Math 46 - Final Exam Sample Packet A

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the slope of the line.1) 11x + y = 9

A) m = - 111

B) m = 11 C) m = 119

D) m = -11

1)

2) -x + 5y = 30

A) m = - 15

B) m = 15

C) m = -1 D) m = 5

2)

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points.3) (8, -6) and (4, 7)

A) (a) - 413; (b) 13

4B) (a) 13

4; (b) - 4

13

C) (a) - 134; (b) 4

13D) (a) - 13

4; (b) 13

4

3)

Use the slope-intercept form to graph the equation.4) y = 2x + 4

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

4)

Appendix A - 1

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

Write an equation of the line with the given slope, m, and y-intercept (0, b).

5) m = 73, b = -3

A) y = - 73x + 3 B) y = 7

3x - 3 C) y = - 7

3x - 3 D) y = 7

3x + 3

5)

Find an equation of the line through the pair of points. Write the equation in the form Ax + By = C.6) (-6, -9) and (-4, 0)

A) -3x + 4y = 12 B) 3x - 4y = 12 C) -9x - 2y = -36 D) 9x - 2y = -366)

Find an equation of the line described. Write the equation in slope-intercept form if possible.7) Through (-10, -57) and (3, 8)

A) y = 15x - 55 B) y = - 1

5x - 59 C) y = 5x - 7 D) y = -5x - 107

7)

Solve. Assume the exercise describes a linear relationship.8) A faucet is used to add water to a large bottle that already contained some water. After it hasbeen filling for 3 seconds, the gauge on the bottle indicates that it contains 10 ounces of water.After it has been filling for 11 seconds, the gauge indicates the bottle contains 26 ounces of water.Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write alinear equation that models the amount of water in the bottle in terms of x.

A) y = 12x + 172

B) y = 2x + 4 C) y = -2x + 16 D) y = 2x + 15

8)

Simplify the expression.

9) 4x3

y2

4

A) 257x7

y6B) 4x

12

y8C) 256x

12

y2D) 256x

12

y8

9)

10) (-3z2)(5z3)

A) -15z5 B) 1125z5 C) -15z6 D) 15z610)

Appendix A - 2

Simplify the expression. Write the result using positive exponents only.

11) xy4

x3y

-2

A) 1

x5y9B) 1

x8y10C) x

4

y6D) y

6

x4

11)

12) 13r-1(r-4)2

14(r-1)3

A) 13r6

14B) 13r

5

14C) 13

14r5D) 13

14r6

12)

Perform the indicated operation.

13) (7n6 - 19n3 - 19) - (3n6 + 11n3 - 3)

A) 4n6 - 30n3 - 22 B) 4n6 - 30n3 - 16

C) 4n6 - 16n3 - 22 D) -42n9

13)

Simplify the following by combining like terms.

14) 7r + 12r6 - 3r6 + 12r

A) 28r6 B) 28r

C) 19r + 9r6 D) cannot be simplified

14)

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."

15) y2 - 4y - 21A) (y - 21)(y + 1) B) prime C) (y - 7)(y + 3) D) (y + 7)(y - 3)

15)

16) x2 + 4xy - 21y2

A) (x - 7y)(x + 3y) B) prime C) (x - 7y)(x + y) D) (x + 7y)(x - 3y)16)

17) 4t2 + t - 5A) (4t + 1)(t - 5) B) (4t + 5)(t - 1) C) (4t - 5)(t + 1) D) (4t - 1)(t + 5)

17)

18) xy2 + 6y2 - 4x - 24

A) (x + 6)(y - 2)2 B) (x + 6)(y2 - 4)

C) (x - 6)(y + 2)(y - 2) D) (x + 6)(y + 2)(y - 2)

18)

19) -yz5- y5z

A) -yz(y4 + z4) B) -yz(y - z)(y4 + yz + z4)

C) -yz(y + z)(y4 - yz + z4) D) -yz(y - z)(y - z)

19)

Appendix A - 3

Solve the equation.

20) 9t3 - 64t = 0

A) 0 B) - 83, 83

C) - 83, 83, 0 D) 8

3

20)

21) 17x2 = 8x

A) - 817, 0 B) 0, 8

17C) - 17

8, 0 D) 0, 17

8

21)

Solve.22) The sum of two numbers is 16 and the sum of their squares is 146. Find the numbers.

A) 10 and 6 B) 11 and 5 C) 13 and 3 D) 12 and 422)

Multiply or divide as indicated.

23) 2x + 6y

x2 + 6xy + 9y2 ∙ x + 3y

3

A) 2x2 + 18xy + 18y2

3x2 + 18xy + 27y2B) 2x + 6y3(x + 3y)

C) 418xy

D) 2x2 + 18xy

3x2 + 18xy + 27y2

23)

24) (x + 3)2

x - 3 ÷ x

2 - 93x - 9

A) 3(x + 3)x - 3

B) (x + 3)3

3(x - 3)C) (x + 3)2

(x - 3)2D) 6(x

2 + 9)

x2 - 9

24)

Simplify the expression.

25) (x2)4

(3x)3

A) x11

27B) x

5

27C) x

5

3D) x

3

27

25)

Perform the indicated operation. Simplify if possible.

26) 8a + 6b 2

- 8a - 6b2

A) 36b B) 0 C) 8a D) 6b

26)

27) x

x2 + 7x - 44 - 4

x2 + 7x - 44

A) x + 11 B) x - 4 C) 12(x + 11)

D) 1x + 11

27)

Appendix A - 4

Find the perimeter.28)

(x2 + 3x + 9) units

(x2 + 3x + 9)units

A) (4x2 + 12x + 36) units B) (x2 + 6x + 18) units

C) (x4 + 6x2 + 18) units D) (x4 + 12x2 + 36) units

28)

Factor the sum or difference of two cubes.

29) t3 + 64

A) (t - 4)(t2 + 4t + 16) B) (t + 4)(t2 + 16)

C) (t + 4)(t2 - 4t + 16) D) (t - 64)(t + 1)(t - 1)

29)

Find an equation of the line.30) Perpendicular to y = 6, through (8, 11)

A) y = 11 B) x = 8 C) x = - 18

D) y = - 85x + 119

5

30)

Appendix A - 5

!

Math 46 - Final Exam Sample Packet B

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve.1) The house numbers of two adjacent homes are two consecutive even numbers. If their sum is326, find the house numbers.A) 162, 324 B) 161, 163 C) 162, 164 D) 163, 165

1)

Solve the formula for the specified variable.2) A = P + PRT for R

A) R = AT

B) R = PTA - P

C) R = P - APT

D) R = A - PPT

2)

3) S = 2πrh + 2πr2 for h

A) h = S - r B) h = S2πr

- 1 C) h = S - 2πr22πr

D) h = 2π(S - r)

3)

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.4) A store is advertising 20% off sale on everything in the store. Find the discount of a painting thatregularly sells for $280.A) $5.60 B) $274.40 C) $56.00 D) $224.00

4)

Multiply.5) 7y2(5y2 - 5y + 8)

A) 35y4 - 35y2 + 56 B) 12y4 + 2y + 15C) 35y4 - 35y + 56 D) 35y4 - 35y3 + 56y2

5)

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.6) A store is advertising 15% off sale on everything in the store. Find the sale price of a paintingthat regularly sells for $260.A) $2561.00 B) $39.00 C) $3.90 D) $221.00

6)

7) Because of budget cutbacks, MaryAnn was required to take a 18% pay cut. If she earned $28,000before the pay cut, find her salary after the pay cut.A) $27,949.60 B) $22,960 C) $27,496 D) $2296

7)

8) A chemist needs 100 milliliters of a 76% solution but has only 55% and 85% solutions available.Find how many milliliters of each that should be mixed to get the desired solution.A) 70 ml of 55%; 30 ml of 85% B) 40 ml of 55%; 60 ml of 85%C) 60 ml of 55%; 40 ml of 85% D) 30 ml of 55%; 70 ml of 85%

8)

9) The radiator in a certain make of car needs to contain 50 liters of 40% antifreeze. The radiatornow contains 50 liters of 20% antifreeze. How many liters of this solution must be drained andreplaced with 100% antifreeze to get the desired strength?A) 12.5 L B) 25 L C) 16.7 L D) 20 L

9)

Appendix B - 1

Solve the problem.10) Sue took her collection of nickels and dimes to deposit in the bank. She has five fewer nickels

than dimes. Her total deposit was $55.40. How many dimes did she deposit?A) 376 dimes B) 371 dimes C) 737 dimes D) 366 dimes

10)

Solve.11) Jeff starts driving at 65 miles per hour from the same point that Lauren starts driving at 40 milesper hour. They drive in opposite directions, and Lauren has a half-hour head start. How longwill they be able to talk on their cell phones that have a 480-mile range?

A) 4 47

hr B) 4 821

hr C) 4 1730

hr D) 4 1621

hr

11)

Solve the problem.12) Devon purchased tickets to an air show for 7 adults and 2 children. The total cost was $92. The

cost of a child's ticket was $8 less than the cost of an adult's ticket. Find the price of an adult'sticket and a child's ticket.A) adult's ticket: $13; child's ticket: $5 B) adult's ticket: $14; child's ticket: $6C) adult's ticket: $12; child's ticket: $4 D) adult's ticket: $11; child's ticket: $3

12)

Multiply.13) (y + 6)(y + 7)

A) 2y2 + 42 B) y2 + 13y + 42 C) 2y + 42 D) y2 + 13y + 1313)

Solve the inequality. Graph the solution set and write it in interval notation.14) -2(4x - 7) < -10x + 10

A) (-∞, -2)

-5 -4 -3 -2 -1 0 1-5 -4 -3 -2 -1 0 1

B) [-2, ∞)

-5 -4 -3 -2 -1 0 1-5 -4 -3 -2 -1 0 1

C) (-∞, -2]

-5 -4 -3 -2 -1 0 1-5 -4 -3 -2 -1 0 1

D) (-2, ∞)

-5 -4 -3 -2 -1 0 1-5 -4 -3 -2 -1 0 1

14)

Appendix B - 2

15) 15x - 35 > 5(2x - 11)

A) [-4, ∞)

-7 -6 -5 -4 -3 -2 -1-7 -6 -5 -4 -3 -2 -1

B) (-∞, -4]

-7 -6 -5 -4 -3 -2 -1-7 -6 -5 -4 -3 -2 -1

C) (-∞, -4)

-7 -6 -5 -4 -3 -2 -1-7 -6 -5 -4 -3 -2 -1

D) (-4, ∞)

-7 -6 -5 -4 -3 -2 -1-7 -6 -5 -4 -3 -2 -1

15)

Find the domain and the range of the relation.16) {(7, 3), (7, -7), (7, -5)}

A) domain: {-7, -5, 3} ; range: {7} B) domain: {7} ; range: {-7, -5, 3, 7}C) domain: {3, 7} ; range: {-7, -5} D) domain: {7} ; range: {-7, -5, 3}

16)

Find the domain of the function.

17) g(x) = 2x - 15

A) (-∞, 15) ∪ (15, ∞) B) (-∞, 2) ∪ (2, ∞)C) (-∞, ∞) D) (-∞, -15) ∪ (-15, ∞)

17)

Evaluate the function.18) Find f(11) when f(x) = 6x - 11

A) -55 B) 55 C) 56 D) 7718)

Solve the system of equations by the substitution method.

19) -5x + y = -26-6x - 3y = -6A) (5, -7) B) (-6, 4) C) (4, -6) D) no solution

19)

Solve the system of equations by the addition method.

20) x + 3y = 11-6x + 2y = -6A) (1, 4) B) (2, 3) C) no solution D) (-2, 4)

20)

21) -2x + 2y = -54x - 4y = 10A) (-2, 2) B) no solutionC) (0, 0) D) infinite number of solutions

21)

Appendix B - 3

Multiply.

22) (z - 5)(z2 + 5z - 3)

A) z3 + 22z - 15 B) z3 - 10z2 - 28z + 15

C) z3 + 10z2 + 28z - 15 D) z3 - 28z + 15

22)

23) (6y + x)(6y - x)

A) 12y2 - x2 B) 36y2 + 12xy - x2

C) 36y2 - x2 D) 36y2 - 12xy - x2

23)

Find the product and simplify.

24) 5x3y3

-45xy12 ∙ y9

A) x3

-9yB) x

2y-9

C) x3

-9D) x

2

-9

24)

25) 8p - 8p

∙ 8p2

9p - 9

A) 72p2 + 144p + 72

8p3B) 964p

C) 64p9

D) 64p3 - 64p2

9p2 - 9p

25)

26) x2 + 10x + 21

x2 + 15x + 56 ∙ x2 + 16x + 64

x2 + 11x + 24

A) x + 3x + 8

B) 1x + 8

C) x + 8x + 8

D) 1

26)

Find the quotient and simplify.

27) 3x2

5 ÷ x

3

15

A) 9x2

x3B) 9x

C) x9

D) 45x2

5x3

27)

28) m2 - n2

m + n ÷ m

m2 - mn

A) (m + n)2 B) (m - n)2 C) (m - n)(m + n) D) (m + n)

28)

Appendix B - 4

29) (x - 6)(x + 7)3x

÷ 5x - 30

15x8

A) x8(x + 7) B) x7(x + 7)5

C) x7(x + 7) D) 5x7(x + 7)

29)

30) p2 - 9p + pq - 9q

6p2 - 6q2 ÷ p - 94p - 4q

A) 23

B) 4(p2 - 9p + pq - 9q)6(p + q)(p - 9)

C) 1 D) (p - 9)2

24(p - q)2

30)

Appendix B - 5

!

Math 46 - Final Exam Sample Packet C

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Simplify the expression.1) (-9)0 + (-14)0

A) 0 B) 2 C) -2 D) -231)

Simplify.2)

x6

7x + 4

A) 42x(x + 4) B) x(x + 4)42

C) x + 442x

D) 6x7(x + 4)

2)

3)x4

7x + 7

A) x(x + 7)28

B) 4x7(x + 7)

C) x + 728x

D) 28x(x + 7)

3)

4) If Q(x) = 4x2 + 3x + 2, find Q(-1).A) 1 B) -5 C) 9 D) 3

4)

Perform the division.

5) -18x6 - 15x4 - 12x2

-3x4

A) 6x2 + 5 + 4x

B) 6x + 5 + 4

x2C) 6x2 + 5 + 4

x2D) 6x + 5 + 4

x

5)

Perform the indicated operation. Simplify if possible.

6) x

x2 - 16 - 6

x2 + 5x + 4

A) x2 - 5x + 24(x - 4)(x + 4)(x + 1)

B) x2 - 5(x - 4)(x + 4)(x + 1)

C) x2 + 5x + 24(x - 4)(x + 4)(x + 1)

D) x2 - 5x + 24(x - 4)(x + 4)

6)

Appendix C - 1

Write the number in standard notation.

7) 1.59 × 10-4A) 0.000159 B) -159,000 C) 0.0000159 D) -0.000159

7)

Solve the inequality. Graph the solution set.8) |x + 16| < 17

A) (-∞, 1) -15 -10 -5 0 5 10 15 20-15 -10 -5 0 5 10 15 20

B) (-33, 1) -30 -25 -20 -15 -10 -5 0 5-30 -25 -20 -15 -10 -5 0 5

C) (-1, 33) 0 5 10 15 20 25 30 350 5 10 15 20 25 30 35

D) (-∞, -33) -50 -45 -40 -35 -30 -25 -20 -15-50 -45 -40 -35 -30 -25 -20 -15

8)

Find an equation of the line. Write the equation in standard form.9) Through (2, 3); perpendicular to 2x - 5y = 2

A) 2x + 5y = 16 B) 2x - 5y = 16 C) 5x + 2y = 16 D) 5x - 2y = 169)

Solve the equation.

10) 2(8 - x)3

= -x

A) -2 B) -16 C) 2 D) 16

10)

11) x2x + 2

= -2x4x + 4

+ 2x - 3x + 1

A) 3 B) 32

C) no solution D) -3

11)

Solve.12) -3(2p + 5) - 10 = -2(p + 6) + 3

A) p = 6 B) p = 4 C) p = -4 D) p = -612)

13) Linda and Dave leave simultaneously from the same starting point biking in opposite directions.Linda bikes at 7 miles per hour and Dave bikes at 8 miles per hour. How long will it be untilthey are 20 miles apart from each other?

A) 20 hr B) 1 13

hr C) 34

hr D) 514

hr

13)

Appendix C - 2

Subtract as indicated.

14) 69

- 47

A) 23

B) 29

C) 263

D) 221

14)

Find the slope of the line that passes through the given points.15) (9, 1) and (2, -7)

A) - 611

B) 78

C) - 87

D) 87

15)

Solve the compound inequality. Graph the solution set.16) 6x - 4 < 2x or -4x ≤ -12

A) (-∞, 1) ∪ [3, ∞) 1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

B) (1, 3) 1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

C) [1, 3] 1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

D) ∅ -3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3

16)

Multiply.

17) (x - 6)(x2 - 8)

A) x2 - 14x + 48 B) x3 - 8x2 - 6x + 48

C) x3 - 6x2 - 8x + 48 D) -6x2 + x + 48

17)

Appendix C - 3

Solve the system of equations by graphing.

18) y = -x - 3y = 2x + 3

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A) no solution B) (-2, -1) C) (1, -2) D) (-2, 1)

18)

Perform the indicated operation.

19) (8n7 - 6n5 - 19) - (2n7 + 13n5 - 5)

A) 6n7 - 19n5 - 24 B) -27n12

C) 6n7 - 19n5 - 14 D) 6n7 - 4n5 - 24

19)

Factor out the GCF, greatest common factor, from the polynomial.

20) 80m7 + 64m5 + 24m3

A) 8m3(10m4 + 8m2 + 3) B) -m3(-80m4 + 64m2 - 24)

C) m3(80m4 + 64m2 + 24) D) 8(10m7 + 8m5 + 3m3)

20)

Simplify.

21) 14(12x - 8)

A) 48x - 32 B) x C) 3x - 2 D) 3x - 8

21)

Appendix C - 4

Use the slope-intercept form to graph the equation.

22) y = - 13x + 3

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

22)

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."

23) x2 - 2x - 15A) prime B) (x + 5)(x + 1) C) (x - 5)(x + 3) D) (x + 5)(x + 3)

23)

24) x2 - 5x - 6A) prime B) (x + 1)(x - 6) C) (x - 1)(x - 6) D) (x - 1)(x + 1)

24)

Appendix C - 5

Solve the inequality. Graph the solution set and write it in interval notation.25) 10 ≤ 2(x - 1) ≤ 14

A) [6, 8) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B) (6, 8) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15

C) [6, 8] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15

D) (6, 8] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15

25)

Find the product and simplify.

26) 7x4y4

-56xy8 ∙ y4

A) x3

-8B) x

4

-8C) x

3y-8

D) x4

-8y

26)

Solve the absolute value equation.27) |5x + 8| + 12 = 8

A) - 45, - 12

5B) 45, 125

C) - 12, - 32

D) ∅

27)

Appendix C - 6

The figure shows two parallel lines intersected by a transversal. One of the angle measures is given. Find the measureof the indicated angle.

28)

37°

Find the measure of ∠2.A) 53° B) 27° C) 127° D) 37°

28)

Graph the solution of the system of linear inequalities.

29) x ≥ 2yx + 2y ≤ 5

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

29)

Appendix C - 7

Graph the function.30) g(x) = |x - 5|

A)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

30)

Appendix C - 8

i

Final Exam Sample Packet Answer Keys Form A Form B Form C

1. D C B 2. B D B 3. C C A 4. C C D 5. B D C 6. D D A 7. C B A 8. B D B 9. D A C 10. A B B 11. C B A 12. D C C 13. B B B 14. C A D 15. C D D 16. D D A 17. B A C 18. D B B 19. A C C 20. C B A 21. B D C 22. B D A 23. B C C 24. A D B 25. B C C 26. D D A 27. D B D 28. A B D 29. C C D 30. B A A