SAT Secret 27: The SAT Math Test: Heart of Algebra

In this series of articles, we take a closer look at the SAT Math Test.

Math questions on the test fall into different categories called “domains.” One of these domains is Heart of Algebra.

You will not need to know domain names for the test; domains are a way for the College Board to break down your math score into helpful subscores on your score report, and they also ensure that each new SAT is balanced in the same way every time. The SAT focuses strongly on algebra — especially on the areas of the subject that are most essential for success in college and careers. Questions in the Heart of Algebra domain will assess your ability to analyze, fluently solve, and create linear equations and inequalities, as well as systems of equations using multiple techniques. Heart of Algebra questions may be straightforward fluency exercises or may pose bigger challenges, such as asking you to interpret the relationship between linear equations and their graphs. Just a few examples of skills you will be asked to use:

  • Solve linear equations in one variable
  • Solve linear equations in two variables
  • Create and use a system of two variables and two linear equations
  • Create and use linear equalities in one or two variables
  • Identifying equations of lines on a graph [Explain]The answer is C. In order to get this question right, you’ll need to recall that the slopes of perpendicular lines are negative reciprocals. The slope of the line shown is -2 (it goes down 2 units for every 1 unit it moves to the right). Therefore, the correct choice must have a slope of +1/2.
  • Interpreting two variables in a linear equation [Explain]The answer is D. One way to get there is to see what happens when you plug in values for T. When T is 1, what happens? Well, 1 day after the drive begins, T = 1, and we have 3450 + 65(1) voters. The next day when T = 2, we have 3450 + 65(2) voters. When T = 3, we have 3450 +65(3) voters, and so forth. So: as each day passes, the number of registered voters increases by 65.
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