Math Strategies

Math Strategies for SAT & ACT

Math is not about memorizing procedures — it is about knowing which approach to use and when. These strategies will help you solve problems faster, avoid common traps, and maximize your math score.

Problem-Solving Approaches

Plug In Numbers

When a problem uses variables, substitute simple numbers (like 2, 3, or 10) to make it concrete. This is especially powerful for "which of the following" questions and percent problems.

When to use: Variables in the question and answer choices

Example: If a problem says "x percent of y," plug in x=10 and y=50 to work with real numbers.

Backsolve from Answers

Start with the middle answer choice and plug it back into the problem. If it is too high, try a lower choice; if too low, try higher. This eliminates algebra entirely.

When to use: Specific numerical answer choices that are easy to test

Example: If asked "what value of x satisfies...?" start with answer choice C and test it.

Draw a Picture

For geometry, rate, and word problems, sketch a diagram. Label all given information. Visual representation helps you see relationships you might miss in text.

When to use: Geometry problems, word problems with spatial relationships, or any problem you cannot visualize

Example: For a distance/rate problem, draw a timeline showing departure and arrival.

Estimate and Eliminate

Before solving precisely, estimate the answer. Eliminate choices that are clearly too large or too small. Even a rough estimate can eliminate 2-3 wrong answers.

When to use: Time pressure or complex calculations

Example: If the area of a circle with radius 5 is asked, you know it is about 75-80 (since pi is about 3.14).

Work Backwards

Start from what you need to find and work backwards to what you are given. This is especially useful for multi-step problems where the path forward is unclear.

When to use: Multi-step problems or when you are stuck

Example: If asked to find the original price after a 20% discount, start with the discounted price and reverse the calculation.

Time Management for Math

SAT Math: You have about 1 minute 35 seconds per question. Easy questions come first — do not spend 3 minutes on question 5.
ACT Math: You have 60 questions in 60 minutes — exactly one minute per question. Keep a strict pace.
Skip strategically: If a problem will take more than 2 minutes, mark it and move on. Come back if time allows.
Use your calculator wisely: It saves time on arithmetic but slows you down if you rely on it for every step.
Practice pacing with a watch: Check your time every 10 questions to make sure you are on track.
Easy points first: Secure all the questions you know how to solve before wrestling with hard ones.

Common Question Patterns

Knowing what to expect is half the battle. Here are the most common question types broken down by category.

Algebra (35-40% of SAT Math)

-Linear equations and inequalities
-Systems of two equations
-Linear functions and their graphs
-Absolute value equations
-Word problems translating to equations

Advanced Math (25-30% of SAT Math)

-Quadratic equations and the quadratic formula
-Polynomial operations and factoring
-Exponential functions and growth/decay
-Radical and rational equations
-Function notation and transformations

Problem Solving & Data (25-30% of SAT Math)

-Ratios, proportions, and percentages
-Unit conversion and rates
-Scatterplots and lines of best fit
-Probability and statistics (mean, median, standard deviation)
-Reading and interpreting tables and graphs

Geometry & Trigonometry (10-15% of SAT, Higher on ACT)

-Area and volume of common shapes
-Coordinate geometry — distance, midpoint, slope
-Circle equations and arc length
-Right triangle trigonometry (SOH-CAH-TOA)
-Angle relationships: supplementary, complementary, vertical

Formula Reference

The SAT provides a reference sheet with some formulas, but the ACT does not. Either way, having formulas memorized saves time and builds confidence.

Algebra

Slopem = (y2 - y1) / (x2 - x1)

Slope-intercept formy = mx + b

Point-slope formy - y1 = m(x - x1)

Quadratic formulax = (-b +/- sqrt(b^2 - 4ac)) / 2a

Difference of squaresa^2 - b^2 = (a+b)(a-b)

Geometry

Area of triangleA = (1/2)bh

Area of circleA = pi * r^2

CircumferenceC = 2 * pi * r

Pythagorean theorema^2 + b^2 = c^2

Volume of cylinderV = pi * r^2 * h

Volume of rectangular prismV = l * w * h

Statistics & Probability

Mean (average)mean = sum of values / number of values

ProbabilityP(event) = favorable outcomes / total outcomes

Percent change((new - old) / old) * 100

Trigonometry (ACT focus)

SOH-CAH-TOAsin = opp/hyp, cos = adj/hyp, tan = opp/adj

Special right triangles30-60-90: x, x*sqrt(3), 2x | 45-45-90: x, x, x*sqrt(2)

Unit circle valuessin(30)=1/2, cos(30)=sqrt(3)/2, sin(45)=sqrt(2)/2

Practice These Strategies Now

Apply these problem-solving approaches to thousands of free math questions on Larry Learns. Get AI explanations for every question to understand the best approach.

Frequently Asked Questions

What are the best math strategies for the SAT and ACT?

The five highest-leverage techniques are plugging in numbers when variables appear, backsolving from the answer choices, drawing a picture for geometry and word problems, estimating to eliminate wrong choices, and working backwards from what the problem asks. Each one trades algebraic complexity for arithmetic, which is much faster under time pressure.

How much time do I have per question on SAT Math vs ACT Math?

SAT Math gives you roughly 1 minute and 35 seconds per question, since you answer 44 questions across two 35-minute modules with the Desmos calculator available throughout. ACT Math is tighter — exactly 1 minute per question (45 questions in 50 minutes under the Enhanced ACT format) with a calculator allowed for the entire section.

When should I plug in numbers instead of solving algebraically?

Plug in numbers whenever the question and answer choices contain variables rather than specific values. Substitute small, easy numbers like 2, 3, or 10 to make the problem concrete. This is especially powerful for percent problems and any question that asks "which of the following expressions is equivalent to...". It is almost always faster than algebraic manipulation.

Do I need to memorize math formulas for the SAT?

The Digital SAT provides a reference sheet with common geometry formulas (area, volume, Pythagorean theorem, special right triangles), but you should still memorize the quadratic formula, slope formulas, percent change, and basic trig ratios. The ACT does not provide a formula sheet at all, so memorization matters more there — especially for trigonometry and coordinate geometry.

What math topics are most common on the SAT?

Algebra accounts for 35-40% of SAT Math, followed by Advanced Math (25-30%, including quadratics, exponential functions, and polynomial operations), Problem Solving & Data Analysis (25-30%, including ratios, percentages, and statistics), and Geometry & Trigonometry (10-15%). The ACT weights geometry and trigonometry more heavily than the SAT.

How do I improve my SAT or ACT math score quickly?

Focus on the topics you miss most, not the ones you already know. Take a practice section, identify your three weakest patterns (often word problems, systems of equations, or coordinate geometry), and drill those specifically for two weeks. Pair targeted practice with timed full sections to build pacing alongside accuracy. Most students see a measurable score lift within three to four weeks of focused practice.