What Types of Questions Are in the Heart of Algebra?

Heart of algebra questions on SAT

Heart of Algebra questions occur in the calculator and no-calculator sections of the SAT® Math test. These questions assess your skills with linear equations, inequalities, and functions.

Linear Equations

Heart of Algebra questions will ask you to assess and produce linear equations. You will also be required to solve for variables within linear equations.

Here is an example of a question that focuses on linear equations:

  • Sarah is buying some chairs for $97.50. A tax of 8% is applied to the purchase, and there is an additional charge of $18.00 for shipping costs. Which of the following equations represents Sarah’s total charge for x chairs?

Here is an example of a question that focuses on systems of linear equations:

  • The amusement park charges $50.00 for adults and $30.00 for children under the age of 12. Between its opening at 8:00 a.m. and 11:00 a.m., the park sold 643 tickets and made $21,450. Solving which system of equations produces the number of children, x, and adults, y, that entered the park.

Linear Inequalities

Heart of Algebra questions will ask you to interpret and construct linear inequalities. You will also find questions that ask you to solve for variables within systems of linear inequalities.

Here is an example of a question that focuses on your skills with linear inequalities:

  • If − 7/3 − 2r + 7 < − 5/2, what is a possible value of 4r − 14?

Linear Functions

Heart of Algebra questions will ask you to evaluate and produce linear functions.

Here is an example of a question that focuses on your skills with linear functions:

  • An airplane burns an average of 750 gallons of fuel per hour, flying at an average speed of 580 miles per hour. The plane has 5,000 gallons of fuel at the start of the trip. If the plane flies at an average of 580 miles per hour, which of the following functions ƒ represents the number of gallons in the gas tank after a 4-hour flight?

Other Concepts

Heart of Algebra questions test other skills, including understanding relationships between graphs and expressions, graphing equations, solving how many ( x,y ) solutions a system of equations have, finding linear equations representing a given graphed line, and calculating slope.

Here is an example from a College Board® practice exam:

  • Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?

As you prepare for the SAT exam’s Math test, practice the skills tested in Heart of Algebra questions. Consider the skills we have outlined here, and get some practice through UWorld’s SAT Prep Course.

The prep course will include performance tracking tools to help navigate your strengths and weaknesses. It will also provide you with detailed question explanations to guide your studies and thousands of practice problems to hone your skills. Try it out!

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