SAT Math

SAT Math concepts, explained

Short guides to the ideas SAT Math tests most. Each one starts with the answer, then gives the formulas, worked SAT-style examples, common mistakes, and an explorer you can drag to see the math move.

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  • Algebraabout 35% of the test
  • Advanced Mathabout 35% of the test
  • Data and Statisticsabout 15% of the test
  • Geometry and Trigabout 15% of the test

11 guides

Algebra

about 35% of SAT Math

Slope-intercept form−6−4−2246−6−4−226y = 2x + 1(0, 1)

Slope-intercept form

y=mx+by = mx + b

Read a line's slope and y-intercept straight from y = mx + b, and write one from a graph or two points.

Interval notationx > 2 → (2, ∞)−5−4−3−2−1012345−1 ≤ x < 4 → [−1, 4)−5−4−3−2−1012345x ≤ 0 → (−∞, 0]−5−4−3−2−1012345

Interval notation

[  included(  not included[\;\text{included} \qquad (\;\text{not included}

Brackets, parentheses, and infinity: how to write the solution to an inequality.

Advanced Math

about 35% of SAT Math

The quadratic formula−4−2246−6−4−2246(−1, 0)(3, 0)

The quadratic formula

x=−b±b2−4ac2ax = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Solve any ax² + bx + c = 0, and use the discriminant to count solutions without solving.

Exponential growth and decay2468102030405060y = 10(1.25)ˣy = 5x + 10(0, 10)

Exponential growth and decay

y=a(1±r)xy = a(1 \pm r)^x

Read the starting value and the percent rate from y = a(1 ± r)ˣ, and tell exponential from linear.

Problem-Solving and Data Analysis

about 15% of SAT Math

Percent change80Original100New+25%

Percent change

% change=new−originaloriginal\%\ \text{change} = \dfrac{\text{new} - \text{original}}{\text{original}}

Percent increase, decrease, and back-to-back changes, done with one multiplier instead of guesswork.

Mean vs. median02468101214161820median 4.5mean 68 values

Mean vs. median

mean=sumcount\text{mean} = \dfrac{\text{sum}}{\text{count}}

How to find each one, and why an outlier pulls the mean but barely moves the median.

Geometry and Trigonometry

about 15% of SAT Math

The Pythagorean theoremb²a²c²

The Pythagorean theorem

a2+b2=c2a^2 + b^2 = c^2

a² + b² = c² for any right triangle, plus the triples and special triangles that save time on SAT Math.

Volume of a cone and a pyramidhrhlw

Volume of a cone and a pyramid

V=13πr2hV=13BhV = \tfrac{1}{3}\pi r^2 h \qquad V = \tfrac{1}{3}Bh

Why both formulas have a one third in them, and how to use them on SAT Math.

Surface area of a spherer

Surface area of a sphere

SA=4πr2SA = 4\pi r^2

The one sphere formula the SAT reference sheet leaves out, and how to use it.

Equation of a circle−4−268−6−4−2246r = 3(2, −1)

Equation of a circle

(x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2

Read the center and radius from (x − h)² + (y − k)² = r², and complete the square when the equation is expanded.

The unit circle30°(√3/2, 1/2)(1, 0)(0, 1)(−1, 0)(0, −1)

The unit circle

(x,y)=(cos⁡θ,sin⁡θ)(x, y) = (\cos\theta, \sin\theta)

Sine, cosine, and radians from one circle, with the values SAT Math expects you to know.

A learner having an idea, surrounded by maps and equations

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