Math 8- Final Review

Laws of Exponents

100

(x⁴y³)(-3x²y)

-3x⁶y⁴

200

(15x⁶y⁴)

_______

(3x²y)

5x⁴y³

300

Rewrite using a positive exponent: x^-3

 1

__

 x³

400

(2x³y⁴)²

4x⁶y⁸

500

(4x²y³)²

^_________

  8x³y²

2xy⁴

Properties

100

(4+7)+3 = 4+(7+3)

Associative Property

200

x(y+z)=xy+xz

Distributive Property

300

a+(b+c)=a+(c+b)

Commutative Property

400

4+(-4)=0

Additive Inverse

500

a x 1 = a

Multiplicative Identity

Linear Equations/Slope

100

A horizontal line

Zero Slope

200

A vertical line

Undefined Slope

300

3x+y=9

y=-3x+9

400

Jack earns $18 per hour and a bonus of $20 at the end of the week.  Write an equation to determine how many hours, h, Jack needs to work to earn $164.

18h+20=164

500

Write an equation of the line that passes through the points (0,4) and (2,10).

y=3x+4

Functions/Equations

100

An equation is not linear if...

It has an exponent other than zero or one.

200

Solve for m:

m

__   + 3 =12

4

m=36

300

Solve for p:

2(p+12)=8p+18

p=1

400

How many solutions will the equation 5x+8=5x-2 have?  Explain how you know.

No solution because the variable has the same coefficient, and the constants are different.

500

Is the following set a function: {(12,4), (9,5), (12,9)}

Explain why or why not.

No because the x-value repeats itself.

Miscellaneous

100

What is 675,000,000 written in scientific notation?

6.75x10⁸

200

Suppose the measure of two adjacent angles that form a straight line are x and 3x.  Determine the value of x.

x=45

300

Translate into a mathematical expression: "Five less than twice a number"

2x-5

400

Determine the volume of a cylinder, in terms of pi, whose height is 10in and diameter is 24in.

V=1440pi

500

Determine the height of a cylinder whose volume is 32pi and diameter is 4.

h=8