ACT Math Formulas

Question 1

Algebra: Slope

Answer 1

(y2-y1) / (x2-x1)

Question 2

Algebra: Slope-Intercept Form

Answer 2

y = mx + b
- m: slope, b: y-int

Question 3

Algebra: Midpoint of a Line

Answer 3

((x1+x2)/2) , (y1+y2)/2)

Question 4

Algebra: Distance between 2 Points

Answer 4

√(x2-x1)^2 + (y2-y1)^2

Question 5

logbx asks

Answer 5

to what power does b have to be raised to result in x

Question 6

Logarithms formulas

Answer 6

logbx = y → b^y = x
logbxy = logbx +logby
logb(x/y) = logbx - logby

Question 7

Probability: Outcome happening

Answer 7

of desired outcomes / total # of possible outcomes

Question 8

Probability: 2 Ind Outcomes both happening

Answer 8

probability of event A x probability of event B

Question 9

Combination

Answer 9

• order doesn’t matter
  possible combinations = # of element A x # of B x # of C…

Question 10

Percent: find x % of given # n

Answer 10

n(x/100)

Question 11

Percent: what % a # n is of another # m

Answer 11

(100n)/m

Question 12

Percent: what # n is x % of

Answer 12

(100n)/x

Question 13

Pythagorean Theorem

Answer 13

a^2 + b^2 = c^2

Question 14

Special Right Triangles

Answer 14

30-60-90 degrees: side lengths are x, x√3, 2x
45-45-90 degrees: side lengths are x, x, x√2

Question 15

Area of a Trapezoid

Answer 15

A = ((a+b)/2)h
- a & b are parallel sides
(bases)

Question 16

Area of a circle

Answer 16

A = πr^2

Question 17

Area of an arc

Answer 17

A = (πr^2)(deg measure of center of arc/360)

Question 18

Circumference

Answer 18

C = 2πr or C = πd

Question 19

Circumference of an arc

Answer 19

(2πr)(deg measure of center of arc/360)

Question 20

Circle Equation (given center point & radius)

Answer 20

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

Question 21

Volume of a Cylinder

Answer 21

V = πr^2h

Question 22

Trig- SOH, CAH, TOA

Answer 22

sine = opp/hypotenuse
cosine = adj/hyp
tangent = opp/adj

Question 23

Trig- Cosec, Sec, Cot

Answer 23

Cosecant- reciprocal of sin
Secant- recip of cos
Cotangent- recip of tan

Question 24

Trig- sine & cosine

Answer 24

sin^2x + cos^2x = 1
sinx / cosx = tanx

Question 25

Area of a parallelogram

Answer 25

A = bh

Question 26

Arithmetic Sequence: Missing Term

Answer 26

an = a1 + (n-1)d
- a1: first term in seq
- an: missing term you need
- d: common difference

Question 27

Arithmetic Sequence: Sum of terms

Answer 27

S = (n/2)(a1 + an)

Question 28

Geometric Sequence: Missing Term

Answer 28

an = a1(r^n-1)
- r is raised to the n-1 power (r is multiplier)