# ACT Math Formulas

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Pythagorean theorem

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## Description and Tags

Formulas to know for ACT

### 40 Terms

1

Pythagorean theorem

a^2 + b^2 = c^2

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2

Circumference of a circle

C= (3.14)(d)

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3

Area of a circle

A=(3.14)(r^2)

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4

distance formula

D=(r)(t)

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5

arithmetic sequence formula (explicit)

an = a1 + (n - 1)d

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6

Sum of arithmetic sequence

S = (n/2) (a1 +(a1+(n-1)d)) or S = (n/2) (a1 + an)

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7

Geometric sequence formula

an=a1(r)^n-1

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8

Geometric Series formula Finite

Sn = a1 (1-r^n) / (1-r)

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9

Combination formula

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

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10

Permutation

nPr=n!/(n-r)!

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11

parabola

y=a(x-h)^2+k

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12

circle

(x-h)^2+(y-k)^2

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13

ellipse

((x-h)^2/a^2) + ((y-k)^2/b^2)= 1

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14

hyperbola

((x-h)^2/a^2) - ((y-k)^2/b^2)= 1

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15

Inscribed angle

IA=central angle(or intercepted arc)/2

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16

Property of Parallelogram

Opposite sides are parallel and congruent

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17

opposite angles are congruent

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18

consecutive angles are supplementary

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19

diagonals bisect each other

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20

Property of Rectangle

4 90 degree angles

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21

Property of Rhombus

4 congruent sides

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22

Property of Square

4 90 degree angles and sides

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23

Property of Trapezoid

one set of parallel sides

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24

isosceles trapezoid

one set of parallel sides and 2 congruent sides

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25

trigonometry functions

a sin (b(x-c))+d

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26

area of trapezoid

a= (b1+b2/2)(h)

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27

volume of a pyramid

B(length x width) x H

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28

volume of a cone

(1/3)(pi)(r^2)(h)

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29

volume of a cylinder

(pi)(r^2)(h)

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30

volume of sphere

4/3(pi)(r^3)

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31

volume of rectangular prisim

b x w x h

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32

sum of angles in polygon

n=(n-2)(180)

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33

single interior angle

n= (n-2)(180)/n

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34

Trig Ratios/SOHCAHTOA

s=o/h, c=a/h, t=o/a

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35

Reciprocal Trig Ratios

Csc=h/o, sec=h/a, cot=a/o

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36

Slope formula 2 points on a line

Slope formula:

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37

the slope of a line and a point on the line

Point-slope formula: y - y1 = m(x - x1)

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38

the slope and y-intercept of a line

Slope-intercept formula: y = mx + b

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39

Parallel lines have equal slopes

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40

The slopes of perpendicular lines are opposite reciprocals

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