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 multiple-choice questions.  Follow centralfallout to get updated.

They include pre-algebra 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.

• Pre-Algebra / 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.

Pre-Algebra / Elementary Algebra

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 + -b2-4ac/2a

This is used to determine the x-intercepts 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=x1-x2+ (y1-y2)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

    • Secant is the reciprocal of cosine
      • Secant‌Θ=
        

        hypotenuse

        adjacent

    • Cotangent is the reciprocal of tangent
      • Cotangent‌Θ=
        

        adjacent

        opposite

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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