Math 96 - Final Exam Sample Packet A

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

Solve.1) Find the volume of the circular cylinder below whose diameter is 12 m and height is 8 m.

12 m

8 m

A) 288π m3 B) 108π m3 C) 648π m3 D) 54π m3

1)

2) The sum of two numbers is -2. Three times the first number equals 4 times the second number.Find the two numbers.

A) 87

and 67

B) -2 and 12 C) -8 and -6 D) - 87

and - 67

2)

3) A boat moves 5 kilometers upstream in the same amount of time it moves 20 kilometersdownstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in stillwater.

A) 6 23

km/hr B) 9 km/hr C) 3 km/hr D) 15 km/hr

3)

4)34x - 2 =

3x + 6

A) 2 B) 83

C) 43

D) 45

4)

5) The amount of water in a leaky bucket is given by the linear function f(t) = 125 - 7t, where f(t) isin ounces and t is in minutes. Find the amount of water in the bucket after 4 minutes.A) 28 oz B) 118 oz C) 153 oz D) 97 oz

5)

6) x4 + 36 = 37x2

A) -1, 1, -6, 6 B) 1, 36 C) -i, i, -6i, 6i D) -1, 1, -6i, 6i6)

7) 4x + 6 - 3 = 0

A) 34

B) 43

C) 12 D) ∅

7)

Appendix A - 1

Graph the piecewise defined function.8)

f(x) = -4 if x ≤ -1-2 + x if x > -1

A)

x-4 -2 2 4 6

y

4

2

-2

-4

x-4 -2 2 4 6

y

4

2

-2

-4

B)

x-4 -2 2 4 6

y

4

2

-2

-4

x-4 -2 2 4 6

y

4

2

-2

-4

C)

x-4 -2 2 4 6

y

4

2

-2

-4

x-4 -2 2 4 6

y

4

2

-2

-4

D)

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

8)

Solve the equation.

9) (4x + 2)2 = 36A) 10, -10 B) 0, 1 C) 1, 2 D) 1, -2

9)

Find the vertex of the graph of the quadratic function.

10) f(x) = -7x2 - 14x - 5A) (1, -26) B) (-1, 2) C) (-2, -19) D) (2, -61)

10)

Solve for x.11) log

3/5 x = 2

A) 925

B) 23/5 C) 95

D) 35

11)

Appendix A - 2

Graph the function. Find the vertex.

12) f(x) = -5x2

A) vertex: (0, 0)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B) vertex: (0, 0)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C) vertex: (0, 0)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D) vertex: (0, -5)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

12)

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor thetrinomial.

13) x2 + 13x + _______

A) x2 + 13x + 19

= x + 13

2B) x2 + 1

3x + 36 = (x +6)2

C) x2 + 13x + 136

= x + 16

2D) x2 + 1

3x + 16

= x + 13

2

13)

Appendix A - 3

Graph the exponential function.

14) f(x) = 4x + 1

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

14)

Find the power of i.

15) i15

A) 1 B) -i C) i D) -115)

Solve the equation.

16) x2 + 2x - 35 = 0A) -7, 1 B) 7, -5 C) 7, 5 D) -7, 5

16)

17) 11x

= 6 - 1x

A) 116

B) 2 C) 1 D) 35

17)

18) 1x + 6

+ 2x + 3

= -3

x2 + 9x + 18

A) -6 B) 0 C) 3 D) no solution

18)

Appendix A - 4

19) 4( 3x - 5 )

= 256

A) 128 B) 3 C) 164

D) -3

19)

20) log9 (x + 2) - log

9 x = 2

A) 140

B) 40 C) 9 D) 281

20)

Solve the proportion.

21) 4y - 6

= 5y + 6

A) 54 B) 12 C) - 54 D) - 43

21)

Graph the function.22) f(x) = -|x + 2| + 6

x-10 10

y

10

-10

x-10 10

y

10

-10

A)

x-10 10

y

10

-10

x-10 10

y

10

-10

B)

x-10 10

y

10

-10

x-10 10

y

10

-10

22)

Appendix A - 5

C)

x-10 10

y

10

-10

x-10 10

y

10

-10

D)

x-10 10

y

10

-10

x-10 10

y

10

-10

23) f(x) = x - 4A)

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

23)

Rationalize the denominator and simplify.

24) 3 - 43 + 4

A) -7 - 2 12 B) 7 + 2 12 C) 2 12 - 7 D) 7 - 2 12

24)

Appendix A - 6

Write the series with summation notation.25) 14 + 20 + 26 + 32

A)4

i = 1

(6i + 2)∑ B)4

i = 1

(6i + 8)∑ C)4

i = 1

(i + 13)∑ D)4

i = 1

14i∑

25)

Use the quadratic formula to solve the equation.

26) 4x2 + 1 = 3x

A) -3 - i 78

, -3 + i 78

B) -3 - i 78

, 3 + i 78

C) 3 - i 78

, -3 + i 78

D) 3 - i 78

, 3 + i 78

26)

Evaluate.27)

7 0 06 3 96 2 8A) -42 B) 294 C) 47 D) 42

27)

Write the first five terms of the sequence whose general term is given.

28) an = n2 - nA) 2, 6, 12, 20, 30 B) 1, 4, 9, 16, 25 C) 0, 2, 6, 12, 20 D) 0, 3, 8, 15, 24

28)

Find an equation of the line.29) Through (-2, 4); perpendicular to y = 2x - 2

A) y= -2x + 3 B) y = 2x + 3 C) y = 12x + 3 D) y= - 1

2x + 3

29)

Write the function in the form y = a(x - h)2 + k.

30) f(x) = -2x2 + 4x - 9

A) y = -2(x + 1)2 - 15 B) y = -2(x + 2)2 - 25

C) y = -2(x - 1)2 - 7 D) y = -2(x - 2)2 - 13

30)

Appendix A - 7

!

Math 96 - Final Exam Sample Packet B

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

Solve the equation.1) log

5 (x + 2) - log

5 x = 2

A) 12 B) 225 C) 5 D) 112

1)

2) x2 + 9x - 36 = 0A) 12, -3 B) -12, 3 C) -12, 1 D) 12, 3

2)

3) 1x + 7

+ 4x + 5

= -2x2 + 12x + 35

A) 5 B) no solution C) 0 D) -7

3)

4) 273x - 5

= 95x

A) 115 B) - 115 C) 15 D) - 15

4)

Solve the proportion.

5) 3y + 2

= 2y - 2

A) 4 B) 45 C) 10 D) - 10

5)

Solve.6) 3x - 2 - 2 = 0

A) 23 B) 2 C) 4 D) ∅

6)

7) One number is four more than a second number. Two times the first number is 12 more than fourtimes the second number. Find the two numbers.A) - 10 and - 14 B) 2 and - 2 C) 1 and - 3 D) 3 and - 1

7)

8) How many real solutions are possible for a system of equations whose graphs are a parabola anda hyperbola?A) 1, 2, 3, or 4 real solutions B) 0, 1, 2, or 3 real solutionsC) 1, 2, or 3 real solutions D) 0, 1, 2, 3, or 4 real solutions

8)

Appendix B - 1

9) Find the volume of the circular cylinder below. Leave your answer in terms of π.

10 m

17 m

A) 220π m3 B) 2420π m3 C) 110π m3 D) 425π m3

9)

10) x4 - 7x2 - 144 = 0A) -4, 4, -3, 3 B) -16, 16, -9i, 9i C) -3, 3, -4i, 4i D) -4, 4, -3i, 3i

10)

11) A painter can finish painting a house in 6 hours. Her assistant takes 8 hours to finish the samejob. How long would it take for them to complete the job if they were working together?

A) 5 hr B) 3 37

hr C) 7 hr D) 724

hr

11)

12) A boat moves 5 kilometers upstream in the same amount of time it moves 18 kilometersdownstream. If the rate of the current is 8 kilometers per hour, find the rate of the boat in stillwater.

A) 6 1213

km/hr B) 3 113

km/hr C) 14 213

km/hr D) 8 km/hr

12)

13) An arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet ofthe arrow t seconds after it was shot into the air is given by the function h(t) = -16t2 + 160t. Findthe maximum height of the arrow.A) 720 ft B) 80 ft C) 1200 ft D) 400 ft

13)

Evaluate the expression.

14) 5

i=2(2i - 2)∑

A) 12 B) 18 C) 16 D) 20

14)

Solve the nonlinear system of equations for real solutions.

15) 4x2 - 2y2 = 6-x2 + y2 = 1A) ( 5, 2), ( 5, -2), (- 5, 2), (- 5, -2) B) (2, 5), (2, - 5)C) (2, 5), (2, - 5), (-2, 5), (-2, - 5) D) (2, 5), (-2, - 5)

15)

Write in terms of i.16) -1600

A) ±40 B) -40i C) i 40 D) 40i16)

Appendix B - 2

Graph the function.17) y = log

2x

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y

4

2

-2

-4

x-6 -4 -2 2 4 6

y

4

2

-2

-4

17)

Appendix B - 3

18) f(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

18)

Solve the equation. Give an exact solution.

19) e(x + 6)

= 3

A) -3 B) e3 C) ln 3 - 6 D) e3 - 6

19)

Find the value of the logarithmic expression.

20) log5

1125

A) 3 B) -3 C) - 125

D) 13

20)

Find the indicated term of the sequence.21) The eighth term of the arithmetic sequence whose first term is -3 and whose common difference

is -3A) -27 B) 18 C) -24 D) 21

21)

Appendix B - 4

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.

22) f(x) = 15(x - 3)2 - 1

A) vertex (1, -3); axis x = 1

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B) vertex (-1, 3); axis x = -1

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C) vertex (3, -1); axis x = 3

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D) vertex (-3, -1); axis x = -3

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

22)

Write an equation of the circle with the given center and radius.23) (1, 2); 5

A) (x + 3)2 + (y - 9)2 = 5 B) (x + 1)2 + (y + 2)2 = 5

C) (x - 1)2 + (y - 2)2 = 5 D) (x + 2)2 + (y + 1)2 = 25

23)

Use the Pythagorean theorem to find the unknown side of the right triangle.24)

6

5A) 11 B) 31 C) 41 D) 31

24)

Appendix B - 5

Find the power of i.

25) i13

A) -1 B) i C) 1 D) -i25)

Solve the equation for x. Give an exact solution.26) ln 3x = 4

A) e3

4B) e

43 C) e

4

3D) 12

26)

Simplify the radical expression. Assume that all variables represent positive real numbers.

27) 50k7q8

A) 5k7q8 2k B) 5k3q4 2 C) 5k3q4 2k D) 5q4 2k727)

Solve the equation for the indicated variable.

28) P = A1 + rt

for t

A) t = P - 1Ar

B) t = A - PPr

C) t = P - Ar D) t = P - A1 + r

28)

Find the inverse of the one-to-one function.

29) f(x) =3x - 7

A) f-1(x) = x + 7 B) f-1(x) = x3 + 49 C) f-1(x) = x3 + 7 D) f-1(x) = 1

x3 + 7

29)

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.

30) 5x + 6

A) - 30 - 5 xx - 36

B) - 30 + 5 xx - 36

C) - 30 + 5 x

x2 - 36D) - 30 - 5 x

x + 36

30)

Appendix B - 6

Math 96 - Final Exam Sample Packet C

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

Given the matrix in echelon form, find the solution for the system.1)

1 1 4 20 1 -2 60 0 1 -3A) (2, 6, -3) B) (14, 0, -3) C) (-3, 0, 14) D) (2, 12, -3)

1)

Complete the indicated row operation.2) Replace R2 in -5 8 1

-3 0 6 with -4R1 + R2.

A) -5 8 1 -8 8 7

B) -5 8 1 17 -32 2

C) 17 -32 2 -3 0 6

D) -5 8 1

-23 32 10

2)

Find the sum of the terms of the infinite geometric sequence.

3) 2, - 23, 29, ...

A) 43

B) 2 C) - 23

D) 32

3)

Graph the function.4) f(x) = -3x2

A)

x-4 -2 2 4

y

4

2

-2

-4

x-4 -2 2 4

y

4

2

-2

-4

B)

x-4 -2 2 4

y

4

2

-2

-4

x-4 -2 2 4

y

4

2

-2

-4

C)

x-4 -2 2 4

y

4

2

-2

-4

x-4 -2 2 4

y

4

2

-2

-4

D)

x-4 -2 2 4

y4

2

-2

-4

x-4 -2 2 4

y4

2

-2

-4

4)

Appendix C - 1

5) f(x) = -|x| - 4

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

5)

Appendix C - 2

6) y = log4x

A)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

B)

x-6 -4 -2 2 4 6

y

4

2

-2

-4

x-6 -4 -2 2 4 6

y

4

2

-2

-4

C)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

D)

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

x-6 -4 -2 2 4 6

y6

4

2

-2

-4

-6

6)

Solve the equation.7) x2 + 6x + 5 = 0

A) -1, -5 B) 2, -1 C) 10, -5 D) 1, 5

7)

Solve.8) A boat moves 7 kilometers upstream in the same amount of time it moves 15 kilometersdownstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in stillwater.

A) 13 18

km/hr B) 7 78

km/hr C) 9 km/hr D) 24 34

km/hr

8)

9) An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet ofthe arrow t seconds after it was shot into the air is given by the function h(t) = -16t2 + 96t. Findthe maximum height of the arrow.A) 240 ft B) 144 ft C) 432 ft D) 48 ft

9)

10) How many real solutions are possible for a system of equations whose graphs are an ellipse anda circle?A) 0, 1, 2, or 3 real solutions B) 0, 1, 2, 3, or 4 real solutionsC) 1, 2, or 3 real solutions D) 1, 2, 3, or 4 real solutions

10)

Appendix C - 3

11) One number is four more than a second number. Two times the first number is 6 more than fourtimes the second number.A) - 7 and - 11 B) 6 and 2 C) 5 and 1 D) 4 and 0

11)

12) x4 - 21x2 - 100 = 0A) -5, 5, -2i, 2i B) -2, 2, -5i, 5i C) -5, 5, -2, 2 D) -25, 25, -4i, 4i

12)

13) 5x - 4 - 4 = 0

A) 4 B) 16 C) 125

D) ∅

13)

Use the Pythagorean theorem to find the unknown side of the right triangle.14)

5

3

A) 4 B) 2 7 C) 22 D) 22

14)

Find the distance between the pair of points.15) (7, -7) and (3, -5)

A) 12 3 units B) 6 units C) 2 5 units D) 12 units15)

Solve the equation.16) log

5 (x + 2) - log

5 x = 2

A) 112

B) 5 C) 225

D) 12

16)

17) 274x - 3

= 92x

A) 98

B) 89

C) - 98

D) - 89

17)

18) 1x + 7

+ 3x + 4

= -3x2 + 11x + 28

A) 4 B) 0 C) -7 D) no solution

18)

Appendix C - 4

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.

19) 4x + 7

A) - 28 + 4 x

x2 - 49B) - 28 + 4 x

x - 49C) - 28 - 4 x

x + 49D) - 28 - 4 x

x - 49

19)

Use the quadratic formula to solve the equation.

20) 2x2 + 12x = - 7

A) -12 - 222

, -12 + 222

B) -6 - 22

, -6 + 22

C) -6 - 224

, -6 + 224

D) -6 - 222

, -6 + 222

20)

Find the indicated term of the sequence.21) The eighth term of the arithmetic sequence whose first term is 6 and whose common difference is

-4A) -26 B) 34 C) 38 D) -22

21)

Find the indicated term for the sequence whose general term is given.

22) an = (-1)n

n + 4; a

18

A) - 911

B) 172

C) - 122

D) 122

22)

Appendix C - 5

Graph the piecewise defined function.23)

f(x) = -x + 4 if x < 03x - 4 if x ≥ 0

A)

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

B)

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

C)

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

D)

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

23)

Appendix C - 6

Sketch the graph of the equation. Find its vertex.

24) x = y2 + 2

A) vertex (0, 2)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

B) vertex (2, 0)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

C) vertex (0, -2)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

D) vertex (-2, 0)

x-10 -5 5 10

y10

5

-5

-10

x-10 -5 5 10

y10

5

-5

-10

24)

Write as a logarithmic equation.

25) 4-2

= 116

A) log4116

= -2 B) log4

-2 = 116

C) log-2

116

= 4 D) log1/16

4 = -2

25)

For the given functions f and g, find the composition.

26) f(x) = x3 + 2x; g(x) = 3x Find (g ∘ f)(x).

A) 27x3 + 6x B) 3x3 + 2x C) 3x3 + 6x D) 27x2 + 6x

26)

Appendix C - 7

Find the surface area of the figure.27)

2 m

6 m

4 m

A) 88 m2 B) 48 m2 C) 96 m2 D) 44 m2

27)

Solve the equation. Give an exact solution.

28) e(x + 6)

= 3

A) -3 B) ln 3 - 6 C) e3 - 6 D) e-328)

Use the given right triangle to find the trigonometric function.29) sin A

A) 35

B) 54

C) 45

D) 34

29)

Solve the equation for x. Give an exact solution.30) ln 11x = -2

A) e11

-2B) e

-2

11C) e

- 211 D) -22

30)

Appendix C - 8

1

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

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