The dozens of math questions on the SAT can be broken down into four types of math questions: **Heart of Algebra**, **Problem Solving and Data Analysis**, **Passport to Advanced Math, and Additional Topics in Math**.* *

Understanding the content that falls under these four question categories will help you study for the SAT with greater focus. And with more focused practice, you’re more likely to see an increase in your SAT score.

ACT, SAT Math Practice Questions with Explanations

## Four Types of Questions on the SAT Math Section

### Heart of Algebra

Heart of Algebra questions cover linear algebra and manipulation of equations.

For the **Heart of Algebra **questions (roughly 33% of total questions) you may need to:

- Find distance on a number line, between points on a coordinate plane, or in terms of absolute value
- Use word to symbol translation and linear equations and inequalities to solve real-world problems in context
- Manipulate and evaluate variable expressions and equations (including absolute value)
- Solve linear and quadratic inequalities and match with appropriate graphs
- Find and interpret slope and intercepts from equations, word problems and graphs (also using properties of parallel and perpendicular lines)
- Match, interpret, and analyze information from graphs in the coordinate plane
- Solve and interpret systems of linear equations and linear inequalities both in context of real-world problems and without context

### Problem Solving and Data Analysis

These questions cover your understanding of numbers, data, and rational problem solving.

For **Problem Solving and Data Analysis **concepts (roughly 29% of total questions) you will need to:

- Solve multi-step problems using ratios, proportions, rate, percentages, and/or conversion of units of measure
- Refer to data, charts, frequency tables, and graphs to interpret information
- Demonstrate knowledge of measures of central tendency and distribution (mean, median, mode, range), how to compute each, and how to compute for a missing data point given a measure of central tendency
- Compute probabilities of an event, its complement, and combinations (conditional and joint probability) in context
- Demonstrate knowledge of the fundamental counting principle and Venn Diagrams
- Understand the fundamentals of statistics (random sampling, distribution, standard deviation, confidence interval, and interpretation of results)
- Interpret key features and relationships between variables in graphs
- Understand differences between linear, quadratic, and exponential relationships in context (frequently as simple and compound interest or growth/decay)
- Extend patterns, both arithmetic and geometric, increasing and decreasing by common factors or ratios

### Passport to Advanced Math

These questions test your ability to solve complex equations.

**Passport to Advanced Math **concepts (roughly 28% of total questions) may test your ability to:

- Manipulate exponents in powers of 10, and scientific notation, and apply properties of rational exponents
- Demonstrate knowledge of the real number system – rational, irrational, and complex numbers
- Add, subtract, multiply, and divide polynomials
- Create and interpret quadratic or exponential functions in context
- Analyze, solve, and graph quadratic or other nonlinear equations and systems
- Manipulate expressions and equations with exponents, integer and rational powers, radicals, and fractions with variables in the denominator
- Interpret and evaluate functions and composite functions
- Interpret functions and their graphs
- Identify intercepts and maximum and minimum values
- Find domain and range and asymptotes
- Understand increasing and decreasing, end behavior, and transformations/translations

- Write functions that are directly or inversely proportional or exponential

### Additional Topics in Math

**Additional Topics in Math **questions (roughly 10% of total questions) frequently **combine** multiple geometry concepts into one question in context. These concepts include your ability to:

- Calculate lengths and midpoints of line segments (overlapping segments and those in the coordinate plane)
- Compute perimeter and area of polygons and circumference and area of circles
- Use properties of parallel lines, other angle properties, and similar figures and ratios to find missing angle measures or side lengths/distances
- Use properties of isosceles and right triangles to compute unknown side lengths and angle measures (symmetry, Pythagorean theorem, etc…)
- Demonstrate knowledge of right triangles (30o, 60o, 90o; 45o, 45o, 90o) and apply trigonometric ratios (sine, cosine, tangent) to solve for missing values
- Manipulate between area, volume, and surface area
- Understand the trigonometry of the unit circle and basic trig identities to solve problems involving radians and angle measures
- Understand circle relationships such as central and inscribed angles, arc length and sector area, tangents and chords
- Create the equation of a circle in the coordinate plane by finding the center and radius
- Manipulate (add, subtract, multiply, divide, simplify) complex numbers (i=-1)

## What About Grid-Ins?

Although most of the SAT math test is multiple choice, 22% of the test is student produced response, otherwise known as grid-ins. These questions require students to produce their own answer without the aid of answer choices. Grid-in questions can cover any type of math question.

## SAT Math Section Study Resources

Now that you’ve learned about the types of SAT math questions you’ll see on the test, it’s time to get practicing. Olive Book’s SAT course contains hundreds of math practice questions with explanations that more than cover each area of math. The course is literally all you need to study successfully for the SAT. Enroll at www.olive-book.com.

### Further Reading:

ACT, SAT Math Practice Questions with Explanations

SAT Math Strategies

The Best Calculator To Use on the SAT

SAT Math Formulas To Know for Test Day