College Math Clep Formulas - Flashcards

College Math Clep Formulas - Flashcards

Simple interest formula

I = Prt

Compound interest formula when compounded n times per year

A = P(1 + r/n)ⁿᵗ

Quarterly compounding value of n

n = 4

Continuous compounding formula

A = Peʳᵗ

APY formula for nominal rate r compounded n times per year

APY = (1 + r/n)ⁿ − 1

Expansion of (a + b)²

a² + 2ab + b²

Expansion of (a − b)²

a² − 2ab + b²

Factorization of a² − b²

(a − b)(a + b)

Factorization of a³ − b³

(a − b)(a² + ab + b²)

Factorization of a³ + b³

(a + b)(a² − ab + b²)

Even function rule

f(−x) = f(x)

Odd function rule

f(−x) = −f(x)

Y-axis symmetry point rule

(x, y) also has (−x, y)

Reflection across the x-axis

(x, y) → (x, −y)

Reflection across the y-axis

(x, y) → (−x, y)

Reflection across the origin

(x, y) → (−x, −y)

Reflection across the line y = x

(x, y) → (y, x)

Logarithm product rule

logₐ(xy) = logₐ(x) + logₐ(y)

Logarithm quotient rule

logₐ(x/y) = logₐ(x) − logₐ(y)

Logarithm power rule

logₐ(xᵏ) = k·logₐ(x)

Logarithmic form equivalent to exponential form

logₙ(x) = y means nʸ = x

Change-of-base formula for logₙ(x)

logₙ(x) = log(x)/log(n)

Area formula for a triangle

A = ½bh

Area formula for a rectangle

A = lw

Area formula for a square with side s

A = s²

Area formula for a circle

A = πr²

Circumference formula for a circle with radius r

C = 2πr

Perimeter formula for a rectangle

P = 2l + 2w

Area change under scale factor k

Area is multiplied by k²

Volume change under scale factor k

Volume is multiplied by k³

Diagonal of a square with side length s

s√2

Space diagonal of a cube with side length s

s√3

Volume of a cube with side length s

V = s³

Volume of a prism

V = Bh

Volume of a cylinder

V = πr²h

Volume of a cone

V = ⅓πr²h

Volume of a sphere

V = ⁴⁄₃πr³

Volume of a pyramid

V = ⅓Bh

Surface area of a cube with side s

SA = 6s²

Arc length formula for central angle θ in degrees

L = (θ/360)(2πr)

Sector area formula for central angle θ in degrees

A = (θ/360)(πr²)

Distance formula between (x₁, y₁) and (x₂, y₂)

√((x₂ − x₁)² + (y₂ − y₁)²)

Midpoint formula between (x₁, y₁) and (x₂, y₂)

((x₁ + x₂)/2, (y₁ + y₂)/2)

Z-score formula

z = (x − μ)/σ

Interquartile range (IQR)

Q₃ − Q₁

Range of a data set

maximum − minimum

Best graph for numerical data in intervals or bins

Histogram

Best graph for the relationship between two numerical variables

Scatterplot

Best graph for parts of one whole

Pie chart

Best graph for comparing counts across categories

Bar chart

Meaning of A ∪ B

Elements in A or B or both

Meaning of A ∩ B

Elements in A and B

Counting formula for A ∪ B

n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

De Morgan's Law for the complement of A ∪ B

¬(A ∪ B) = ¬A ∩ ¬B

De Morgan's Law for the complement of A ∩ B

¬(A ∩ B) = ¬A ∪ ¬B

Contrapositive of 'If p, then q'

If ¬q, then ¬p

Converse of 'If p, then q'

If q, then p

Inverse of 'If p, then q'

If ¬p, then ¬q

Natural numbers

{1, 2, 3, …}

Whole numbers

{0, 1, 2, 3, …}

Integers

{…, −2, −1, 0, 1, 2, …}

Rational numbers

Numbers that can be written as a ratio of integers

Irrational numbers

Numbers that cannot be written as a ratio of integers

Real numbers

All rational and irrational numbers

When to use a permutation

Use a permutation when order matters

When to use a combination

Use a combination when order does not matter

Permutation formula ⁿPᵣ

n!/(n − r)!

Combination formula ⁿCᵣ

n!/[r!(n − r)!]

Password selection with different letters and order matters

Use a permutation

Committee selection when order does not matter

Use a combination