MATH 023 Final Exam Review

Linear Equations & Inequalities

100

Evaluate. x = -7, y = -4, z = 8 -4x² - 5y + 11z

-88

200

Solve. 12x + 36 < -4(x - 8)

x < -1/4

300

Solve for r. A = P(1 + r*n)

(A - P) / (P*n)

400

A car rental business rents a compact car at a daily rate of $43.50 plus 25¢ per mile. Mike can afford to spend $96.50 on the car rental for one day. What is the maximum number of miles he can drive and stay within his budget?

212 miles

500

Solve. -4(x + 9) - (-4x - 36) = 0

Infinitely many solutions

Graphing

100

The slope of the line that passes through (-4, 9) and (-5, -3).

12

200

These are the intercepts of the line -4x + 7y = 28

x-intercept: (-7, 0) y-intercept: (0, 4)

300

This is the equation of the line with a slope of -1/3 that passes through (-9, 4).

y = (-1/3)x + 1

400

This is the equation of the line that passes through (-8, -4) and (-3, -1)

y = (3/5)x + (4/5)

500

Graph y = (-2/5)x - 3

Check with your instructor

Exponents & Polynomials

100

(-7)²

49

200

(4x³y⁵z⁸)⁴

256x¹²y²⁰z³²

300

-8x⁴(-6x³+x²-9x+1)

48x⁴⁸-8x⁶+72x²-8x

400

(5x - 7)(x + 9)

5x² + 38x - 63

500

(5a^-4b^-7)^-3

(1/125)a¹²b²¹

Factoring & More Polynomials

100

This is the GCF. 9x⁵ and -36x³

9x³

200

Multiply. (-3w - 7)²

9w² + 42w + 49

300

Factor. p² - 2p - 35

(p - 7)(p + 5)

400

Factor. 27x³ + 64

What is (3x + 4)(9x² - 12x + 16)

500

Factor. 6x³ - 39x² + 60x

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

Applications

100

A local business produced 5,400 widgets last month. Their total revenue from selling all of these widgets was $45,900,000. Assuming the same rate per unit, how much revenue did each unit produce? Express your answer in scientific notation.

8.5 X 10³

200

Suzie drove to her friend's house for a holiday weekend. The total distance (one-way) was 211 miles and it took her 13 hours. How fast was Suzie driving? Round answer to the nearest whole number.

16 mph

300

A moving firm charges a flat fee of $35 plus $60 per hour. Let y be the cost in dollars of using the moving firm for x hours. Find the slope-intercept form of the equation.

y = 60x + 35

400

If Rebecca received a 3.5% raise and is now making $42,500 a year, what was her salary before the raise? Round to the nearest dollar.

$41,063

500

(9n⁴ - 5n⁵ + 6) - (12n⁵ - 4n⁴ + 7)

5n⁴ + 7n⁵