Introduction to Algebra I/Pre-Algebra Review

Laws of Exponents

100

In this law, the exponents add.

What is (x^m)(xⁿ)=x^m+n?

200

In this law, the exponents subtract.

What is (x^m)/(xⁿ)=x^m-n?

300

In this law, the exponents multiply.

What is (x^m)ⁿ=x^mn?

400

In this law, the solution is 1.

What is x⁰=1?

500

In this law, the base and the exponent is inverted.

What is (1/x)^-m=x^m?

Linear Equations

100

The slope-intercept equation

What is y=mx+b?

200

Solve for x:

9x+3=30

What is x=3?

300

Solve for x:

3(x-6)=3x-18

What is x=x?

400

Solve for x:

x+10=x

What is no solution?

500

This is the point-slope equation.

What is y-y₁=m(x-x₁)?

Linear Systems

100

Solve:

y=x+3

y=2x

What is (3,6)?

200

Solve:

4x-y=-14

5y-2x=16

What is (-3,2)?

300

Solve:

2x-5y=23

3x+4y=0

What is (4,-3)?

400

Solve:

y=26-3x

3x=2y-16

What is (4,14)?

500

An athletic club has two payment options.  Option A has a membership fee of $49 and weekly dues of $10.50.  Option B has a membership fee of $10 and weekly dues of $12.  After how many weeks would the cost be the same for Options A and B?  What is the cost for that many weeks?

For a 26-week membership, Option A and Option B cost the same amount, $322.

Polynomial Expressions

100

(a+b)²

What is a²+b²+2ab?

200

-10x¹²(-xy)

What is 10x¹³y?

300

(2x²-x+2)+(-x²+3x-1)

What is x² + 2x+1?

400

(5a-3b)(2a-4b)

What is 10a²-26ab+12b²?

500

This is what FOIL stands for.

First

Outer

Inner

Last

Solving Basic Inequalities

100

—2x—1 ≥ 5

x ≤ —3

200

3x ≥ 7x + 12

—3 ≥ x, or x ≤ —3

300

These two words form compound inequalities. 

What are and and or?

400

x/2 < 5 - (3x)/4

What is x < 4?

500

E-Glou Communications offers two text messaging plans. The monthly fees are shown below.

Plan A: $9.99 plus $.03 per message                                       Plan B: $4.99 plus $.05 per message

For how many messages is plan A cheaper than plan B?  Let m be the number of text messages.

m > 250