MAT110 Final Review

Real Numbers

100

Provide an example of a Natural Number.

{1, 2, 3, 4, 5, ...}

200

Provide an example of a Whole Number.

{0, 1, 2, 3, 4, 5, ...}

300

Provide an example of an Integer.

{... -3, -2, -1, 0, 1, 2, 3, ...}

400

Provide an example of a Rational Number.

{a/b: a, b are integers and b does not equal zero}

500

Provide an example of an Irrational Number.

Infinite decimal that does not repeat

Solving Equations & Inequalities

100

Solve this equation.

2(2x+5)+5(x-7)=5(3x+1)

x=-5

200

Solve this equation.

5|1-x|-15=0

x=-2 or x=4

300

Solve this inequality.

-4x+3<19

x>-4

For a bonus, express this solution on a number line.

400

Solve this inequality.

-2|x-4|+11>-3

-3<x<11

For a bonus, express this solution on a number line.

500

A car can be rented from Company A for $80 a day plus $0.90 per mile. Company B charges $100 a day plus $0.50 per mile to rent the same car. How many miles must be driven in a day to make the rental cost for Company A a better deal than Company B's?

Less than 50 miles must be driven in a day for Company A to be a better deal than Company B.

Exponent Rules

100

Simplify this expression. Make sure all exponents are positive.

x³ _* x⁶

x⁹

200

Simplify this expression. Make sure all exponents are positive.

x²/x⁵

1/x³

300

Simplify this expression. Make sure all exponents are positive.

(4x³y)²

16x⁶y²

400

Simplify this expression. Make sure all exponents are positive.

(2j²k⁵)(3j⁷k³)

6j⁹k⁸

500

Simplify this expression. Make sure all exponents are positive.

6x³y⁸/3xy⁷

2x²y

Linear Equations

100

What is the slope and y-intercept of this linear equation?

y=-3x+5

m=-3

b=5

200

Find the x-intercept and y-intercept of this linear equation.

2x-4y=8

x=4

y=-2

300

Convert this equation into Slope-Intercept Form.

6x+3y=-12

y=-2x-4

400

Convert this equation into Slope-Intercept Form.

y-3=-7(x-1)

y=-7x+10

500

Write an equation of a line in Slope-Intercept Form passing through (-2, 5) and parallel to the line y=3x+1.

y=3x+11

Graphs

100

Find f(2).

f(2)=0

200

Find f(0).

f(0)=-1

300

What is the Domain?

[0, 5)

400

What is the Range?

[-1, 5)

500

Find f(5).

f(5) is undefined.