17" may result from mistaking the x-intercept for the y-intercept.
Things to remember:
- The function notation f(x) means the output (or value) of the function f when the input is x.
- On a graph in the xy-plane, f(x) corresponds to y.
- The y-intercept of a line is the point where the line crosses the y-axis. Its coordinates are (0, y).
Question
Last week, a nonprofit organization recorded 1,980 items used for meal packs. The equation 4x + 10y = 1,980 represents this situation, where x is the number of snack packs and y is the number of dinner packs. Which of the following is the best interpretation of 10 in this context?
| A. There were 10 total items used in snack packs. | |
| B. There were 10 items used per snack pack. | |
| C. There were 10 total items used in dinner packs. | |
| D. There were 10 items used per dinner pack. |
To determine the best interpretation of 10 in the given context, first use the given information to determine the meaning of 10y.
Explanation
The given equation represents the sum of the number of items used in snack and dinner packs that is equal to the given total items (1,980). To interpret 10, first find the meaning of 10y.
It is given that there were x snack packs, so 4x must represent the number of items in snack packs.
It is given that there were y dinner packs, so 10y must represent the number of items in dinner packs.
The term 10y represents the number of items in dinner packs recorded by the organization, and the variable y represents the number of dinner packs.
Therefore, 10 must represent the number of items per dinner pack.
Therefore, the best interpretation of 10 is "There were 10 items used per dinner pack."
(Choice A) "There were 10 total items used in snack packs" may result from the combination of errors described in Choices B and C.
(Choice B) "There were 10 items used per snack pack" may result from mistaking 10 to represent snack pack items (instead of dinner pack items).
(Choice C) "There were 10 total items used in dinner packs" may result from mistaking 10 to represent all dinner items (instead of items per dinner pack).
Things to remember:
For an equation in the form
,
the terms Ax and By are variable amounts whose sum is a total C.
Question
A certain thrift store uses a guideline to set sales prices for gently used designer items they've purchased. The recommended minimum sale price of any thrift item, s dollars, is 7 more than 2 times the amount paid for that item, p dollars. Which inequality shows the possible values of s ?
| A. s ≤ 7p + 2 | |
| B. s ≥ 7p + 2 | |
| C. s ≤ 7 + 2p | |
| D. s ≥ 7 + 2p |
The phrase "more than" means addition, and the phrase "times" means multiplication.
Explanation
It is given that the minimum sale price of any thrift item, s dollars, is 7 more than 2 times the amount paid for that item, p dollars. Therefore, s must be greater than or equal to 7 more than 2 times the amount paid p.
Now build the expression on the right. The phrase "more than" means addition, and the phrase "times" means multiplication.
Therefore, the inequality that shows the possible values of s is .
(Choice A) may result from the combination of errors described in Choices B and C.
(Choice B) is incorrect because represents 2 more than 7 times p, instead of 7 more than 2 times p.
(Choice C) is incorrect because represents the maximum, instead of the minimum, value of s.
Things to remember:
- If the maximum value of a is b, then (a ≤ b).
- If the minimum value of a is b, then (a ≥ b).
SAT Math Practice Test 2: Advanced Math
Question
How many distinct real solutions does the given equation have?
| A. Zero | |
| B. Exactly one | |
| C. Exactly two | |
| D. Infinitely many |
It is possible to analyze the number of solutions to a quadratic equation from its discriminant.
Explanation
A quadratic equation may have 0, 1, or 2 solutions. It is possible to analyze the number of solutions to a quadratic equation from the discriminant.
The discriminant of a quadratic equation in standard form ax2 + bx + c = 0 is the expression under the square root in the quadratic formula.
Compare the given equation 3x2 + 12x + 25 = 0 to standard form to identify the values of a, b, and c.
Plug the values of a, b, and c into the discriminant b2 − 4ac and simplify.
| b2 − 4ac | Discriminant |
| (12)2 − 4(3)(25) | Plug in a = 3, b = 12, and c = 25 |
| 144 − 300 | Simplify |
| −156 | Subtract |
The discriminant is −156.
A quadratic equation with a negative discriminant has zero solutions. Therefore, the given equation has zero distinct real solutions.
Things to remember:
The number of solutions to a quadratic equation can be determined by
the discriminant b2 − 4ac, the quantity under the square root in
the quadratic formula.
The real solutions to a quadratic equation in the form 0 = ax2 + bx + c correspond to the x-intercepts on the graph of y = ax2 + bx + c because x-intercepts have a y-value of 0.
To find the number of solutions to the given equation 3x2 + 12x + 25 = 0, graph y = 3x2 + 12x + 25 and count the x-intercepts.
The graph of y = 3x2 + 12x + 25 never intersects the x-axis, so it has zero x-intercepts.
Therefore, the equation 3x2 + 12x + 25 = 0 has zero distinct real solutions.
Things to remember:
The solutions to a quadratic equation in the form 0
= ax2 + bx + c correspond to
the x-intercepts on the graph
of y = ax2 + bx + c.
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) |
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
If x is negative and the square of x is equal to the sum of three times x and 18, what is the value of x ?
Explanation
Correct Answer : -3
It is given that the square of x is equal to the sum of three times x and 18, so first write an equation in terms of x.
To solve for x, first rewrite the equation x2 = 3x + 18 in standard form ax2 + bx + c = 0 and then factor.
| x2 = 3x + 18 | |
| x2 − 3x − 18 = 0 | Subtract 3x and 18 from both sides |
| (x + 3)(x − 6) = 0 | Factor x2 − 3x − 18 |
The expression (x + 3)(x − 6) equals 0 when either of its factors equals 0. Set both factors equal to 0 and then solve for x.
| x + 3 = 0 | Set both factors equal to 0 | x − 6 = 0 |
| x = −3 | Solve for x | x = 6 |
The possible values of x are −3 and 6. It is given that x is negative, so the value of x must be −3.
Note: Although less efficient, it is also possible to use the quadratic formula to solve x2 − 3x − 18 = 0 for x.
Things to remember:
- To solve a quadratic equation by factoring or with the quadratic formula, it is necessary to first write the equation in standard form ax2 + bx + c = 0 (if it is not already in this form).
- It may be possible to factor a quadratic expression x2 + bx + c as (x + m)(x + n), where m and n are integers that multiply to c and add to b.
- It is possible to use the quadratic formula to solve any quadratic equation.
SAT Math Practice Test 3: Problem-Solving and Data Analysis
Question
A parking space has an area of 270 square feet. What is the area, in square yards, of this space? (1 yard = 3 feet).
The given conversion is 1 yard = 3 feet, so it is necessary to first find a conversion between square feet and square yards.
Explanation
To convert from one unit to another, 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.
The old unit is square feet, and the new unit is square yards. The given conversion is 1 yard = 3 feet, so it is necessary to first find a conversion for square feet and square yards.
The desired units are square units, so square both sides of the given conversion to determine the relationship between square feet and square yards.
| 1 yard = 3 feet | Given conversion |
| (1 yard)2 = (3 feet)2 | Square both sides |
| (1 yard)(1 yard) = (3 feet)(3 feet) | Apply exponent on both sides |
| 1 square yard = 9 square feet | Multiply |
Now use the conversion 1 square yard = 9 square feet to convert the given area of the parking space from 270 square feet to square yards.
Multiply the 270 by the conversion factor 1 square yard9 square feet to calculate the area in square yards.
The area of the parking space is 30 square yards.
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.
- To get a conversion between square units (ex. square feet and square inches), square both sides of the conversion between their linear units (feet and inches).
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.
| Mean number of points | |
| Plug in values | |
| Add in numerator | |
| 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
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 :
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).
SAT Math Practice Test 4: Geometry and Trigonometry
Question
In triangles ABC and DEF, angles A and D each measure 30°, AB = 12, and DE = 24. Which additional piece of information is sufficient to prove that triangle ABC is similar to triangle DEF ?
| A. BC = 4 and EF = 4 | |
| B. BC = 4 and EF = 8 | |
| C. The measures of angles C and E are 70° and 80°, respectively. | |
| D. The measures of angles C and F are 70° and 30°, respectively. |
Hint :
The three triangle similarity theorems are Angle-Angle, Side-Angle-Side, and Side-Side-Side.
Explanation
Similar triangles have 3 pairs of congruent angles and 3 pairs of corresponding sides with proportional lengths.
To prove triangle similarity, use one of the three triangle similarity theorems: Angle-Angle (AA), Side-Angle-Side (SAS) similarity, and Side-Side-Side (SSS) similarity.
For triangles ABC and DEF, it is given that corresponding angles ∠A and ∠D each measure 30°, so they form one pair of congruent angles. One pair of corresponding side lengths AB = 12 and DE = 24 is also given.
Choices A and B give lengths for corresponding sides and . Two pairs of corresponding sides and a non-included angle (side-side-angle) are not sufficient information to prove similarity. Eliminate Choices A and B.
Choice D gives unequal measures for corresponding angles C and F. Eliminate Choice D because each pair of corresponding angles in similar triangles must be congruent.
Therefore, the information in Choice C must be sufficient to prove similarity: The measures of angles C and E are 70° and 80°, respectively.
Note: It is possible use the information in Choice C to calculate the measure of ∠B and prove that triangles ABC and DEF are similar.
Things to remember:
To prove triangle similarity, use one of the three triangle
similarity theorems: Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS).
Question
In the figure shown above, ABCD is a square and AECF is a parallelogram. The area of ABCD is 144 square feet (ft2) and the area of AECF is 36 ft2. What is the length, in feet, of line segment ?
| A. 3 | |
| B. 9 | |
| C. 12 | |
| D. 15 |
Hint :
Segments and are the sides of triangle AFD. Segment is also a side of square ABCD.
Explanation
Notice that and are the legs of right triangle AFD, and that segment is also a side of square ABCD. Use the given area of square ABCD to find the length of .
The area of parallelogram AECF is also given. Use the given areas to find the area of triangle AFD, and then use the area of the triangle to find the length of .
length of
The formula for the area of a square is A = s2, where s is the side length. It is given that the area of square ABCD is 144 ft2, so plug A = 144 into the formula and solve for s.
Square ABCD has side length s = 12, so the length of is 12 ft.
area of triangle AFD
The combined area of triangles AFD and CEB is equal to the area of square ABCD minus the area of parallelogram AECF.
The given area of square ABCD is 144 ft2 and that of parallelogram AECF is 36 ft2. Subtract to find that the combined the area of triangles ADF and CEB is 108 ft2.
Triangles AFD and CEB are congruent (proof), so they have equal areas. Therefore, the area of triangle AFD is half of the combined area.
Divide 108 by 2 to find that the area of triangle AFD is 54 ft2.
Now use the length of (12) and the area of triangle AFD (54) to solve for the length of .
The formula for the area of a triangle is where b is the length of the base and h is the height. Let be the base and let be the height. Plug A = 54 and b = 12 into the area formula and solve for h.
The value of h is 9, so the length of is 9.
(Choice A) 3 is the length of the shorter side of parallelogram AECF. This may result from mistakenly finding the length of (instead of ).
(Choice C) 12 is the side length of square ABCD. This may result from mistaking the length of to be equal to the length of , but is not a side of square ABCD.
(Choice D) 15 is the length of the hypotenuse of triangle AFD. This may result from mistakenly finding the length of (instead of ).
Things to remember:
- The formula for the area of a square is A = s2, where s is the side length.
- The formula for the area of a triangle is , where b is the length of the base and h is the height.
- If two right triangles have congruent hypotenuses and a pair of congruent legs, the triangles are congruent (hypotenuse-leg congruence theorem).
- If two triangles are congruent, they have equal areas.
Question
In the figure above, angles PSQ and PSR are right angles. What is the length of ?
Hint :
Explanation
It is given that angles and are right angles, so triangles and are right triangles. It is not given that is a right angle, so do not assume that is a right triangle.
Find the length of first. The Pythagorean theorem states that , where and are the lengths of the legs of a right triangle with a hypotenuse of length .
The legs of are and , and the hypotenuse is . Plug in , , and , then solve for .
The length of is 8. Now that two side lengths of right triangle are known, use the Pythagorean theorem again to solve for .
The legs of are and , and the hypotenuse is . Plug in , , and , then solve for .
The length of is 15.
Things to remember:
The Pythagorean theorem states that , where and are the lengths of the legs of a right triangle and is the length of the hypotenuse.
SAT Reading & Writing Practice Test 1: Information and Ideas
Passage
A volcano that erupted on Krakatoa in 1883 resulted in an ash cloud that spread across the earth, creating colorful sunsets that inspired Edvard Munch. A visual artist living in Norway, Munch was walking with friends one evening as the sun descended through the haze. After viewing the deep blue, yellow, and red in the sky, Munch noticed his companions' faces looked yellow-white. The unearthly sight ultimately became the inspiration for his widely recognized painting The Scream.
Question
Which choice best states the main idea of the text?
| A. The haze following Krakatoa's volcanic blast prevented people worldwide from viewing the sun during sunsets. | |
| B. The Scream is well known because it depicts a typical reaction to a volcanic eruption. | |
| C. Munch created a multi-colored work of art that reflected his feelings for his friends. | |
| D. Munch created his famous painting after viewing a colorful sunset and his friends' faces. |
Explanation
 |
The main idea summarizes what is discussed throughout the text. |
Paraphrase each sentence and look for a common idea developed throughout the text.
| S1 | A volcanic ash cloud created a colorful sunset that inspired Munch. |
| S2 | When out with his friends one evening, Munch watched the sunset. |
| S3 | He noted the colors in the sky and on the faces of his friends. |
| S4 | These colors inspired him to paint The Scream. |
All the sentences mention either Munch or what inspired him to paint The Scream: the colorful sunset and his friends' weirdly colored faces. Of the answer choices provided, the one that mentions these ideas says that Munch created his famous painting after viewing a colorful sunset and his friends' faces.
(Choice A) Although hazy skies are mentioned in the text, there is no discussion about whether the sun was blocked from view during the colorful sunsets.
(Choice B) Although the sunset that inspired Munch to paint The Scream happened as a result of a volcanic eruption, the text does not say that this painting is a depiction of anyone's reaction to a volcano exploding. Also, the text doesn't give a reason why the painting is well known.
(Choice C) Although the text mentions Munch seeing his friends' weirdly lit faces, it doesn't mention how he felt about his friends.
Things to remember:
The answer to a main idea question will be the one containing information found throughout the text.
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 RĂo acted in significantly fewer films than did Emilio FernĂ¡ndez Romo, who is credited with 33 acting performances. | |
| B. JoaquĂn PardavĂ©'s 28 writing credits include only film scripts he wrote between 1942 and 1955. | |
| C. Dolores del RĂo 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
A country's unemployment rate is the percentage of people in the labor force who are actively looking for work but are unable to find jobs. A group of economists compared the unemployment rates of several countries in March 2025. These economists determined that the country with the highest unemployment rate was ______.
Question
Which choice most effectively uses data from the graph to complete the sentence?
| A. Japan | |
| B. Australia | |
| C. Canada | |
| D. Spain |
Explanation
To fill in the blank, determine what the sentence is discussing and then locate the corresponding data in the graph. Then, select the answer that is supported by that data.
In this case, the sentence with the missing word is discussing the country with the highest unemployment rate. Each bar in the graph represents one country's rate, so the correct answer corresponds to the tallest bar on the graph.
The last bar on the graph—the one that is the farthest to the right—belongs to Spain. That bar represents an unemployment rate of more than 10% but less than 12%. Because it has the tallest bar on the graph, the country with the highest unemployment rate was Spain.
(Choice A) Japan had the lowest, not the highest, unemployment rate, at approximately 2–3%.
(Choice B) Australia's unemployment rate was about 4%, which was less than Spain's (over 10%).
(Choice C) Canada had an unemployment rate of roughly 6–7%. Its bar is lower than that of Spain, so Canada didn't have the highest unemployment rate.
Things to remember:
Fill in the blank based on the sentence's topic and the data addressing that topic in the graph.
SAT Reading & Writing Practice Test 2: Craft and Structure
Passage
The following text is adapted from Sarah Orne Jewett's 1886 short story "A White Heron." Sylvia is a child who has walked from her rural home to the far edge of the woods.
But the stately head of this old pine towered above them all and made a landmark for sea and shore miles and miles away. Sylvia knew it well. She had always believed that whoever climbed to the top of it could see the ocean; and the little girl had often laid her hand on the great rough trunk and looked up wistfully at those dark boughs that the wind always stirred, no matter how hot and still the air might be below. Now she thought of the tree with a new excitement, for why, if one climbed it at break of day, could not one see all the world, and easily discover from whence the white heron flew, and mark the place, and find the hidden nest?
Question
Which choice best describes the function of the underlined sentence in the text as a whole?
| A. It presents a detailed description of an area where Sylvia likes to play. | |
| B. It shows knowledge that Sylvia gained from frequent visits to the woods near her home. | |
| C. It depicts Sylvia's anticipated adventure compared to the adventures of other children. | |
| D. It indicates Sylvia's thrill about an experience that she thinks will satisfy her desire. |
Explanation
Examine details in the text about the character and consider that context to identify the function of a single sentence.
The preceding sentences explain what Sylvia "had always believed" about a treetop experience and describe her as looking up "wistfully," indicating that she longed to climb it. In the underlined sentence, she now thinks with "excitement" about the thrill of being able to "discover," "mark," and "find" unknown things about the white heron.
The underlined sentence expresses Sylvia's feelings about experiencing what she yearns for; therefore, it indicates Sylvia's thrill about an experience that she thinks will satisfy her desire.
(Choice A) The underlined sentence describes Sylvia's thoughts about climbing one towering tree with a rough trunk but doesn't describe the woods where she plays.
(Choice B) The underlined sentence focuses on a tree view that would enable Sylvia to find out about "all the world" and the heron's "hidden nest." Although the text mentions that Sylvia "knew" one tree well, it doesn't discuss knowledge that Sylvia gained from her time spent in the woods.
(Choice C) The underlined sentence expresses Sylvia's "excitement" at the adventure of climbing the tall tree to "see all the world." However, the text doesn't discuss the adventures other children might have and, therefore, doesn't compare their experiences with Sylvia's.
Things to remember:
Analyze the details in each sentence of the text to determine how a specific sentence functions.
Passage
The following text is from Washington Irving's 1820 short story "The Legend of Sleepy Hollow."
As Ichabod approached this fearful tree, he began to whistle; he thought his whistle was answered—it was but a blast sweeping sharply through the dry branches. As he approached a little nearer, he thought he saw something white, hanging in the midst of the tree—he paused and ceased whistling; but on looking more narrowly, perceived that it was a place where the tree had been scathed by lightning, and the white wood laid bare.
Question
As used in the text, what does the word "narrowly" most nearly mean?
| A. slenderly | |
| B. formally | |
| C. slightly | |
| D. carefully |
Explanation
|
Answer choices are often synonyms of the word in question, but only one will have a meaning that works in context. |
Look for clues that signal how the word in question is used in the text.
The text describes a moment where Ichabod saw a "fearful tree" with what looks like a white object hanging from it. As he gets a "little nearer," he can look more "narrowly" at the tree. During this pause to take a closer look, he realizes that the object is a white mark left by lightning.
"Carefully" can mean attentively or thoroughly. Ichabod's closer examination of the tree indicates that "narrowly" is used in this context to mean carefully.
(Choices A and C) Although synonyms of "narrowly," the words "slenderly" and "slightly" don't work in this context because they are used to refer to something being done in a way that is small or to a minimal degree. Thus, to look at something "slenderly" or "slightly" would mean to do so with limited vision; however, the text indicates that Ichabod was able to see better, not worse.
(Choice B) "Formally" doesn't work in this context because it references something done with good manners or in an official capacity. Neither is applicable to Ichabod's investigation of the white object. either good manners or something official.
Things to remember:
Clues in the text will hint at the intended meaning of the word in question.
Passage
Antonio Márez y Luna, the protagonist of Rudolfo Anaya's 1972 novel Bless Me, Ultima, is on a spiritual journey of self-discovery, a story arc that, in Anaya's work, is not ______: many of his narratives illustrate similar explorations of identity.
Question
Which choice completes the text with the most logical and precise word or phrase?
| A. monotonous | |
| B. unorthodox | |
| C. advantageous | |
| D. undeniable |
Explanation
Try each word in the blank and use the process of elimination to determine which word has a meaning that works best given the context of the text.
The text states that many of Anaya's narratives (stories) include a character exploring their identity and references one of his novels as an example. Notice that the word immediately before the blank is "not." This signals that Anaya's story arcs are the opposite of the word that completes the sentence.
|
Because the prefix "un-" means not, when "not" and "un-" are used together, they cancel each other out. (Ex. Not unordinary = ordinary) |
| (Choice A) monotonous = lacking in variety | This answer suggests that Anaya's stories are not all the same. However, the text reveals that many of Anaya's story arcs are similar, which means they could be described as lacking variety. |
| (Choice B) unorthodox = contrary to what is expected or traditional | This answer suggests that Anaya's story arc is expected. The text says that "many of his narratives illustrate similar explorations" as the story in Bless Me, Ultima; therefore, this answer is correct. |
| (Choice C) advantageous = favorable; beneficial | This answer suggests that Anaya's stories are not favorable. However, the text doesn't provide any details about whether Anaya's story arcs are beneficial. |
| (Choice D) undeniable = plainly true; certain | This answer suggests that Anaya's stories are not certain, but this isn't supported by the statement that his other works explore similar themes. |
Things to remember:
Eliminate answers not supported by the text's discussion.
SAT Reading & Writing Practice Test 3: Expression of Ideas
Passage
In 1912, during the First Balkan War, Milunka Savić chopped off her hair and dressed in men's clothing to join the Serbian army disguised as her brother, who was sick with tuberculosis. _______ Savić proved to be a skilled soldier and eventually became—after her true identity was discovered in 1913—the most decorated female in world military history.
Question
Which choice completes the text with the most logical transition?
| A. Subsequently, | |
| B. Likewise, | |
| C. Nevertheless, | |
| D. Furthermore, |
Explanation
|
Transitions help show the specific relationship between sentences. |
Examine the information before and after the blank to determine the relationship between the sentences. Then, choose the conjunctive adverb that expresses that relationship.
The first sentence provides details about how Savić joined the army as a woman. The second sentence reveals that she was awarded many medals after joining the army. The correct answer will indicate this sequence of events.
"Subsequently" refers to events that came after another. Because it refers to the events in the second sentence occurring after the events in the first sentence, subsequently, is correct.
(Choice B) "Likewise" indicates a similarity between two ideas. This answer doesn't work because the second sentence states that Savić was highly decorated as a soldier, which isn't similar to the first sentence's description of her joining the army.
(Choice C) "Nevertheless" signals that something is happening despite another thing. The second sentence reveals that Savić earned her medals because she joined the army, not in spite of joining.
(Choice D) "Furthermore" shows an idea that is related and an addition to the idea that precedes it. The idea presented in the second sentence indicates what happened after Savić joined the army; it is not an additional detail describing how she became a soldier.
Things to remember:
The correct answer will reflect the relationship between the ideas in the two sentences.
Passage
Some celestial bodies emit intense bursts of energy that are extremely powerful. Magnetars (neutron stars with strong magnetic fields), ______ release more energy in a single second than the Sun emits in 100,000 years.
Question
Which choice completes the text with the most logical transition?
| A. on the other hand, | |
| B. in fact, | |
| C. in turn, | |
| D. therefore, |
Explanation
Compare the information in the two sentences to determine their relationship. Then, select the transition with a meaning that shows that relationship.
"In fact" emphasizes the truth of a statement, especially when the information is hard to believe. The fact that magnetars "release more energy in a single second than the Sun emits in 100,000 years" is hard to believe and reinforces the previous idea that "some celestial bodies emit intense bursts of energy." Therefore, in fact, is the transition that best shows the relationship between the two sentences.
(Choice A) "On the other hand" signals a contrast with the previous idea. (Ex. Ted talks a lot. Myra, on the other hand, rarely says anything.) Because magnetars are celestial bodies like those described in the previous sentence, no contrast is intended.
(Choice C) "In turn" indicates something different happening in an order or sequence. (Ex. The speaker argued her point during the debate. The opposition, in turn, offered a different view.) However, the text doesn't describe the age of magnetars compared with that of "some celestial bodies," so no sequence of events is implied.
(Choice D) "Therefore" introduces a consequence of what was previously stated. (Ex. The city invested in road improvements. Potholes, therefore, are now much fewer in number.) Magnetars are not a result of energy bursts, so no cause-and-effect relationship is set up in the text.
Things to remember:
The best transition is the one that accurately shows the relationship between the preceding idea and the one that follows.
Passage
While researching a topic, a student has taken the following notes:
- In 2016, historian Mathieu Ossendrijver deciphered clay tablets from the ruins of an ancient Babylonian city in present-day Iraq.
- The tablets were dated to approximately 2,300 years ago.
- After examination, he determined that the tablets' cuneiform markings represented geometric calculations predicting the motion of the planet Jupiter.
- These figures indicate that advanced mathematical astronomy, similar to calculus computations, was developed much earlier than previously believed.
Question
The student wants to present Ossendrijver's discovery and the resulting conclusion. Which choice most effectively uses relevant information from the notes to accomplish this goal?
| A. In a 2016 study of ancient mathematical astronomy, an in-depth examination was conducted on tablets found in present-day Iraq. | |
| B. A 2016 examination of clay tablets from an ancient city in present-day Iraq suggests that Babylonians had developed advanced mathematical astronomy about 2,300 years ago. | |
| C. In 2016, Ossendrijver deciphered cuneiform markings on ancient Babylonian tablets that were created over 2,000 years ago. | |
| D. Clay tablets estimated to be 2,300 years old were translated in 2016 after being found in the ruins of an ancient Babylonian city. |
Explanation
Identify the specifics that the question is asking for. Then, select the answer that fulfills those criteria with similar information
|
On many notes questions, only one answer will fully address the requirements of the question, so you may not need to check the notes to identify the correct answer. |
This question contains two criteria: Ossendrijver's discovery and conclusion.
The first three notes indicate that in 2016, Ossendrijver discovered that 2,300-year-old Babylonian tablets contained cuneiform markings predicting the motion of Jupiter. The last bulleted note presents the conclusion: "advanced mathematical astronomy…was developed much earlier than previously believed."
The answer that provides similar information states that a 2016 examination of clay tablets from an ancient city in present-day Iraq suggests that Babylonians had developed advanced mathematical astronomy about 2,300 years ago.
(Choices A, C, and D) All of these answers provide information about Ossendrijver's discovery. However, none of them mention the conclusion that these tablets represent evidence that ancient peoples had developed "mathematical astronomy" long before scholars had thought.
Things to remember:
ALL the question's criteria must be met in order for an answer to be correct.
SAT Reading & Writing Practice Test 4: Standard English Conventions
Passage
In 1948, before DNA was understood, African American physical science instructor Marie Maynard Daly began to examine how proteins are constructed in the body. Daly's later research would include more than just this preliminary ______ as a ground-breaking biochemist, Daly would ultimately discover the connection between elevated cholesterol levels and heart disease.
Question
Which choice completes the text so that it conforms to the conventions of Standard English?
| A. examination, however: | |
| B. examination. However: | |
| C. examination however | |
| D. examination, however, |
Explanation
|
A colon can join two independent clauses. |
Locate the independent clause(s). If there is more than one, make sure the correct punctuation mark is used between them. If a transition is included in each answer choice, determine if it belongs at the end of the first clause or at the beginning of the next, and then apply the appropriate punctuation.
Transitions are set off from the rest of the clause with a comma, while two independent clauses must be separated by a colon, semicolon, or period. In this context, the transition "however" fits best at the end of the first clause, so a comma is needed before this transition word.
Because it correctly sets off the transition word with a comma and separates the two independent clauses with a colon, examination, however: is the correct answer.
(Choice B) This answer places the transition at the beginning of a new sentence, requiring a comma, not a colon, after "However" to be grammatically correct.
(Choice C) Because it doesn't include any punctuation between two independent clauses, this answer would result in a run-on sentence.
(Choice D) While this answer correctly separates the transition from the first clause with a comma, it places another comma between two independent clauses, resulting in a comma splice.
Things to remember:
A colon can be used between two independent clauses. A transition is set off from the rest of the clause with a comma.
Passage
In 1968, 3M scientist Spencer Silver was trying to develop a strong adhesive when he accidentally created a weak adhesive that was reusable and left no residue when removed. Many doubted its usefulness until his coworker, Art Fry, found Silver's adhesive perfect for a removable bookmark. Later, Fry ______ the company to market these sticky notes under a name that would become familiar worldwide: Post-it® Notes.
Question
Which choice completes the text so that it conforms to the conventions of Standard English?
| A. persuaded | |
| B. persuades | |
| C. had persuaded | |
| D. was persuading |
Explanation
Rule: Unless a shift in time is clearly indicated, verb tenses in a passage should agree.
Examine the verb tense used throughout the text and choose the answer with a verb in the same tense.
The text includes past tense verbs such as "doubted" and "found." Because the text describes past actions, the correct answer should also use a past tense verb: persuaded.
(Choices B, C, and D) These answers don't agree with the other past tense verbs in the text.
- Choice B: "Persuades" is a present tense verb.
- Choice C: "Had persuaded" refers to a past action that happened earlier than another stated action. (Ex. Saket was upset; he had crashed his car.) However, "had persuaded" doesn't fit here because Fry persuaded the company AFTER people doubted—not before.
- Choice D: "Was persuading" indicates that this action continued when another event took place. However, the text doesn't describe any action that occurred when Fry persuaded the company.
Things to remember:
Identify the tense of the verbs in the text and choose the answer that logically agrees with the nearest verbs.
Passage
While some video game players think that violent video games provide a healthy way to socialize and escape from life's ______ people critical of violence in entertainment point to research indicating that playing games featuring graphic violence can lower a player's self-esteem and lessen empathy for others. (The term "violent video game" refers to a game that includes graphic depictions of violent action.)
Question
Which choice completes the text so that it conforms to the conventions of Standard English?
| A. stress and | |
| B. stress | |
| C. stress, | |
| D. stress, and |
Explanation
Rule : An introductory dependent clause is separated from the main sentence by a comma.
Look for subjects and verbs to identify clauses in a sentence. When a clause at the beginning of a sentence doesn't express a complete thought, choose the answer with a comma after it.
The introductory clause "While…stress" doesn't express a complete thought, which means a comma should follow "stress" to separate the introductory dependent clause from the independent clause that comes after it.
A FANBOYS conjunction joins two or more independent clauses, not two different types of clauses. Only one answer includes a comma without a FANBOYS conjunction after the dependent clause; therefore, stress, is correct.
(Choices A and D) These answers add the FANBOYS conjunction "and," which can join two dependent clauses. However, Sentence 1 has an introductory dependent clause followed by an independent clause, not two dependent clauses.
(Choice B) The subordinating conjunction "while" makes the first clause dependent. However, an introductory dependent clause should be separated from the independent clause by a comma, and this answer lacks the required comma.
Things to remember:
Use a comma to separate an introductory dependent clause and the independent clause that follows it.
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