ACT Math Formulas and Vocab

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All the math formulas needed to smash the math section of the ACT!

Math

ACT

Math

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42 Terms

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midpoint

add end points together and divide by two

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distance

√(x-x)²- (y-y)²

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slope

rise/run

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slope-intercept

y=mx+b

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point slope

y-y1=m(x-x1)

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circle

(x-h)²+(y-k)²=r²

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ellipse

((x-h)²/a²)+((y-k)²/b²)=1

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volume of cube

s³

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volume of rectangular prism

lwh

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volume of triangular prism

1/2lwh

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volume of cylinder

πr²h

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volume of cone

1/3πr²h

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volume of sphere

4/3πr³

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area of square

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area of rectangle

lw

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area of triangle

1/2bh

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area of trapezoid

1/2(b1+b2)*h

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surface area of rectangular prism

2lw+2wh+2lh

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surface area of cube

6s²

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circumference of circle

2πr

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area of circle

πr²

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degrees to radians

180°=1 radian

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similar triangles

same angles different side lengths

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Imaginary (complex) numbers

i²=-1

i^4=1

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Integers

positive whole numbers

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Absolute Value

The positive distance on a number line from 0

[3]=3, [-3]=3, [3-5]=[-2]=2

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Logarithm

logB A=P, B^P=A

log2 8=3, 2³=8

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PEMDAS

The preformed order of operations

1.Parentheses, 2.Exponents, 3.Multi, 4.Divide, 5.Add, 6. Subtract

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Commutative Property

a + b = b + a

a x b = b x a

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Associative Property

a+(b+c) = (a+b)+c

a x (b x c)=(a x b) x c

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Distributive Property

a x (b+c)=(a x b) + (a x c)

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Percent Change

% Change= (amount of change/original amount) x 100%

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Sale Price

initial $ - discount OR

(initial $ - % discount) x initial price

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FOIL (First, Outer, Inner, Last)

(x+5) (x+2)= x² - 2x + 5x - 10 → x² + 3x - 10

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Factoring Quadratic

Given: ax² + bx + c = 0

x² + 9x + 18 = 0 → (x+6) (x+3) = 0 → x = -6,-3

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Quadratic Formula

x = -b + √b² - 4ac / 2a

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Discriminant

b² - 4ac

b² - 4ac > 0, there are 2 solutions

b² - 4ac < 0, there are NO solutions

b² - 4ac = 0, there are 1 solution

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vertical angles

m<1 = m<3, m<2 = m<4

m<1 + m<3 = 180° , m<2 + m<4 =180°

<p>m&lt;1 = m&lt;3, m&lt;2 = m&lt;4</p><p>m&lt;1 + m&lt;3 = 180° , m&lt;2 + m&lt;4 =180°</p>
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SOH CAH TOA

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent

<p>sin = opposite/hypotenuse</p><p>cos = adjacent/hypotenuse</p><p>tan = opposite/adjacent</p>
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CSC SEC COT

csc = hypotenuse/opposite

sec = hypotenuse/adjacent

cot = adjacent/opposite

<p>csc = hypotenuse/opposite</p><p>sec = hypotenuse/adjacent</p><p>cot = adjacent/opposite</p>
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triangle degrees of SOH CAH TOA

sin 30° = ½ sin 60°=√3/2

cos 30° = √3/2 cos 60°= 1/2

tan 30°= 1/√3 tan 60°=√3

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special right triangles

45° - 45° - 90°,

hypotenuse = x√2 , sides = x

30° - 60° - 90°

hypotenuse = 2x , adjacent(of 30°)= x√3 , opposite(of 30°) = x

<p>45° - 45° - 90°, </p><p>hypotenuse = x√2 , sides = x</p><p>30° - 60° - 90°</p><p>hypotenuse = 2x , adjacent(of 30°)= x√3 , opposite(of 30°) = x</p>