College Math CLEP

Taxes Formula

Effective Rate = Tax paid/principal amount

Mark-up Formula

Selling price - cost

Simple Interest Formula

Principal x Rate x Time

Compound Interest Formula

A = P (1+ r/n)^nt

Continuous Compounding Formula

A = Pe^rt

Real numbers

no imaginary components

Integers

numbers without decimals or fractions, can be positive or negative (0 is included)

Rational Numbers

ratios/fractions of integers

Algebraic numbers

roots of polynomials with integer coefficients (ex. square root of 2)

Conversion Rule

Unit A x (Unit B/Unit A) = Unit B

A U B

A or B - Union

A ∩ B (arrow pointing up)

A and B - Intersection

~ A

denotes not A (or opposite)

Converse of A → B

B → A

Inverse of A → B

~A → ~B

Contrapositive of A → B

~B → ~A

True or False: A→B is logically equivalent to its contrapositive

True

Biconditional of A → B

A↔ B

Factorial

the product of itself with all positive integers less than it (5! → 5×4×3×2×1)

Binomial coefficent formula (order doesn’t matter)

n! / k!(n-k)!

Binomial coefficent formula (order does matter)

n! / (n-k)!

A^c

the event when A doesn’t occur

Or probability formula P(AUB)

P(A) - P(B) - P(A∩B)

And probability formula - P(A∩B)

P(A) x P(B)

A, given B formula - P(A|B)

P(A∩B) / P(B)

True or False: Probabilities are independent if they can not be multiplied together to equal a certain value

False

What does i equal?

square root of -1

What does i squared equal?

-1

How do you find the inverse of a function?

Switch x and y

Equation of a circle

r² = (x-h)² + (y-k)² → (h,k) is the center

y=logb(x) is equivalent to…

y=b^x

Point slope form

y-b = m(x-a)

Quadratic Formula

x = [-b+- √(b²-4ac)]/2ac

Completing the square

x²+bx+(b/2)² = D+(b/2)²

True or False: The x-coordinate for a vertex is exactly between 2 zeroes

True - to find h (h,k) → -b/2a

Law of Cos A

(b²+c²-a²)/2bc

Law of CosB

(a²+c²-b²)/2ac

Law of CosC

(b²+a²-c²)/2ab

Law of sines

(length opposite angle 1/sin of angle 1)/(length opposite angle 2/ sin of angle 2)

Sin

Opp/Hyp

Cos

Adj/Hyp

Tan

Opp/Adj

Csc

Hyp/Opp

Sec

Hyp/Adj

Cot

Adj/Opp

In a 45, 45, 90 triangle, the hypotenuse is longer than a leg by a factor of…

Square root of 2

In a 30, 60, 90 triangle, the hypotenuse is ___ as long as the short left and the long leg is ___ times as long as the short leg

twice, square root of 3

Complementary angles

angles = 90 degree straight

Supplementary angles

angles = 180 degrees straight line

Quadrilateral

2 dimension closed shape with 4 straight sides, 4 vertices, and 4 angles

Parallelogram

2 pairs of parallel opposite sides

Polygon

3 or more straight sides

Trapezoid

a quadrilateral with at least one pair of sides that never cross

Rhombus

a quadrilateral with 4 equal sides

isosceles

2 equal sides and 2 equal angles

Scalene

3 different lengths for each side and 3 different angles

Triangle inequality theorem

any side of a triangle is always shorter than the sum of the other 2 sides

Area of a trapezoid

1/2(b1+b2)h

Circumference of a circle

2pi x diameter

Sector area of a circle

angle/360 x pi r²

Product property of square roots

√ab = √a x √b

X ^0 = ?

1

Work formula

Rate x time

(xy)³/2 is equivalent to what?

√(xy)³

Volume of a cylinder

pi x r²h

Volume of a sphere

4/3 x pi x r³

Exponential growth equation

y = a(1+b)^x

Distance between 2 points equation

D = √(x2-x1)²+(y2-y1)²

Area of a triangle

(bh)/2

Hypotenuse (pythag)

c=√a²+b²

Relative change

(New value-original value)/original value

Central angle formula

relative frequency x 360

Right skewed (positively skewed)

tail is on the right side of the media and right is more positive on the number line

Left skewed (negatively skewed)

tail is on the left side of the media and left is more negative on the number line

Mode

most common