SAT Math

Volume of a right pyramid with rectangular base

V = (1/3)lwh; l = base length, w = base width, h = height

Interior angles of a quadrilateral

The total number of degrees in the interior of a quadrilateral is 360°

Area of a rectangle

A = lw

Volume of a rectangular solid

V = lwh

Surface area of a rectangular prism

SA = 2lw + 2lh + 2wh

Square perimeter

P = 4s

Square area

A = s²

Cube surface area

SA = 6s²

Cube volume

V = s³

Cube diagonal

d = s√3

Area of a trapezoid

A = (1/2)(b₁ + b₂)h

Volume of a right cylinder

V = πr²h

Cylinder radius

r is the radius of the cylinder

Cylinder height

h is the height of the cylinder

Volume of a cone

V = (1/3)πr²h

Cone radius

r is the radius of the cone

Cone height

h is the height of the cone

Volume of a sphere

V = (4/3)πr³

Sphere radius

r is the radius of the sphere

Surface area of a cylinder

SA = 2πr² + 2πrh

Central angle and 360°

A central angle's degree measure is a fraction of 360°

Central angle and arc length

The arc created by a central angle is the same fraction of the circumference as the angle is of 360°

Central angle and sector area

The sector created by a central angle is the same fraction of the circle's area as the angle is of 360°

Circle circumference

C = πd

Circle area

A = πr²

Degrees in a circle

360°

45-45-90 triangle side ratio

a : a : a√2; the legs are a and a, and the hypotenuse is a√2

30-60-90 triangle side ratio

a : a√3 : 2a; the side opposite 30° is a, the side opposite 60° is a√3, and the hypotenuse is 2a

Sine of angle x

sin x = opposite/hypotenuse

Cosine of angle x

cos x = adjacent/hypotenuse

Tangent of angle x

tan x = opposite/adjacent = sin x/cos x

Complementary angle identity

The sine of an acute angle equals the cosine of the other acute angle

Hypotenuse definition

In a right triangle, the side opposite the right angle is the hypotenuse

Legs definition

In a right triangle, the two sides that form the right angle are the legs

Pythagorean theorem

a² + b² = c²

Pythagorean theorem meaning

The square of the hypotenuse equals the sum of the squares of the two legs

Common Pythagorean triple 1

3, 4, 5

Common Pythagorean triple 2

6, 8, 10

Common Pythagorean triple 3

5, 12, 13

Similar triangles: angles

Corresponding angles are congruent (equal in measure)

Similar triangles: sides

Corresponding sides are proportional (have the same ratio)

Triangle and rectangle relationship

A triangle is half of a rectangle that shares the same base and height

Area of a triangle

A = (1/2)bh

Interior angles of a triangle

The total number of degrees in the interior of a triangle is 180°

Angles on a straight line

The total number of degrees on a straight line is 180°

Function notation

f(x) = y

Function output on a graph

The result/output of a function is represented by the y-coordinate

Equation of a circle

(x − h)² + (y − k)² = r²

Circle equation: center

In (x − h)² + (y − k)² = r², the center is (h, k)

Circle equation: radius

In (x − h)² + (y − k)² = r², r is the radius

Circle equation: x and y

In (x − h)² + (y − k)² = r², x and y represent a point on the circle

Radians and degrees

π radians = 180°

Slope-intercept form

y = mx + b

Slope-intercept form: m

m is the slope

Slope-intercept form: b

b is the y-intercept

Slope formula

m = (y₂ − y₁)/(x₂ − x₁)

Slope formula: points

(x₁, y₁) and (x₂, y₂) are two points on the line

Quadratic standard form

y = ax² + bx + c

Quadratic formula

x = [−b ± √(b² − 4ac)]/(2a)

Sum of roots of a quadratic

Sum of roots = −b/a

Product of roots of a quadratic

Product of roots = c/a

x-coordinate of the vertex of a parabola

x = −b/(2a)

Standard form of a parabola

f(x) = ax² + bx + c

Parabola standard form: c

c is the y-intercept of the parabola

Vertex form of a parabola

f(x) = a(x − h)² + k

Parabola vertex form: h

h is the x-coordinate of the vertex

Parabola vertex form: k

k is the y-coordinate of the vertex

Factored form of a parabola

f(x) = a(x − r)(x − s)

Parabola factored form: r and s

r and s are the x-intercepts of the parabola

Discriminant

b² − 4ac

Discriminant greater than zero

If b² − 4ac > 0, the quadratic has two real solutions

Discriminant equal to zero

If b² − 4ac = 0, the quadratic has one real solution; the roots are the same

Discriminant less than zero

If b² − 4ac < 0, the quadratic has no real solutions

Difference of two squares

a² − b² = (a + b)(a − b)

Density formula

d = m/V; density = mass divided by volume

Power of zero

Any nonzero base raised to the 0 power equals 1: x⁰ = 1, x ≠ 0

Power of one

Any base raised to the 1st power equals itself: x¹ = x

Negative exponents

A negative exponent moves the base to the denominator and makes the exponent positive: x⁻ⁿ = 1/xⁿ

Fractional exponents

x^(1/n) = ⁿ√x; a fractional exponent represents a root

Parallel lines

Parallel lines have equal slopes, never intersect, and have no solution when their equations are solved simultaneously

Perpendicular lines

Perpendicular lines intersect at one point and form four 90° angles

Slopes of perpendicular lines

The slopes of perpendicular lines are negative reciprocals of each other

Slopes of parallel lines

Parallel lines have equal slopes

Exponential growth

y = a(1 + r)^t

Exponential decay

y = a(1 − r)^t

Exponential growth/decay: a

a is the initial amount

Exponential growth/decay: r

r is the percent growth/decay rate written as a decimal

Exponential growth/decay: t

t is the number of time intervals

Exponential growth/decay: y

y is the amount after t time intervals

Finding the number before a percent increase/decrease

Original amount = end number/(1 ± percent change as a decimal); use + for an increase and − for a decrease

Percent change

Percent change = [(new value − old value)/old value] × 100

Percent change: old value

The old value is the number before the change

Percent change: new value

The new value is the number after the change