Final Exam Review

Systems

100

2x + y = 4

3x + y = 3

(-1, 6)

200

x = y - 7

-y - 2x = 8

(-5, 2)

300

x + y = 12

2x + 5y = 27

(11, 1)

400

y = 1/3 x - 6

y = -2x + 1

(3, -5)

500

The Smith family needs to repair their car. Motor Works charges $650 for parts and $70 an hour for labor. Jim's Car Care charges $800 for parts and $55 an hour for labor. For how many hours of labor will both car repair places cost the same?

10 hours

Polynomials

100

(3x⁵)(2xy)

6x⁶y

200

(3x³y²)(2xy⁴)(1/2 x²y⁸)

3x⁶y¹⁴

300

2x(x² - 4x + 6)

2x³ - 8x² + 12x

400

(2x + 6)(4x + 5)

8x² + 34x + 30

500

(x - 2)(x² + 4x - 5)

x³ + 2x² - 13x + 10

Factoring

100

5x - 15x³

5x(1 - 3x²)

200

40x² - 10x + 30

10(4x² - x + 3)

300

x² - 8x + 12

(x - 6)(x - 2)

400

3x² - 11x - 4

(3x + 1)(x - 4)

500

121x² - 25

(11x - 5)(11x + 5)

Exponents and Roots

100

 √81x⁴y¹⁰

9x²y⁵

200

(25x²y⁶)^1/2  √ x⁸y¹²

5x⁵y⁹

300

 √40

2 √ 10

400

 √180

6 √ 5

500

 √112

4 √ 7

Anything goes

100

-3(2 - x) > 6(x + 1)

x < - 4

200

6 / (3x - 1) =  5 / (x + 2)

x = 17/9

300

the length of a rectangle is 6 inches more than the width. What are the dimensions if the perimeter is 54 inches?

width is 10.5, length is 16.5

400

Solve.

4x² - 36x = -81

x = 4.5

500

A rectangle is twice as long as it is wide. The area of the rectangle is 32 square feet, Find the width.

4 ft