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.