ACT Math Memorization
Intermediate Algebra
Concept
Quadratic Formula
Arithmetic Sequences
Geometric Sequences
Complex Numbers
Logarithms
Formula
−𝑏 ± 𝑏 & − 4𝑎𝑐
𝑥=
2𝑎
𝑎- = 𝑎. + 𝑛 − 1 𝑑
𝑛 𝑎. + 𝑎=
2
-
Variable Meaning
𝑦 = 𝑎𝑥 + 𝑏𝑥 + 𝑐
&
𝑎. = first term and d = common
difference
- = partial sum of first n terms,
𝑎- = last term
r = common ratio
- = partial sum of first n terms
𝑎- = 𝑎. 𝑟 -3.
45 .36 7
- =
.36
𝑖 = imaginary number
𝑏 = base of logarithm
𝑖 = −1 and 𝑖 & = −1
Log form: 𝑙𝑜𝑔< 𝑥 = 𝑛
Exponential form: 𝑏 - = 𝑥
Coordinate Geometry
Concept
Slope
Slope-intercept form
Distance between two points
Midpoint
Parabola
𝑦& − 𝑦.
𝑚=
𝑥& − 𝑥.
𝑦 = 𝑚𝑥 + 𝑏
Formula
𝑥& − 𝑥. & + 𝑦& − 𝑦.
𝑥. + 𝑥& 𝑦. + 𝑦&
𝑀=
,
2
2
3< @4A3< B
Vertex located at
,
𝑑=
&4
Axis of symmetry: 𝑥 =
Circle
𝑥−ℎ
&
+ 𝑦−𝑘
&
Ellipse
𝑥−ℎ
𝑎&
&
𝑦−𝑘
+
𝑏&
&
@4
3<
&4
= 𝑟&
=1
&
Variable Meaning
𝑥. , 𝑦. and 𝑥& , 𝑦& are points in
the coordinate plane
m = slope
b = y-intercept of the line
d = distance
M = midpoint coordinate
𝑦 = 𝑎𝑥 & + 𝑏𝑥 + 𝑐
ℎ, 𝑘 = center of circle
r = radius of circle
ℎ, 𝑘 = center of ellipse,
a = length of horizontal axis
b = length of vertical axis
Plane Geometry
Concept
Formula
Circle
𝐶 = 2𝜋𝑟
𝐴 = 𝜋𝑟 &
Triangle
1
𝐴 = 𝑏ℎ
2
Pythagorean Theorem
𝑎& + 𝑏& = 𝑐 &
Square
𝑃 = 4𝑠
𝐴 = 𝑠&
Rectangle
𝑃 = 2𝑏 + 2ℎ
𝐴 = 𝑏ℎ
𝑃 = 2𝑏 + 2ℎ
𝐴 = 𝑏ℎ
𝑆𝑢𝑚 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒𝑠
= 180° 𝑛 − 2
𝑉 = 𝑙𝑤ℎ
𝑆𝐴 = 2𝑙𝑤 + 2𝑤ℎ + 2𝑙ℎ
Parallelogram
Other Polygons
Rectangular Prism (Solid)
Sphere
Cylinder
Cone
4
𝑉 = 𝜋𝑟 V
3
𝑆𝐴 = 4𝜋𝑟 &
𝑉 = 𝜋𝑟 & ℎ
𝑆𝐴 = 2𝜋𝑟 & + 2𝜋𝑟ℎ
1
𝑉 = 𝜋𝑟 & ℎ
3
𝑆𝐴 = 𝜋𝑟 & + 𝜋𝑟𝑠
Variable Meaning
C = circumference of circle
r = radius of circle
A = area of circle
A = area of triangle
b = length of base
h = perpendicular height to base
a and b = lengths of shorter sides
c = length of hypotenuse
P = perimeter of square
s = length of side
A = area of square
b = base of rectangle
h = height of rectangle
b = base of parallelogram
h = perpendicular height
n = number of sides of polygon
V = volume
SA = surface area
l = length
w = width
V = volume
SA = surface area
r = radius of sphere
r = radius of cylinder
h = height of cylinder
r = radius of cone
h = height of cone
s = slant height = 𝑟 & + ℎ&
Trigonometry
Concept
Trigonometric Ratios
Formula
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑠𝑖𝑛𝜃 =
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑐𝑜𝑠𝜃 =
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑡𝑎𝑛𝜃 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Variable Meaning
sin = sine
cos = cosine
tan = tangent
𝜃 = “theta” reference angle
SOH – CAH - TOA