Algebra Final Exam

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Math 012 6386 Final Exam Spring 2019 ID: 8 ©H `2u0a1N9v FKkuvtMam LSJoofFtSwAayrVeu \LeLMCM.K S oAPlzl] ursiKgrhJt[sk TrsehsZeCrHvheFdF.

-1-

Solve each equation.

1) 3(a - 6) = 8(a - 1) 2)

1

3 n +

23

6 n = -

5

2

Solve each inequality, write its solution set in interval notation, and graph the solution set on a number line.

3) 6(2a + 2) ³ -4 + 5(a - 1) 4) -

2

3 - 1

1

3 m ³

19

3

Solve each compound inequality, write its solution set in interval notation, and graph the solution set on a number line.

5) -12 < 5m + 3 £ 8 6) -

11

10 < -

1

2 x <

7

10

Write the equation of the line described in standard form, Ax + By = C, where A, B, and C are integers.

7) through: (3, -2), perpendicular to y = 3 7 x - 5

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-2-

Rewrite the equation in slope-intercept form and then use the slope and y-intercept to sketch a graph of the line with the given equation.

8) 3x + 5y = 5

Show all work as you solve the linear modeling problem below.

9) In 1965, 42.4% of American adults described themselves as regular cigarette smokers. By 2010, only 19.9% of American adults described themselves as regular cigarette smokers. Write a linear equation that models this decline in smoking. Let x represent the number of years after 1965 and let y represent the percentage of American adults who described themselves as regular cigarette smokers.

Simplify. Your answer should contain only positive exponents.

10) 5u2v2 × 2u5v3 11)

3b0 × -4a4b3

a4

12) (-3x3y-4)-4 13) (x4y2)2 × -2x-2y2

Perform the indicated operation and simplify.

14) (6x3 + 4x4 - 3) - (3x - 1 - 3x3)

Multiply as indicated and simplify.

15) (6n - 3)(4n2 - 7n + 8)

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-3-

Solve the equation by factoring.

16) 3k2 = -17k - 24

Solve the equation by completing the square.

17) p2 - 2p - 20 = -3

Solve the equation by use of the quadratic formula.

18) 4a2 - 1 = 2a

State the excluded values for the following expression. Then simplify the expression.

19) 10n2 + 50n n2 - 3n - 40

Solve the equation and show the check of the potential answer(s). If any answers are excluded values, state this on your answer sheet.

20) 3n - 9

n2 - 11n + 30 - 1 =

1

n2 - 11n + 30

Simplify the radical expressions.

21) 216x3yz4 22) ( 5 + 4)(-4 5 - 2)

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-4-

Solve the equation and show the check of the potential answer(s). If any answers are extraneous solutions, state this on your answer sheet.

23) -a + 4a + 8 = 3

Show all work as you solve the following problems and write complete answers, including appropriate units.

24) Eugene left school and traveled west. Mary left one hour later traveling 20 mph faster in an effort to catch up to him. After two hours Mary finally caught up. What was Eugene's average speed?

25) Christine put $48,000 in an education account on the day her daughter was born. If the account earned 4.55% interest compounded quarterly, what was the total in the account when her daughter turned 18? Round the final answer to the nearest cent.