SAT Math Must-Know Facts & Formulas - Core Math Review

Sep 14, 2026

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SAT Math must-know facts and formulas organized by key topic areas: numbers and algebraic sequences, factors and multiples, percents, averages and central tendency, fundamental counting and probability, and exponent/radical rules. It also consolidates core equation-solving and factoring identities, function and proportion relationships, absolute value, distance and midpoint, slope and line equations including parallel and perpendicular conditions, and essential geometry results such as special right triangles, the Pythagorean Theorem, and triangle area and angle facts.

LanguageEnglish

CategoryExam

FormatPDF

Pages6

Reading Time15 min

AccessFree to download

Numbers and Operations

Integers, rationals, and reals

Order of operations (PEMDAS)

Arithmetic and geometric sequences

Factors, multiples, and percents

Averages, Counting, and Probability

Average, mode, median

Fundamental counting principle

Probability and independence

Powers, Exponents, and Roots

Exponent rules and reciprocal powers

Factoring and Solving

Quadratic factoring and FOIL

Solving quadratic and linear systems

Functions and Linear Equations

Direct/inverse proportionality

Absolute value

Distance, midpoint, and slope

Parallel and perpendicular lines

Geometry

Special right triangles and Pythagorean Theorem

Triangle area and angle sums

SAT Math Must-Know Facts & Formulas Numbers, Sequences, Factors Integers: . . . , -3, -2, -1, 0, 1, 2, 3, . . . Rationals: fractions, that is, anything expressable as a ratio of integers Reals: integers plus rationals plus special numbers such as √2 , √3 and π Order Of Operations: PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract) Arithmetic Sequences: each term is equal to the previous term plus d Sequence: t 1 , t 1 + d, t 1 + 2d, . . . Example: d = 4 and t 1 = 3 gives the sequence 3, 7, 11, 15, . . . Geometric Sequences: each term is equal to the previous term times r Sequence: t 1 , t 1 · r , t 1 · r 2 , . . . Example: r = 2 and t 1 = 3 gives the sequence 3, 6, 12, 24, . . . Factors: the factors of a number divide into that number without a remainder Example: the factors of 52 are 1, 2, 4, 13, 26, and 52 Multiples: the multiples of a number are divisible by that number without a remainder Example: the positive multiples of 20 are 20, 40, 60, 80, . . . Percents: use the following formula to ﬁnd part, whole, or percent percent part = × whole 100 Example: 75% of 300 is what? Solve x = (75/100) × 300 to get 225 Example: 45 is what percent of 60? Solve 45 = (x/100) × 60 to get 75% Example: 30 is 20% of what? Solve 30 = (20/100) × x to get 150 [www.erikthered.com/tutor](www.erikthered.com/tutor) pg. 1 SAT Math Must-Know Facts & Formulas Averages, Counting, Statistics, Probability average = nsuum~~ ~~omberfotfermsterms total distance average speed = total time sum = average × (number of terms) mode = value in the list that appears most often median = middle value in the list (which must be sorted) Example: median of {3, 10 , 9 , 27 , 50} = 10 Example: median of {3, 9 , 10 , 27} = (9 + 10)/2 = 9 .5 Fundamental Counting Principle: If an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N × M ways. Probability: number of desired outcomes probability = number of total outcomes Example: each SAT math multiple choice question has ﬁve possible answers, one of which is the correct answer. If you guess the answer to a question completely at ran dom, your probability of getting it right is 1/5 = 20% . The probability of two diﬀerent events A and B both happening is P (A and B) = P(A) · P(B), as long as the events are independent (not mutually exclusive) . Powers, Exponents, Roots xa · xb = xa+b (xa )b = xa·bx0 = 1 xa /xb = xa−b (xy)a = xa · ya √xy = √x · √y 1/xb = x −b (−1)n = 􀀚 11,, if n is even; if n is odd. [www.erikthered.com/tutor](www.erikthered.com/tutor) pg. 2 SAT Math Must-Know Facts & Formulas Factoring, Solving (x + a)(x + b) = x2 + (b + a)x + aba2 − b2 = (a + b)(a − b) a2 + 2ab + b2 = (a + b)(a + b) a2 − 2ab + b2 = (a − b)(a − b) “FOIL” “Diﬀerence Of Squares” To solve a quadratic such as x2 +bx+c = 0, ﬁrst factor the left side to get (x+a1 )(x+a2 ) = 0, then set each part in parentheses equal to zero. E.g. , x2 + 4x + 3 = (x + 3)(x + 1) = 0 so that x = −3 or x = −1. To solve two linear equations in x and y: use the ﬁrst equation to substitute for a variable in the second. E.g., suppose x + y = 3 and 4x − y = 2 . The ﬁrst equation gives y = 3 − x, so the second equation becomes 4x − (3 − x) = 2 ⇒ 5x − 3 = 2 ⇒ x = 1, y = 2 . Functions A function is a rule to go from one number (x) to another number (y), usually written y = f (x) . For any given value of x, there can only be one corresponding value y. If y = kx for some number k (example: f (x) = 0 .5 · x), then y is said to be directly proportional to x. If y = k/x (example: f (x) = 5/x), then y is said to be inversely proportional to x. Absolute value: |x| = 􀀚 xx,, if xif x 0; 0. Lines (Linear Functions) Consider the line that goes through points A (x1 , y 1 ) and B (x2 , y2 ) . Distance from A to B: p (x2 − x1 )2 + (y2 − y1 )2 Mid-point

FAQs

What are the basic number sets covered (integers, rationals, and reals)?

Integers are whole-number negatives to positives. Rationals are fractions that can be expressed as ratios of integers. Reals include integers, rationals, and special numbers such as √2, √3, and π.

How do you find a percent of a whole using the given formula?

Use percent = part/whole × 100, equivalently part = (percent/100) × whole. Examples show converting 75% of 300 to 225 and solving for x in equations like 45 = (x/100) × 60.

What geometric facts are included for lines and triangles?

For lines, the slope-intercept form y = mx + b is given, along with conditions for parallel lines (equal slopes) and perpendicular lines (negative reciprocal slopes). For triangles, the Pythagorean Theorem a² + b² = c² and the special right-triangle relationships are highlighted, plus area = 1/2 · b · h and the fact that interior angles sum to 180°.

Sep 14, 2026

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