SAT Math Formulas & Concepts You Need to Know

The SAT Math section tests your ability to apply mathematical concepts under time pressure. 44 questions in 70 minutes means you have roughly 95 seconds per question. Knowing the formulas cold is not optional. Every second spent trying to recall whether slope is rise over run or run over rise is a second not spent solving the problem.

The College Board provides a short reference sheet, but it only covers basic geometry. The rest (quadratic formula, statistics, systems of equations, trigonometry) you need to have memorized before test day. This guide organizes every SAT math formula and concept by topic, with study strategies to help you actually retain them.

If you have been through the "read the textbook and hope it sticks" approach, try a different method. Spaced repetition paired with active recall is the fastest way to move formulas from "I've seen this" to "I know this." Research by Karpicke and Roediger (2008) showed that retrieval practice produced 80% recall on delayed tests versus 36% for re-reading.

Algebra & Functions

Algebra dominates the SAT. Roughly 35% of all math questions test your ability to work with equations, inequalities, and functions. Master these formulas and you have a strong foundation for over a third of the exam.

Linear equations and functions:

• Slope-intercept form: y = mx + b, where m is slope and b is the y-intercept
• Point-slope form: y - y1 = m(x - x1)
• Slope formula: m = (y2 - y1) / (x2 - x1)
• Standard form: Ax + By = C
• Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals (m1 * m2 = -1).

Systems of equations:

• Substitution: Solve one equation for a variable, plug into the other
• Elimination: Add or subtract equations to cancel a variable
• No solution: Lines are parallel (same slope, different intercepts)
• Infinite solutions: Equations describe the same line

Inequalities:

• Flip the inequality sign when multiplying or dividing by a negative number
• Absolute value inequalities: |x| < a means -a < x < a. |x| > a means x < -a or x > a.

Functions:

• Domain: All valid input values (watch for division by zero and negative square roots)
• f(g(x)): Composition of functions, plug g(x) into f
• Interpreting graphs: Be able to identify intercepts, slope, increasing/decreasing intervals, and max/min values from a graph

The SAT loves word problems that translate into linear equations. Practice converting "the cost of x items at $5 each plus a $10 shipping fee" into y = 5x + 10 until it becomes automatic.

Advanced Math

About 35% of SAT Math questions fall into the "advanced math" category. This covers quadratics, polynomials, exponentials, and rational expressions.

Quadratic equations:

• Standard form: ax2 + bx + c = 0
• Quadratic formula: x = (-b +/- sqrt(b2 - 4ac)) / 2a
• Discriminant (b2 - 4ac): Positive means two real solutions, zero means one solution, negative means no real solutions
• Factoring: Look for two numbers that multiply to ac and add to b
• Vertex form: y = a(x - h)2 + k, where (h, k) is the vertex
• Vertex from standard form: x-coordinate of vertex = -b / (2a)

Polynomials:

• Factor theorem: If f(a) = 0, then (x - a) is a factor
• Remainder theorem: f(a) gives the remainder when dividing by (x - a)
• End behavior: Leading term determines behavior as x approaches positive and negative infinity

Exponential functions:

• Growth: f(x) = a * bx where b > 1
• Decay: f(x) = a * bx where 0 < b < 1
• Compound interest: A = P(1 + r/n)nt
• Exponential vs. linear growth: Exponential growth increases by a constant percentage, linear growth increases by a constant amount

Rational expressions:

• Simplify by factoring numerator and denominator, then cancel common factors
• Find undefined values by setting the denominator equal to zero
• Add/subtract rational expressions by finding a common denominator

Quadratic questions on the SAT often test whether you can choose the right approach. Sometimes factoring is fastest. Other times, the quadratic formula saves you from messy factoring. Practice both so you can recognize which is more efficient for a given problem.

Geometry & Trigonometry

Geometry and trigonometry make up about 15% of SAT Math. The formulas here are straightforward, but students who skip memorizing them lose easy points.

Triangles:

• Area: A = (1/2)bh
• Pythagorean theorem: a2 + b2 = c2
• Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17 (and their multiples)
• 30-60-90 triangle sides: x, x*sqrt(3), 2x
• 45-45-90 triangle sides: x, x, x*sqrt(2)
• Triangle inequality: The sum of any two sides must be greater than the third side
• Interior angles of a triangle sum to 180 degrees

Circles:

• Area: A = pi*r2
• Circumference: C = 2pir
• Arc length: (central angle / 360) * 2pir
• Sector area: (central angle / 360) * pi*r2
• Equation of a circle: (x - h)2 + (y - k)2 = r2, where (h, k) is the center

Other shapes:

• Rectangle area: A = lw
• Parallelogram area: A = bh
• Trapezoid area: A = (1/2)(b1 + b2)h
• Volume of a rectangular prism: V = lwh
• Volume of a cylinder: V = pir2h
• Volume of a sphere: V = (4/3)pir3
• Volume of a cone: V = (1/3)pir2*h

Trigonometry:

• SOH CAH TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent
• Complementary angle relationship: sin(x) = cos(90 - x)
• Unit circle values: Know sin and cos for 0, 30, 45, 60, and 90 degrees
• Radians: 180 degrees = pi radians. Convert by multiplying degrees by pi/180.

A common SAT trick: giving you a circle equation like x2 + 6x + y2 - 4y = 12 and asking for the radius. You need to complete the square to get it into standard form. Practice this technique until you can do it quickly.

Data Analysis & Statistics

About 15% of SAT Math questions involve interpreting data, probability, and statistical concepts. These are often the most approachable questions if you know the formulas.

Central tendency and spread:

• Mean: Sum of all values divided by the number of values
• Median: Middle value when data is ordered. For even-numbered sets, average the two middle values.
• Mode: Most frequently occurring value
• Range: Maximum minus minimum
• Standard deviation: Measures spread from the mean. You will not need to calculate it, but you need to understand what it means. Higher standard deviation = more spread out.

Probability:

• Basic probability: P(event) = favorable outcomes / total outcomes
• Complementary events: P(not A) = 1 - P(A)
• Two-way tables: Read carefully. "Given that" language signals conditional probability.
• Conditional probability: P(A given B) = P(A and B) / P(B)

Linear regression and data interpretation:

• Line of best fit: Understand slope as rate of change and y-intercept as starting value in context
• Correlation vs. causation: The SAT will test whether you know that correlation does not imply causation
• Scatterplots: Be able to identify positive, negative, and no correlation

Ratios, proportions, and percentages:

• Percent change: ((new - old) / old) * 100
• Proportional relationships: If a/b = c/d, then ad = bc (cross-multiplication)
• Unit conversion: Use dimensional analysis, set up so units cancel

Statistics questions on the SAT are often embedded in real-world contexts (surveys, experiments, studies). Read the setup carefully. The math is usually simple, but misreading "mean" as "median" or misinterpreting a two-way table costs you points.

Your 8-Week SAT Math Study Plan

Here is a week-by-week plan to take your SAT Math score from "needs work" to "test ready." This plan assumes 30 to 45 minutes of daily study.

Week 8: Diagnostic and setup. Take a full-length practice test from the College Board's Bluebook app. Score it. Identify your weakest areas. Create your first flashcards for the formulas in your two weakest categories. Add 10 to 15 new cards per day.

Week 7: Algebra deep dive. Work through algebra and linear equation problems. Every formula you use should already be on a flashcard. If you encounter one that is not, add it immediately. Continue spaced repetition reviews daily.

Week 6: Advanced math. Focus on quadratics, polynomials, and exponentials. Practice choosing between factoring and the quadratic formula. Add flashcards for any new formulas or problem-solving patterns.

Week 5: Geometry and trig. Work through geometry and trigonometry problems. Memorize special right triangle ratios and circle formulas. Your algebra flashcards from Weeks 7 to 8 are now returning at longer intervals, reinforcing retention.

Week 4: Data analysis. Cover statistics, probability, and data interpretation. Practice with two-way tables and scatterplot questions. Continue all flashcard reviews.

Week 3: Mixed practice. Take another full practice test. Compare your score to Week 8. Focus your remaining study time on question types you are still missing. This is the week to address specific weaknesses, not review broadly.

Week 2: Timed practice sets. Do timed sets of 22 questions in 35 minutes (matching the real module format). Build speed and comfort with time pressure. Your flashcard reviews should feel routine by now, taking only 10 to 15 minutes per day.

Week 1: Final review. Take one final practice test. Review your most-missed flashcards. Go light on new material. Focus on confidence and pacing. Get good sleep in the days before the test.

For more detail on structuring a spaced repetition study schedule, see our exam study plan guide.

Study Tips for SAT Math

Put every formula on a flashcard. This sounds tedious. It works. Write the formula on one side and a sample problem (with solution) on the other. Reviewing a formula in the context of a problem is far more effective than staring at a formula sheet. For tips on formatting math on flashcards, see our guide to LaTeX math flashcards.

Learn to recognize problem types, not just solve them. The SAT reuses the same problem structures with different numbers. Once you spot that a question is really asking you to find the vertex of a parabola, you know exactly which formula to reach for. Pattern recognition comes from doing lots of practice problems and categorizing them.

Do not skip the word problems. Many students skip word problems and come back to them at the end. This is a mistake. SAT word problems are often straightforward once you translate them into equations. Practice the translation step: underline what you are solving for, identify the relationship, write the equation.

Time yourself from day one. The SAT gives you about 95 seconds per question. If you practice without time pressure, you are training a skill (accuracy without speed) that does not match what the test requires. Use a timer for every practice set.

Review wrong answers, not just right ones. When you miss a question, do not just read the correct answer and move on. Write down why you got it wrong. Was it a formula you did not know? A calculation error? A misread question? This diagnosis tells you what to study next. Create flashcards for your specific error patterns.

Use the process of elimination. On multiple choice, eliminating two wrong answers and guessing between the remaining two gives you a 50% chance. The digital SAT has no penalty for guessing, so never leave a question blank. If a question asks for a positive value and two answers are negative, you have already narrowed your odds.

Practice with official materials. Third-party SAT prep materials vary widely in quality. The College Board's official practice tests are the gold standard because they match the real test's difficulty, format, and content distribution. Use third-party resources for extra practice, but always benchmark with official tests.

Consistent daily review beats weekend marathon sessions. Thirty minutes a day for 8 weeks adds up to 28 hours of study, and research on the spacing effect shows that spreading practice across days produces stronger retention than the same total time crammed into a few sessions. Build the habit, trust the process, and let spaced repetition do the heavy lifting.