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Math Strategy Guide

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Comprehensive guide · 10 sections · Domains, calculator tips, traps

Overview

The Math section contains 44 questions split across two 35-minute modules. Questions span four content domains: Algebra, Advanced Math, Problem Solving and Data Analysis, and Geometry and Trigonometry. Roughly 75% of questions are multiple-choice; the remaining ~25% are student-produced responses (SPR) where you type in the answer.

Total Questions

35 min

Time per Module

~95 sec

Avg. Time per Q

You get roughly 95 seconds per question — significantly more time per question than Reading & Writing (71 seconds). Use that extra time to set up problems carefully and double-check your work.

Module 1

22 questions · mixed difficulty · establishes baseline

Module 2

22 questions · harder or easier based on Module 1 performance

How adaptive testing works in Math

Module 1 contains questions of mixed difficulty. Your performance on Module 1 determines whether you receive the harder or easier version of Module 2. To maximize your score, you need to land in the hard Module 2 — that's where the highest-scoring questions live. Focus on accuracy in Module 1.

Content Domains

College Board groups math questions into four domains. Understanding which domain a question belongs to helps you reach for the right tools immediately.

Domain	Approx. share	Key topics
Algebra	35%	Linear equations, inequalities, systems, functions
Advanced Math	35%	Quadratics, polynomials, rational, exponential, radical expressions
Problem Solving & Data	15%	Ratios, rates, percentages, statistics, probability, data interpretation
Geometry & Trig	15%	Area, volume, Pythagorean theorem, circles, trig ratios, radians

Algebra and Advanced Math together make up about 70% of Math questions. Master linear equations, systems, quadratics, and function notation first — the return on study time is highest there.

Calculator Strategy

A built-in graphing calculator (Desmos) is available for every question in the Math section — there is no calculator-free portion. This is a significant advantage if you know how to use it effectively.

When to use the calculator

Graphing equations to find intersections, roots, or vertex coordinates.
Checking algebraic answers by substituting back in.
Evaluating complex arithmetic (multi-step percentages, square roots, exponents).
Confirming the shape of a parabola (opens up/down, vertex location).

When NOT to use the calculator

Simple arithmetic you can do faster mentally.
Conceptual questions about properties of functions (just think it through).
When the algebra is quicker — over-relying on Desmos can cost time.

High-value Desmos tricks

Type a quadratic in standard or vertex form to instantly see the vertex and x-intercepts.
Graph two equations simultaneously to find their intersection point — no algebra needed.
Use the slider feature to explore how changing a parameter shifts a graph.
Type an inequality to visualize the solution region.

Practice using Desmos before test day. It takes 20–30 seconds to switch to the calculator, type an equation, and read the result. On questions where graphing saves you, that investment pays off. On questions where arithmetic is faster, skip it.

Question Types

Multiple Choice (4 options)

About 75% of Math questions. Four answer choices — exactly one is correct. Process of elimination is powerful here: if you can rule out two choices, your odds are 50/50 even on a guess.

Student-Produced Response (SPR)

About 25% of Math questions. You type in the answer — no choices provided. Answers can be integers, decimals, or fractions. The interface accepts fractions (3/4) and decimals (0.75) equivalently. Mixed numbers like 1½ must be entered as improper fractions (3/2) or decimals (1.5).

Context questions

Many questions embed the math in a real-world context: rates, budgets, science experiments, tables, and graphs. Always re-read the question after solving to confirm you answered what was asked — not just that you did the math correctly.

On SPR questions, there is no partial credit and no process of elimination. Double-check your setup (did you answer the right variable?) and your arithmetic before submitting.

Algebra on the SAT

Algebra makes up about 35% of Math questions and is the highest-leverage area to master. The test favors linear equations, systems, and function interpretation.

Linear equations — what the test actually tests

Finding slope and y-intercept from equations in various forms.
Writing the equation of a line given a point and slope, or two points.
Interpreting slope and y-intercept in a real-world context (rate of change, starting value).
Solving one-variable equations and inequalities.

Systems of equations — fastest methods

If one equation already isolates a variable, use substitution. If both equations are in standard form (Ax + By = C), use elimination (add or subtract equations to cancel a variable). For a question that only asks whether a system has no solution or infinitely many, check slopes and intercepts — don't solve.

Functions — the most-missed topic

f(x) = 3x + 2: f(4) means substitute x = 4.
f(g(x)): evaluate the inner function first, use its output as input to the outer.
f(x + k): shifts the graph horizontally by k units (left if k positive).
f(x) + k: shifts the graph vertically by k units.

The test frequently asks you to interpret slope in a model — for example, "a gym charges $30/month plus a one-time $50 fee." The slope (30) is the monthly rate; the y-intercept (50) is the starting value. Always connect the numbers to what they represent in context.

Advanced Math

Advanced Math also makes up about 35% of questions. This domain covers everything beyond linear — quadratics, polynomials, exponential growth/decay, and rational expressions.

Quadratics — three essential skills

Factoring to find roots: if y = (x − 3)(x + 2), roots are x = 3 and x = −2.
Identifying vertex from vertex form: y = a(x − h)² + k → vertex at (h, k).
Using the discriminant to determine the number of solutions: b² − 4ac > 0, = 0, or < 0.

Exponential functions

The general form is y = a · bˣ. If b > 1, it's exponential growth. If 0 < b < 1, it's exponential decay. The test frequently asks you to write or interpret these models in context (population, investment, half-life). Common form: y = a(1 + r)ᵗ for growth or a(1 − r)ᵗ for decay.

Rational and radical expressions

When simplifying rational expressions, factor both numerator and denominator and cancel common factors. For equations with radicals, isolate the radical and square both sides — always check for extraneous solutions by substituting back into the original equation.

The test often presents quadratics in non-standard form. Before using any quadratic technique, set the equation equal to zero. You cannot factor y = x² + 5x + 6 until it becomes 0 = x² + 5x + 6.

Problem Solving & Data Analysis

This domain covers real-world math: ratios, rates, proportions, percentages, statistics, probability, and data interpretation. Questions almost always involve a table, graph, or real-world scenario.

Ratios and proportions

Set up equivalent fractions with consistent units. Cross-multiply to solve. When a question involves a "part-to-whole" relationship, make sure your denominators represent the correct total.

Percent questions — the two types

Percent of a number: Multiply. 35% of 80 = 0.35 × 80 = 28.
Percent change: (New − Old) / Old × 100. Always divide by the original, not the new.

Reading graphs and tables

Before calculating anything, read the title, axis labels, and units. Misreading units (thousands vs. millions, hours vs. minutes) is the most common error on data questions. Many of these questions require no calculation at all — just accurate reading.

Statistics — what you must know

Mean: sum ÷ count. Equivalently, sum = mean × count (use this to find a missing value).
Median: middle value when ordered. Not affected by extreme outliers.
Range and IQR: measures of spread. A larger standard deviation = more spread out data.
Sampling: a random sample is more likely to represent the population than a convenience sample.

Two-way table questions are extremely common and very solvable if you read them carefully. Always identify whether the question asks for a joint probability (cell / grand total) or a conditional probability (cell / row total or column total).

Geometry & Trigonometry

Geometry and Trig makes up about 15% of Math questions. The test provides a reference sheet with key formulas, but knowing them cold saves you from flipping back and losing time.

What the reference sheet gives you

The test provides: area of circle, circumference, area of rectangle, area of triangle, Pythagorean theorem, special right triangles (30-60-90 and 45-45-90), and volume formulas for boxes, cylinders, cones, spheres, and pyramids.

What you must memorize (not on the sheet)

Arc length: (θ/360) × 2πr
Sector area: (θ/360) × πr²
Sum of interior angles of a polygon: (n − 2) × 180°
SOH-CAH-TOA and the co-function identities: sin θ = cos(90° − θ)
The Pythagorean identity: sin²θ + cos²θ = 1

Triangles — the most-tested shape

Angles in any triangle sum to 180°.
Exterior angle = sum of the two non-adjacent interior angles.
Recognize 3-4-5, 5-12-13, and 8-15-17 Pythagorean triples (and their multiples).
In a 30-60-90 triangle, sides are in ratio x : x√3 : 2x.
In a 45-45-90 triangle, sides are in ratio x : x : x√2.

Trigonometry appears in roughly 5–10% of Math questions. The most common question type asks you to find a missing side using SOH-CAH-TOA or to apply sin θ = cos(90° − θ). Know these two cold and trig becomes one of the easiest topics on the section.

Time Management

Each module gives you 35 minutes for 22 questions — about 95 seconds per question. This is more generous than Reading & Writing. Use the extra time for multi-step problems, not for rushing.

Common Traps to Avoid

Answering the wrong thing:The question asks for "the value of 2x + 3" but you solve for x and write that. Re-read the question after you find your variable.

Confusing diameter and radius: If a problem gives you diameter, the radius is half that. Every circle formula uses radius — check before plugging in.

Sign errors when distributing: −(3x − 2) = −3x + 2, not −3x − 2. Distributing a negative flips every term inside the parentheses.

Forgetting to flip the inequality: Multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol.

Extraneous solutions:After solving radical or rational equations, always substitute your answer back into the original to confirm it doesn't make a denominator zero or produce a negative under a square root.

Percent vs. percentage points:"Increased by 5%" vs. "increased by 5 percentage points" are different. If a rate goes from 20% to 25%, that is a 5 percentage-point increase but a 25% relative increase.

Using the wrong total in probability: Conditional probability divides by the relevant row or column total — not the grand total. Always identify the condition first.