ACT Math Equations to Know

Given the two horizontal lines are parallel, what angles (the numbers) are equal?

∠1 = ∠4 = ∠5 = ∠8

and

∠2 = ∠3 = ∠6 = ∠7

Formula for area of a triangle

$$area = \frac{1}{2} b h$$

Formula for area AND perimeter of a rectangle

$$area = w l$$

$$perimeter = 2w + 2l$$

Formula for area of a square

$$area = s²$$

Formula for area AND perimeter of a circle

$$area = \pi r²$$

$$perimeter = 2 \pi r$$

Formula for area of a trapezoid

$$area = \frac{1}{2} (b_1 + b_2)h$$

Formula for volume of a rectangular prism

$$volume = lwh$$

Formula for volume of a cube

$$volume = s³$$

Total interior angles of a triangle

180

Total interior angles of a rectangle/4 sided shape

360

Formula for Pythagorean Theorem

$$a²+b²=c²$$

Formula for the slope of a line given 2 points

$$slope = m = \frac{rise}{run} = \frac{y_1 - y_2}{x_1 - x_2}$$

Formula to find the midpoint between 2 points

$$midpoint = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$$

Formula to find the distance between two points

What are integers?

Whole numbers (Ex: −4, 3, 102)

What are prime numbers?

Prime Numbers are integers that are only divisible by 1 and itself (Ex: 2, 3, 5, 7, 11 …).

Note that 1 is not a prime number and 2 is the only prime even number.

What are rational numbers?

Rational numbers are any number that can be expressed as a fraction (Ex: $\frac{2}{5}$, $- \frac{11}{3}$). Any integer is also a rational number (Ex: −22, 3, 600, 12).

What are irrational numbers?

Irrational numbers are any numbers that cannot be expressed as a fraction (Ex: $\pi$, √5).

What are undefined numbers?

Undefined numbers are numbers with a zero in the denominator (Ex: $\frac{6}{0}$ ).

What are imaginary numbers?

Imaginary numbers are real numbers multiplied by the imaginary unit & (Ex: −3i, 8i).

What is the mean?

Mean is the average.

What is the median?

When a set of numbers are ordered from lowest to highest, the median is the middle number.

Ex) 1, 2, 3, 4, 5 ← median is 3

Ex) 1, 2, 3, 4 ← median is 2.5 (in an even set of numbers, take the middle two numbers and divide by 2)

What is mode?

The mode is the number that appears most often in a set of numbers.

Ex) 1,1, 1, 2, 3, 4, 5 ← Mode is 1

What is the range?

The range is the lowest number, minus the highest number. It is the difference between the highest and lowest number.

What is the Greatest Common Factor (GCF)?

A set of numbers is the largest positive integer that divides evenly into all numbers in the set with no remainder. For example, for the set of numbers 12, 18, and 30, the greatest common factor is 6.

What is the Least Common Multiple (LCM)?

The smallest positive integer that is divisible by all numbers in the set. For example, the least common multiple of 2 and 3 is 6