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Act Math Formulas That You Must Know
Act Math Formulas: Let’s take a look at the Math section of ACT. Six areas of high school mathematics are covered by 60 multiplechoice questions. Follow centralfallout to get updated.
They include prealgebra and elementary algebra as well as intermediate algebra, coordinate geometry, plane geometry, trigonometry, and interpolation. This is how the scoring works and what math formulas are required.
 PreAlgebra / Elementary Algebra: 24 Questions, 24 Points
 Intermediate Algebra / Coordinate Geometry: 18 Questions, 24 Points
 Plane Geometry/Trigonometry: 18 Questions and 24 Points
The problem with the ACT’s math section is that even with all your ACT math prep, you won’t receive a cheat sheet with all the formulas written on it.
It’s up you to memorize, learn and understand these formulas. Some formulae are more important than others for ACT math. These are the essentials. It’s tempting to make guesses and then move on, but it’s better to be prepared.
PreAlgebra / Elementary Algebra
Table of Contents
These algebra formulas require basic math and algebra. It requires that the student solves for an unknown variable.
1. Arithmetic mean = Sum of Values / Number Of Terms
This is used to determine the average value of a set of numbers.
For example, (10 + 12 + 14 + 16,) / 4 = 13.
2. Probability = Target outcomes/Total outcomes
This is used to determine the likelihood of something happening from a set possible outcomes.
Example: A jar may contain five blue, five red, and ten white marmalades. How likely is it that you will randomly pick a red marble?
5 / 20 = 0.25 or 25%
3. Quadratic Formula: x = b + b24ac/2a
This is used to determine the xintercepts for a quadratic equation (parabolic).
Example: A = 1, C = 4, D = 4.
x = 4 + 42 – 4 (1)(4)/ 2(1)
= 4 + 16 – 4(4) / 2.
x = 4 + 16 – 16/ 2.
= +4 +0 / 2
x = 4 / 2
x = 2
Intermediate Algebra / Coordinate Geometry
These formulas can be used to calculate distances, lengths and other properties of points on a plane as well as to solve complex algebraic equations for variables.
4. Distance Formula: d=x1x2+ (y1y2)2
This calculates the distance between two points in a coordinate plane.
For example, find the distance between points (6.6) and (2.3)
d=(6 – 2)2 + (6 – 3)2
d=(4)2 + (3)2
d=16 + 9
d=25
d = 5.
5. Slope Formula: Slope = (y2 – y1 /(x2 – x1)
Calculates the slope (angle), of a line connecting two points on a plane.
For example, coordinates = (2.1) (4.3)
s = 3 + (1) / 4 (2)
= 4/6
s = 2/3
6. Slope Intercept:
A formula that defines a line on an plane given a slope and yintercept.
Example: Slope = 2, Intercept Point (0,3)
y = 2x+3
7. Midpoint Formula: (x1+x2) / 2, (y1+y2) / 2
Calculates the midpoint between two points on a plane.
For example, find the middle point between (1, 2, and (3, 6).
(1 + 3) / 2, (2 + 6) / 2
2 / 2, 4 / 2
Midpoint (1, 2)
Act Math Formulas: Plane Geometry
Formulae for calculating attributes of geometric shapes within planes and solving variables based upon the angles of a particular shape (trigonometric identity).
8. Area of Triangle: area = (1/2), (base) (height).
Calculates the area of a triangle by taking into account the lengths and sides.
Example: Base = 5, Height = 8.
A = 1/2 (5)(8)
= 1/2 (40).
A = 20
9. Pythagorean Theory: a2+b2=c2
This is used to determine the length of an unidentified side of a right triangular, provided that two sides are known.
Example: a = 3; b = 4.
c2 = 32 + 42
= 9 + 16
c2 = 25
c = 25
c = 5.
10. Area of Rectangle = area = length x breadth
Calculates the area of a rectangle.
For example, length = 5 and width = 2.
A = 5 x 2.
A = 10
11. Area of Parallelogram: area = height x base
Calculates the area of a parallelogram.
Example: Base = 6; Height = 12
A = 6 x 12.
A = 72
12. Area of Circle:
Calculates the area of a circle.
For example: radius = 4
A = p x 42
= p x 16.
a = 50.24
13. Circumference of the Circle: circumference = 2p * R
Calculates the circumference of a circle’s length.
For example: radius = 7
c = 2px7
c = 43.98
Act Math Formulas: Trigonometry
Continue reading the previous section on plane geometry. These terms should be understood before you proceed.
 Sine Equals Opposite to Hypotenuse
 CAH: Cosine equals Adjacent to Hypotenuse
 TOA: Tangent equals Opposite over Adjacent
14. Sine (SOH: Sine = opposite/hypotenuse
Trigonometric identity is a trigonometric representation of the relative sizes of sides of a triangle. It can also be used for calculating unknown angles or sides of the triangle.
Example: Hypotenuse = 4.9, opposite = 2.8
s = 2.8/4.9
s = 0.57
15. Cosine (CAH: Cosine = adjacent/hypotenuse
Trigonometric identity is a trigonometric representation of the relative sizes of sides of a triangle. It can also be used for calculating unknown angles or sides of the triangle.
Hypotenuse = 13, adjacent = 11
c = 11/13
c = 0.85
16. Tangent (TOA): Tangent = opposite / adjacent
Trigonometric identity is a trigonometric representation of the relative sizes of sides of a triangle. It can also be used for calculating unknown angles or sides of the triangle.
Example: adjacent = 15 and opposite = 15.
t = 15/8
t = 1.87
17. Sine – SOH
SineΘ=
opposite 
hypotenuse 


 Opposite = the side of the triangle directly opposite the angle Θ
 Hypotenuse = the longest side of the triangle

Sometimes the ACT will make you manipulate this equation by giving you the sine and the hypotenuse, but not the measure of the opposite side. Manipulate it as you would any algebraic equation:
SineΘ=
opposite 
hypotenuse 
=> hypotenuse*sineΘ=opposite
18.Cosine – CAH
CosineΘ=
adjacent 
hypotenuse 



 Adjacent = the side of the triangle nearest the angle Θ (that creates the angle) that is not the hypotenuse
 Hypotenuse = the longest side of the triangle


19.Tangent – TOA
TangentΘ=
opposite 
adjacent 



 Opposite = the side of the triangle directly opposite the angle Θ
 Adjacent = the side of the triangle nearest the angle Θ (that creates the angle) that is not the hypotenuse


20.Cosecant, Secant, Cotangent


 Cosecant is the reciprocal of sine
 CosecantΘ=
hypotenuse opposite
 CosecantΘ=
 Secant is the reciprocal of cosine
 SecantΘ=
hypotenuse adjacent
 SecantΘ=
 Cotangent is the reciprocal of tangent
 CotangentΘ=
adjacent opposite
 CotangentΘ=
 Cosecant is the reciprocal of sine

21.Useful Formulas to Know
Sin2Θ+Cos2Θ=1
SinΘ 
CosΘ 
=TanΘ
Other Tips: Act Math Formulas
There are many other formulas, but these are the most popular. These formulas are the most important to remember. These formulas are essential to remember, so practice them and you’ll be fine for the test.
Important Note about ACT Math Formulas
Sometimes, ACT math problems may require a more complex formula such as the surface area for a sphere. These cases will usually be answered in the question. There is no need to assume you have to know everything. But being able to remember basic formulas will help you tackle any problem that doesn’t include one. Below is a list of formulas that are most commonly tested on the ACT.
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