ACT Math Equations

Circle Area

= πr²

Circle Circumference

= 2πr

Trapezoid Area

1/2(b1+b2)h

Kite Area

1/2lw

Cube Volume

= s³

Right Cylinder Volume

= πr²h

45°-45°-90°

x, x, x√2

30°-60°-90°

x, 2x, x√3

Smallest → x

Middle → x√3

Largest → 2x

Area of Equilateral Triangle

s²√3/4

Distance equation

√(x1-x2)²+(y1-y2)²

Irrational numbers are…

Any numbers that cannot be expressed as a fraction (Ex: π< √5)

One Solution

• Coefficients for the x-terms are different.

• Constants (number) can be same or different.

Zero Solutions

• Coefficients for the x-terms are the same.

• Constants (numbers) are different.

Infinite Solutions

• Both sides of the equation must be identical.

• Coefficients for the x-terms and constants are the same..

Weighted average

(average #1)(weight #1)+(average #2)(weight #2)/weight #1+weight #2

Change of Base Rule

logb(a)= log(a)/log(b)

Loga(1)=

0

Discriminant vs. Types of Solutions: b²-4ac>0

2 real solutions

Discriminant vs. Types of Solutions: b²-4ac=0

1 real solution

Discriminant vs. Types of Solutions: b²-4ac<0

0 real solutions, 2 complex solutions

Period for sine, cosine, secant, and cosecant

2π/B

Period for tangent and cotangent =

π/B

Law of Sines:

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

Law of Cosines

a² = b² + c²- 2bc cos(A)

Determinant of a Matriz

ad-bc

Circle

(x-h)²+(y-k)²=r²

Ellipse

(x-h)²/a² + (y-k)²/b² = 1

Horizontal Hyperbola Equation

(x-h)²/a² - (y-k)²/b² = 1

Vertical Hyperbola Equation

(y-k)²/a² - (x-h)²/b² = 1

Horizontal Hyperbola opens…

Left and right

Vertical Hyperbola opens…

Up and down

The sum of probabilities of all possible outcomes is…

Equal to 1

P(A or B) =

P(A) + P(B)

P(A and B)

P(A) × P(B)

Expected Value

P(A)×A + P(B)×B + P(C)×C…

Permutation

Order matters

Permutation (Order Matters) equation

nPr = n!/(n-r)!

Combination

Order Doesn't Matter

Combination (Order Doesn't Matter) equation

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

n! = L

n(n-1)(n-2) …

Arithmetic Sequence to find nth term

tn = t1 + d(n-1)

Geometric Sequence to find the nth term:

tn = t1r^(n-1)

Complex conjugates

a + bi and a - bi

(a + bi)(a - bi) =

a² + b²

|a + bi| =

√a²+b²

For any two complex numbers a + bi and c + di, distance =

√(a-c)²+(b-d)²

Binomial Theorem and Pascal’s Triangle

Row Exponent Pascal’s Triangle

0 (a+b)^0 1

1 (a+b)^1 1 1

2 (a+b)² 1 2 1

3 (a+b)³ 1 3 3 1

4 (a+b)^4 1 4 6 4 1

5 (a+b)^5 1 5 10 10 5 1