Math ACT Formulas Vocab

Key formulas and concept that may appear on the Math section of the ACT. Good luck, and you've got this!

arithmetic sequence

a_n=a_k+ d(n-k)

geometric sequence

g_n = g_k r^(n-k)

rate formula

distance = speed (time)

variation formula

quantity= rate(time)

What does log_a b = c convert into?

a^c= b

f of g(x)

f(g(x)

average/mean

sum of all values/ the number of values

mode

the value that appears the most in a data set

median

the middle number or the average of the 2 middle numbers after arranging the data set from least to greatest

probability formula

target outcomes/ total outcomes

probability of two events

probability (A and B)= P(A) x P(B)

What are two non-adjacent interior angles in a triangle?

2 angles that do not share a vertex with a specific exterior angle

the “not” probability formula (probability an event will NOT happen)

P (not A)= 1- P(A)

percentage formula

(part/whole) x 100

quadratic formula

x= -b ±√(b²-4ac) / 2a

discriminant

(b²-4ac)

How many solutions if the discriminate > 0?

2 real solutions

How many solutions if the discriminate = 0?

1 real solution

How many solutions if the discriminate < 0?

no real solutions

Fundamental Counting Principle

if there are m ways to do one thing and n ways to do another then there are m x n ways

Pythagorean Theroem

a²+b²=c²

Acute Triangle

a²+b² > c²

Obtuse Triangle

a²+b² < c²

equation of a circle

(x-h)²+(y-k)²=r²

What is the method for finding the values of the center of a circle?

1) Locate h and k in the circle equation as the center is (h,k)

2) Reverse the signs. Always use the opposite sign from what you see in the parenthesis.

center of a circle

(h,k)

sum of interior angles of a polygon formula

(number of sides - 2) (180)

45-45-90 Right Triangle

x: x: x√2

30-60-90 Right Triangle

x: x√3, 2x

slope intercept form

y=mx+b

mid point formula

(x₁+x₂/2) , (y₁+y₂/2)

distance formula

d= √(x₂-x₁)² + (y₂-y₁)²

arc length formula

(central angle/360) 2πr

sector length

(central angle/360) πr²

area of a triangle

½bh

area of a circle

πr²

circumference of a circle

dπ

What is sin of an angle?

opposite/hypotenuse

What is cos of an angle?

adjacent/hypotenuse

What is tan of an angle?

opposite/adjacent

What is the trigonometric identity for 1?

sin²x+cos²x=1

What is the complex number i equal to?

√-1

logarithm product rule

log_b(x * y) = log_b(x) + log_b(y)

logarithm quotient rule

log_b(x/y)= log_b(x) - log_b(y)

logarithm power rule

log_b(x^c)= c*log_bx

Triangle Inequality Theroem

In order to be a triangle, the sum of any two sides, must be greater than the 3rd side

Pythagorean Triples

3:4:5

5:12:13

7:24:25

similar triangles

have the exact same angle measurements and proportional sides

congruent triangles

have the exact same shape, angle measurements, and side measurements

Triangle Midsegment Formula

if you connect the midpoints of two sides of any triangle, the resulting line segment (the midsegment) is always parallel to the third side and exactly half its length

compound interest formula

P(1+r/n)^nt

NOTE: n= number compounded per year (e.g. 12 times for months)

t= years

r= annual rate as a decimal

P= initial investment or principal

A small number divided by a LARGEST number is…

The smallest number because the original “small number” is being split up into the most amount parts

A big number divided by the SMALLEST number is..

The largest number because the original “large number” is being split up into the least amount of parts

Exterior Angle Theorem

the exterior angle of a triangle is equal to the sum of the two opposite (non-adjacent) interior angles

vertex form of a quadratic

y=a(x-h)²+ k

NOTE: The vertex is (h,k), and remember that h is the opposite sign of what is in the parenthesis

How do find the x coordinate of the vertex of a parabola in quadratic form?

-b/2a

equation of a hyperbola

((x-h)^²/a^²) - ((y-k)²/b²))

What does (h,k) stand for in a hyperbola?

(h,k) is the midpoint of the transverse axis (the distance between the two parabolas)

What does a stand for in the hyperbola formula?

a is half the length of the transverse axis

What does b stand for in the hyperbola formula?

b is half the length of the conjugate axis (segment that passes through center and endpoints)

What is the difference between a vertical transverse hyperbola and a horizontal transverse hyperbola?

• the h and k values are switched

• the resulting transverse and conjugate axis are switched

Volume of a right cylinder

V= πr²h

What are the foci of an eclipse?

Two points that are equal distant from the center. They can not be a part on the circle, and rather, a point IN the circle.

Binomial Cube Formula

(a - b)³= a³ -3a²b + 3ab²