When you’re beginning to prepare for the SAT, the first thing you need to know is what’s on the SAT math. Most of the SAT math topics themselves are quite basic in terms of mathematical difficulty, the questions can be quite tricky.
Firstly, you get some formulae given to you – this is on the front of every test paper, and it’s the same for the calculator and non-calculator section:
What’s on the SAT Math?
The SAT divides its math up into 3 topics with slightly strange sounding names: Heart of Algebra, Problem Solving & Data Analysis and Passport to Advanced Mathematics. Each topic represents about a third of the test questions, with a few additional questions about areas, volumes of shapes and trigonometry. If you want to, you can also view the College Board’s topic list.
Heart of Algebra is basically all about linear equations. You need to be completely comfortable with linear equations, as there’s almost every possible linear equation problem on this test!
You should be able to:
- Solve linear equations and inequalities with one variable
- Construct a linear equation with two variables from a word problem
- Interpret graphs of linear equations and inequalities
- Solve systems of two linear equations graphically and algebraically
- Use absolute value equations and their graphs
Problem Solving & Data Analysis includes statistical questions, percentage and ratio questions and lots of word problems. For the statistics part, you are required to make some basic calculations, but you need to know about some more advanced concepts to be fully familiar with what’s on the SAT math. You’ll find it helpful to look at some practice questions for these (of course you should anyway), so you know the style of the questions.
You should be able to:
- Set up and solve equations containing ratios, rates and proportions
- Solve percentage problems, including simple and compound interest
- Calculate mean, median, mode and range
- Interpret or explain standard deviation, margins or error, confidence intervals
- Understand the effect that outliers have on the data, reason about cause and effect relationships
Passport to Advanced Math Is algebra beyond linear equations, such as quadratic and other polynomial equations, rational equations and exponential functions. You should know the properties of all these kinds of functions to tackle what’s on the SAT math.
For polynomial and rational equations:
- Know how to find the roots/intercepts
- Use the factor and remainder theorems
- State the domain and range
- State and interpret max and min values and where the functions are increasing and decreasing
- Understand asymptotic behavior in rational graphs
- Transformations (e.g. f(x)+k etc)
- Solve problems using polynomial and rational functions (if you can do this using linear systems and you know the topics above, you can do this using rational equations.
For exponential functions:
- Know basic exponent rules
- Know the properties of exponential functions and their graphs
- Use exponential functions to solve growth and decay problems
Additional Topics. There are only 3 or 4 questions in the entire test on these topics, so if you’re already sure of all the basics, review these too. These questions tend to be less wordy and more like questions you might be asked in a school test on these topics, so they might feel a little more straightforward.
- Complex and imaginary numbers
- Line and angle rules (Z and F angles, complementary and supplementary etc)
- Circles: main circle theorems, calculating arc length or area of sector
- Triangles: inequality theorem, similar and congruent triangles, special triangles, properties of right, equilateral and isosceles triangles.
- Trigonometry: SOHCAHTOA, sine and cosine law, use of the unit circle (CAST rule), radians.