Math Section
Overview
(Total: ~44 Questions, 70 minutes)
The SAT Math section is split into two parts:
1. Math without a calculator (20 questions, 25 minutes)
2. Math with a calculator (24 questions, 45 minutes)
The Math section tests a variety of math topics, ranging from algebra to geometry and data
analysis. You’ll need to demonstrate your ability to apply mathematical concepts to solve
real-world problems. The questions in this section are designed to test both your basic
math knowledge and your ability to think critically about problems.
1. Heart of Algebra (Total: ~15 Questions)
This part of the Math section assesses your ability to solve linear equations, understand
relationships between variables, and manipulate expressions.
Key Topics:
• Linear Equations and Inequalities:
o Solving Single-variable Equations: You’ll be asked to solve equations like
3x+5=113x + 5 = 113x+5=11, and understand concepts such as balance,
combining like terms, and isolating variables.
o Solving Multi-variable Linear Equations: You’ll work with systems of
equations, such as:
▪ Solving systems using substitution or elimination methods.
▪ Understanding solutions that are valid for both equations.
o Linear Inequalities:
▪ Solving inequalities like 2x−5>72x - 5 > 72x−5>7.
▪ Graphing linear inequalities on a number line.
▪ Understanding compound inequalities.
• Functions:
o Understanding Functions: Interpreting and analyzing functions, both
algebraically and graphically. You may be given a function f(x)=2x+3f(x) = 2x +
3f(x)=2x+3 and asked to evaluate it or determine its domain/range.
o Function Notation: Knowing how to use and interpret function notation (e.g.,
f(x)f(x)f(x), g(x)g(x)g(x)) in equations and problem-solving contexts.
2. Problem Solving and Data Analysis (Total:
~17 Questions)
This section tests your ability to apply math to real-world situations, including working with
ratios, percentages, and analyzing data.
Key Topics:
• Ratios, Proportions, and Percentages:
o Solving Ratio Problems: Questions involving proportions, like
ab=cd\frac{a}{b} = \frac{c}{d}ba=dc.
o Percentage Problems: Calculating percentages, including percentage
increase/decrease and word problems. For example, "What is 25% of 200?"
or "What is the percentage increase from 50 to 60?"
o Proportional Relationships: Solving problems that involve proportionality
(e.g., scaling quantities).
• Data Interpretation:
o Reading Tables, Graphs, and Charts: You’ll need to interpret data from
various visual sources, such as bar graphs, scatterplots, and histograms.
o Understanding Measures of Central Tendency: Mean, median, mode, and
range. For example, "What is the median of the following data set: 4, 5, 7, 8,
10?"
o Understanding Data Spread: Calculating and interpreting standard
deviation and interquartile range.
• Probability:
o Basic Probability: Problems involving simple probability, such as drawing
cards from a deck or flipping coins.
o Compound Probability: Probability of multiple events happening (e.g., both
heads in two coin flips).
o Conditional Probability: Understanding how the probability of an event
changes under certain conditions.
3. Passport to Advanced Math (Total: ~12
Questions)
This section covers higher-level algebra and introduces some basic concepts from
advanced mathematics, such as quadratic equations and polynomial expressions.
Key Topics:
• Quadratic Equations:
o Solving Quadratics: Solving equations like ax2+bx+c=0ax^2 + bx + c =
0ax2+bx+c=0 by factoring, completing the square, or using the quadratic
formula. You might also be asked to find the solutions to a quadratic function
or determine its vertex.
o Word Problems: Using quadratics to solve problems, such as projectile
motion or area problems.
• Polynomials:
o Operations on Polynomials: Adding, subtracting, multiplying polynomials.
For example, multiplying (x+3)(x−2)(x + 3)(x - 2)(x+3)(x−2).
o Factoring: Factoring polynomials such as x2+5x+6x^2 + 5x + 6x2+5x+6 into
(x+2)(x+3)(x + 2)(x + 3)(x+2)(x+3).
• Rational Expressions:
o Simplifying Rational Expressions: Simplifying fractions that involve
polynomials, such as x2+2xx+1\frac{x^2 + 2x}{x + 1}x+1x2+2x.
o Solving Rational Equations: Solving equations that involve rational
expressions, such as 3x+1=5\frac{3}{x+1} = 5x+13=5.
o Restrictions on Rational Expressions: Identifying values of variables that
make the denominator zero and are thus undefined.
• Nonlinear Functions:
o Exponential Functions: Recognizing and working with exponential growth
and decay functions. For example, y=2xy = 2^xy=2x.
o Other Nonlinear Functions: Understanding the basic properties and
graphing of non-linear functions, including simple root and reciprocal
functions.
4. Additional Topics in Math (Total: ~4
Questions)
This section includes geometry and basic trigonometry, and it tests your ability to apply
geometric principles to solve real-world problems.
Key Topics:
• Geometry:
o Angles: Working with angles in polygons, finding missing angles, and using
properties of parallel lines cut by a transversal.
o Triangles: Understanding the Pythagorean theorem, properties of right
triangles, and solving for missing sides or angles.
o Circles: Calculating the area, circumference, and sector area of circles.
Understanding the relationships between radius, diameter, and
circumference.
o Coordinate Geometry: Finding the distance between two points on the
coordinate plane using the distance formula and understanding the slope of
a line.
• Trigonometry:
o Basic Trigonometric ratios and identities.
• Complex Numbers:
o Basic Operations: Adding, subtracting, multiplying, and dividing complex
numbers. For example, (3+2i)+(1−4i)(3 + 2i) + (1 - 4i)(3+2i)+(1−4i).
o Graphing Complex Numbers: Understanding how to represent complex
numbers on the complex plane.
Test-Taking Strategy for Math:
• Math without a calculator:
o Focus on mastering basic math operations and algebraic manipulation.
o Practice mental math and problem-solving without relying on a calculator.
o Be familiar with basic formulas and geometric principles.
• Math with a calculator:
o Use the calculator efficiently: avoid unnecessary calculations, and make
sure you're using it for the more complex calculations or for checking your
work.
o Always double-check your answers when working with fractions or decimals.
• Time Management:
o Spend time on easier questions first, and save more challenging questions
for later.
o If you're unsure about a question, try to eliminate obviously incorrect
answers to narrow your choices.
Key Resources for Studying:
• Practice Problems: Regularly work through practice problems in algebra, geometry,
and trigonometry.
• Formulas: Familiarize yourself with important formulas, such as:
o Pythagorean theorem
o Area and volume formulas
o Quadratic formula
o Trigonometric identities
• Graphing: Make sure you're comfortable with graphing functions and interpreting
graphs.
