# Math SAT II: Formulae

## 96 terms

x^(m+n)

x^(m-n)

x^(mn)

(xy)^n

(x/y)^n

(a + b)x

(a - b)x

(ab)x^2

### (a + b)(c + d) = ?

ac + ad + bc + bd

a(x + y)

(a - b)(a + b)

(a + b)^2

### Area of a trapezoid =

((base 1 + base 2)/2) x height

base x height

### Perimeter of rectangle =

2(length + width)

length x width

4 x side

base x height

4 x side

(side)^2

(n - 2) x 180°

360°

2πr

(n/360)(2πr)

πr^2

(n/360)(πr^2)

2lw + 2wh + 2lh

### Distance between opposite vertices of a rectangular solid =

√(l^2 + w^2 + h^2)

Bh

lwh

e^3

hπr^2

### Midpoint =

((x + x)/2, (y + y)/2)

### Distance =

√((x - x)^2 + (y - y)^2)

slope

y-intercept

(y - y)/(x - x)

the same

### Perpendicular lines have _________ slopes

negative-reciprocal

### Equation for a circle:

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

### Equation for a parabola:

y = ax^2 + bx + c

### Equation for an ellipse centered that the origin with axial intersections (±a,0) and (0,±b) :

(x^2/a^2) + (y^2/b^2) = 1

### Equation for a hyperbola:

(x^2/a^2) - (y^2/b^2) = 1

### sine =

opposite/hypotenuse

### cosecant =

hypotenuse/opposite = 1/sine

### sin(A + B) =

sin A cos B + cos A sin B

### cos(A + B) =

cos A cos B - sin A sin B

### tan(A + B) =

(tan A + tan B)/ (1 - tan A tan B)

2 sin x cos x

### cos 2x =

(cos x)^2 - (sin x)^2 = 1- 2(sin x)^2 = 2 cos 2x -1

### tan 2x =

(2 tan x)/(1 - (tan x)^2)

### sin ½A =

±√((1 - cos A)/2)

### cos ½A =

±√((1 + cos A)/2)

### tan ½A =

±√((1 - cos A)/(1 + cos A))

amplitude

2π/b

### Law of Sines

a/sin A = b/sin B = c/sin C

### Law of Cosines

c^2 = a^2 + b^2 - 2ab cos C

### To find the inverse of a function:

1. Replace f(x) with y
2. Solve the equation for x in terms of y
3. Replace x with f⁻¹(x) and replace y with x

y = x

reciprocals

(a + b)i

(a - b)i

-ab

-1

-i

1

### Percent increase =

(amount of increase/original amount) x 100%

### Percent decrease =

(amount of decrease/original amount) x 100%

Total A/Total B

### Average speed =

Total Distance/Total Time

### Average (arithmetic mean) =

sum of the terms/number of terms

middle value

### mode =

most frequent value

### sum of the terms =

average x number of terms

n!

n!/(a!b!)

### number of permutations of n objects taken r at a time =

n P r = n!/(n - r)!

### number of combinations of n objects taken r at a time =

n C r = n!/(r!(n - r)!)

### Probability =

# of favorable outcomes/Total # of possible outcomes

ab

### log₁₀ (XY) = ?

log₁₀ X + log₁₀ X

### log₁₀ (X/Y) = ?

log₁₀ X - log₁₀ Y

n log₁₀ X

1

log₅ X/log₅ 10

### To find a limit:

1. factor the numerator and denominator
2. cancel any common factors
3. plug in the limit and evaluate

a₁ + (5 - 1)d

### Arithmetic sequence: S₅ =

5((a₁ + a₅)/2) = 5/2(2a₁ + (n - 1)d)

a₁r^(5-1)

### Geometric sequence: S₅ =

(a₁ - a₁r^5)/(1 - r)

S∞ = a₁/(1 - r)