25 Problems of Intermediate Algebra

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Math 012 7382 Final Exam, Summer 2015 ID: 27 ©A A2Z0D1P5d SKJuTtXaY kScoPf^tyw[aSrSeL sLULsCp.m K `Akl\lA FrNiYgbhttGsR zrceRseeprdv^eKdL.

-1-

Solve each equation.

1) 2(-4k - 6) = k - (3k + 6) 2) -

4

15 = v +

4

3 +

3

5 v

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

3) 2(a + 1) - 2(7 - 5a) ³ 8a + 3a 4)

1

4 -

2

5 k ³

17

20

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

5) -44 < -2 - 6x < 22 6) -

17

12 < n -

5

3 £ -

1

3

Write the standard form of the equation of the line described.

7) through: (3, -3), perpendicular to y = - 3 2 x - 4

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) 7x - 2y = 6

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-2-

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

9) There were 116 Apple stores worldwide in 2005 and 438 Apple stores worldwide in 2014. Write a linear equation in slope-intercept form that models this growth. Let x stand for the number of years after 2005 and let y = the number of Apple stores worldwide.

Simplify. Your answer should contain only positive exponents.

10) 3x2 × 2x5y3 11) -

4a3b4 × 3a-3

2a3b2

12) (2a3) -4 13) -2x4y-1 × (2x-2y-5)4

Perform the indicated operation and simplify.

14) (4x2 - 2x + 6x3) - (2x4 + x3 - 5x2)

Multiply as indicated and simplify.

15) (7n - 7)(n2 - 5n + 4)

Solve the equation by factoring.

16) 3b2 = 16b + 35

Solve the equation by completing the square.

17) x2 - 2x - 67 = 4

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-3-

Solve the equation by use of the quadratic formula.

18) 5x2 = 5 + 4x

Simplify the expression and state the excluded values.

19) x2 - x - 20 x2 + 3x - 4

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) 1 = b - 2 b + 4

+ 4b + 8

b2 + 3b - 4

Simplify the radical expressions.

21) 512m2pq3 22) (-2 + 3 )(4 + 3 )

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) 4 = -x + x + 46

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-4-

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

24) Mark left Totsakan's house and drove toward the lake. One hour later DeShawn left driving 13 km/h faster in an effort to catch up to him. After four hours DeShawn finally caught up. What was Mark's average speed?

25) Jennifer put $17,000 in an education account on the day her daughter was born. If the account earned 6.55% interest compounded quarterly, what was the total in the account when her daughter turned 18? Round the final answer to the nearest cent.