ACT Prep Math Review

Multistep Equations

100

Solve: 5y - 8 = 3y + 12

y=10

200

Solve: 11 - m = 51 - 6m

m=8

300

Solve: -16 -7(2a + 3) = 23 - 2a

a=-5

400

Solve: 3x - 13 = 7(x + 2) -4(x - 7)

0=55; No Solution

500

Solve: 3(2x + 2) - 3x = 6 + 3x

0=0; Infinite Solutions

Pythagorean Theorem

100

Given a right triangle with legs a, b and hypotenuse c, solve for c if a = 3 and b = 4

5

200

Given a right triangle with legs a, b and hypotenuse c, solve for a if b = 20 and c = 29

21

300

Given a right triangle with legs a, b and hypotenuse c, solve for b if a = 72 and c = 75

21

400

A roofer leaned a 16-foot ladder against a house. If the base of the ladder is 5 feet from the house, how high up the house does the ladder reach?

15.23 feet

500

A 31-foot support wire is attached from the top of a 25 foot telephone pole to a point on the ground. How far from the base of the pole does the wire meet the ground?

18.3 feet

Angle Relationships

100

∠1 and ∠2 are vertical angles. If the   measure of ∠2 is 105°, find the measure of   ∠1.

105

200

∠A and ∠B are complementary angles. If   the measure of ∠A is 42°, find the measure   of ∠B.

48

300

∠1 and ∠2 form a linear pair. If the   measure of ∠1 is 113°, find the measure of   ∠2.

67

400

∠P and ∠Q are supplementary angles. If   m∠P = (4x + 1)° and m∠Q = (9x – 3)°, find   m∠Q.

123

500

∠1 and ∠2 form a linear pair. The   measure of ∠2 is six more than twice the   measure of ∠1. Find m∠2.

122

Distance & Midpoint

100

Find EF given E(-7, -2) and F(11, 3)

18.7

200

Find the midpoint of GH given G(7, -5) and H(9, -1).

(8,-3)

300

Find the coordinates of A if M(-1, 2) is the midpoint of AB and B has coordinates of (3, -5).

(-5,9)

400

If P is the midpoint of XY, XP = 8x – 2, and PY = 12x – 30, find the value of x.

7

500

If G is the midpoint of FH, FG = 14x + 25, and GH = 73 – 2x, find FH.

134

Area, Perimeter & Volume

100

What is the perimeter of a rectangle where length=5 feet and width=3 feet?

16 feet

200

What is the area of a rectangle where length=20 feet and width=15 feet?

300 feet²

300

What is the volume of a cube where length=10 feet, width=10 feet, and height=5 feet?

500 feet³

400

New tile is being laid in the classroom. The room is 40 feet long and 22 feet wide. If each square tile is 6 inches x 6 inches, how many tiles will you need to cover the floor?

25 tiles

500

A large oriental rug measuring 12 ft x 16 ft is placed in the center of a living room, leaving a border of four feet on each side between the rug and the wall. What is the area of the living room?

480 feet²