Math Formulas for AFOQT

Real Numbers

These are all numbers on the number line. These include integers, fractions, decimals, irrational, etc.

Order of Operations

PEDMAS; Division and Multiplication are conducted left to right as are Subtraction and Addition

Ratios

A comparison of two numbers by division

Percentages

Part=(percent/100)×whole

Proportional Ratios

Two ratios are equal

Percent of Change

(New value-old value)/(old value) x 100%

Markup

Selling price - Cost

Markup rate

Markup/Cost

Discount

Multiply the regular price by the rate of discount

Selling price

Original-Discount=?

Tax

Multiply the tax rate by the taxable amount

Distributive Property

A(B+C)=AB+AC

Polynomial

Systems of Equations

Two or more equations working together

Ex. -2x + 2y=3

-2x + y=3

Functions

A rule that goes from one number (x) to another number (y), usually written y=f(x). For any given value of x, there can only be one corresponding value y. If y=kx for some number k (f(x)=0.5x), then y is said to be inversely proportional to x. The graph of y=f(x) + k is the translation of the graph of y= f(x) by (h,k) units in the plane. For example, y= f(x+3) shifts the graph of f(x) by 3 units to the left.

Solving Systems of Equations by Elimination

Ex. x+2y=6 + (-x)+y=3 → [3y =9 → y=3] [x+6=6 → x=0]

Distance from A to B (Distance Formula)

Slope of the Line

Point slope formula

Midpoint of Segment AB

Parabola

Parallel Parabolas to the y-axis are given by y=ax²+bx+c.

If a>0, the parabola opens up

If a<0, the parabola opens down

The y-intercept is C, and the x-coordinate of the vertex is x=-(b/2a)

Triangle (Area)

Area is given by A=(1/2)bh

Triangle (Perimeter)

P=a+b+c

Interior Angles of a Triangle

The sum equals 180°

Right Triangles

A good example is of a=3, b=4, c=5. This is referred to as the 3-4-5 right triangle. These are multiples that when a number is multiple by the we get an equal, larger triangle. Ex. If we multiply by 2 we get 6-8-10, which is also a right triangle.

Equilateral

All sides equal 60°

Isosceles

Has two equal sides, the base angles

Circle (Area)

A=(pi)r²

Circle (circumference)

C=2(pi)r

Full angle/circumference=360°

Circle (Length of Arc)

(n°/360°) × 2(pi)r

Circle (Area of Sector)

A=(n°/360°) × (pi)r²

Circle (Equation of the curve)

(x-h)² + (y-k)² = r²

Rectangle

A=l×w

If square l=w

Parallelogram

Area= l×h

(Rhombus if l=w)

Parallelogram

Regular polygons are n-sided figures with all equal sides and all angles equal. The sum of the inside angles of an n-sided regular polygon is (n-2)×180°

Area of a trapezoid

A=(1/2)h(b+b)

*b=base, the equation calls for the addition of base 1 and base 2

Surface area and volume of a rectangular/right prism

SA=ph+lb, V=bh

Surface Area and Volume of a Cylinder

SA=2(pi)rh + 2(pi)r², v=(pi)r²h

Surface Area and Volume of a Pyramid

SA= (1/2)ps+b, v=(1/3)bh

Surface Area and Volume of a Cone

SA=(pi)rs+(pi)r², v=(1/3)(pi)r²h

Surface Area and Volume of a Sphere

SA=4(pi)r² , v=(4/3)(pi)r³

Solids (Rectangular)

Volume=l×w×h, Area=2(l×w+w×h+l×h)

Solids (Right Cylinder)

V=(pi)r²h, A=2(pi)r(r+h)

Quadratic formula

Simple interest

I=prt

(I=interest, p=principal, r=rate, t=time)

Probability

Number of desired outcomes/Number of total outcomes

Powers, Exponents, Roots

Interest

Total amount: A=P+I=P(1+rt)

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

*n is the number of times interest compounds each year

Factorials

The product of a number and all counting numbers below it

Ex. 8 factorial= 8! =8×7×6×5×4×3×2+1

5 factorial= 5! = 5×4×3×2×1

2 factorial= 2! = 2×1

Permutation

When different orderings of the same item are counted separately

Formula: nPr= (n!)/(n-1)!

Combination

Used when selecting objects from a group where the order is not important

Formula: nCr=(n!)/r!(n-1)!