8th Grade Algebra

Equations & Pythagorean Theorem

100

State the Pythagorean Theorem.

a² + b² = c²

200

Solve for x.

12 = 11x + 10

x = 2/11

300

Define hypotenuse.

The side directly across from the right angle in a right triangle. 

OR

The largest side of a right triangle.

400

Solve for y.

12(6+2y) = 4y - (5-9y)

y = -7

500

Find the missing side length x in a right triangle. Give an exact answer.

Hypotenuse = 18

Legs = 14 and x

square root of 128

Exponents

100

Simplify.

a⁶ * a³

a⁹

200

Simplify.

x⁶/x⁶

1

300

Simplify.

2²/2^-9

2¹¹

400

Simplify.

(7y⁴)²

49y⁸

500

Simplify.

(p⁴q⁵r)⁹

p³⁶q⁴⁵r⁹

Linear Functions

100

Find the slope of the line between the points (-1,3) and (5,11).

(Make sure to simplify!)

m = 4/3

200

What is the slope of a horizontal line?

m = 0

300

What is the slope of a vertical line?

Undefined

400

What is the equation of the line that passes through points (0,24) and (2,14)?

y = -5x + 24

500

What is the equation of the line that passes through points (2,12) and (5,57)?

y = 15x - 18

Number of Solutions

100

Based on the equation, determine the number of solutions.

3 = 4

No Solution

200

Based on the equation, determine the number of solutions.

0 = 0

Infinite Solutions

300

Based on the equation, determine the number of solutions.

2x + 1 = 2x + 2

No Solution

400

Based on the equation, determine the number of solutions.

3x = 0

One solution

x = 0

500

Based on the equation, determine the number of solutions.

2x - 3 = 3 - 2x

One solution

x = 3/2

Polynomials

100

Identify the degree of the polynomial.

11a⁵ + a - 6

5

200

How many terms are in a monomial?

1 term

300

Simplify and write in standard form.

10 - 4x + x⁵ + 3x² - x - 6x²

x⁵ - 3x² - 5x + 10

400

Find the product and write in standard form.

(5x - 3)(2x + 1)

10x² - x -3

500

Find the product and write in standard form.

(3x² + x - 5)(2x - 7)

6x³ - 19x² - 17x + 35