Final Exam - C Name___________________________________Solve the inequality. Express the solution using interval notation.

1) (x + 5)(x + 1)(x - 6) > 0 1)A) (- , -5) or (-1, 6) B) (- , -1)C) (6, ) D) (-5, -1) or (6, )

Use the Remainder Theorem to find the remainder when f(x) is divided by x - c.2) f(x) = 5x6 - 3x3 + 8; x + 1 2)

A) 16 B) 10 C) 8 D) 6

List the potential rational zeros of the polynomial function. Do not find the zeros.3) f(x) = -4x4 + 2x2 - 3x + 6 3)

A) ± 14

, ± 12

, ± 34

, ± 32

, ± 1, ± 2, ± 3, ± 4, ± 6 B) ± 16

, ± 12

, ± 13

, ± 23

, ± 43

, ± 1, ± 2, ± 4

C) ± 14

, ± 12

, ± 34

, ± 32

, ± 1, ± 2, ± 3, ± 6 D) ± 14

, ± 12

, ± 23

, ± 34

, ± 32

, ± 1, ± 2, ± 3, ± 6

Evaluate the expression using the values given in the table.4)

f(g(2))

4)

A) 0 B) 2 C) 3 D) 1

The function f is one-to-one. Find its inverse.5) f(x) = x2 - 5, x 0 5)

A) f-1(x) = x - 5, x 5 B) f-1(x) = x + 5, x < 0C) f-1(x) = x + 5, x -5 D) f-1(x) = x + 5, x 0

Find the exact value of the logarithmic expression.

6) log91

7296)

A) 81 B) 3 C) -81 D) -3

MAC 1147 - Summer 2015 1

Final Exam - CWrite as the sum and/or difference of logarithms. Express powers as factors.

7) log 5pq11

7)

A) 12

log 5 pq -12

log 5 11 B) 12

log 5 p +12

log 5 q -12

log 5 11

C) 12

log 5 p +12

log 5 q - log 5 11 D) 12

log 5 p ·12

log 5 q ÷ 12

log 5 11

Express as a single logarithm.8) log x + log (x2 - 9) - log 5 - log (x - 3) 8)

A) log 2x + 3)8 - x

B) log x(x + 3)5

C) log x(x - 9)(x - 3)5

D) log x(x - 9)5(x - 3)

Solve the equation.9) log2(3x - 2) - log2(x - 5) = 4 9)

A) {6} B) 385

C) {18} D) 313

10) 4(5 + 3x) =1

25610)

A) {128} B) {3} C) 164

D) {-3}

Write the standard form of the equation of the circle.11) 11)

A) (x + 6)2 + (y + 4)2 = 3 B) (x - 6)2 + (y - 4)2 = 3C) (x - 6)2 + (y - 4)2 = 9 D) (x + 6)2 + (y + 4)2 = 9

MAC 1147 - Summer 2015 2

Final Exam - CWrite an equation for the graph.

12) 12)

A) (x - 1)29

+(y + 2)2

4= 1 B) (x + 2)2

9+

(y - 1)24

= 1

C) (x + 1)29

+(y - 2)2

4= 1 D) (x - 1)2

4+

(y + 2)29

= 1

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.13) x2 - 4y2 - 6x + 16y - 11 = 0 13)

A) center at (3, 2)transverse axis is parallel to y-axisvertices at (3, 0) and (3, 4)foci at (3, 2 - 5) and (3, 2 + 5)asymptotes of y + 2 = - 2(x + 3) and y + 2 = 2(x + 3)

B) center at (2, 3)transverse axis is parallel to x-axisvertices at (0, 3) and (4, 3)foci at (2 - 5, 3) and (2 + 5, 3)

asymptotes of y - 3 = -12

(x - 2) and y - 3 =12

(x - 2)

C) center at (3, 2)transverse axis is parallel to x-axisvertices at (2, 2) and (4, 2)foci at (3 - 5, 2) and (3 + 5, 2)asymptotes of y - 2 = - 2(x - 3) and y - 2 = 2(x - 3)

D) center at (3, 2)transverse axis is parallel to x-axisvertices at (1, 2) and (5, 2)foci at (3 - 5, 2) and (3 + 5, 2)

asymptotes of y - 2 = -12

(x - 3) and y - 2 =12

(x - 3)

MAC 1147 - Summer 2015 3

Final Exam - CFind the value of the determinant.

14)3 2 -45 3 1

-2 -5 314)

A) -84 B) 84 C) 162 D) 92

Compute the product.15)

1 3 -22 0 4

3 0-2 1

0 4

15)

A)-3 -5

6 16

B)3 -6 00 0 16

C)-5 -316 6

D) not defined

Write out the first five terms of the sequence.16) {sn} = {2n - 3} 16)

A) s1= 1, s2= -1, s3= -3, s4= -5, s5= -7 B) s1= -1, s2= 0, s3= 1, s4= 2, s5= 3C) s1= 5, s2= 7, s3= 9, s4= 11, s5= 13 D) s1= -1, s2= 1, s3= 3, s4= 5, s5= 7

Expand the expression using the Binomial Theorem.17) (2x + 5)4 17)

A) 16x4 + 160x3 + 600x2 + 1000x + 625 B) 16x3 + 160x2 + 600x + 1000C) (4x2 + 10x + 25)4 D) 80x4 + 800 x3 + 600x2 + 5000x + 625

Find the value of the indicated trigonometric function of the angle in the figure. Give an exact answer with a rationaldenominator.

18)

2

5Find cos .

18)

A) cos =2 29

29B) cos =

292

C) cos =295

D) cos =5 29

29

Use identities to find the exact value of the indicated trigonometric function of the acute angle .

19) sin =7

4, cos =

34

Find csc . 19)

A) 43

B) 4 77

C) 73

D) 3 77

MAC 1147 - Summer 2015 4

Final Exam - CFind the exact value. Do not use a calculator.

20) cot6

20)

A) 33

B) 1 C) 32

D) 3

Use a coterminal angle to find the exact value of the expression. Do not use a calculator.

21) sec 94

21)

A) 22

B) 2 33

C) 2 D) 2

Use the reference angle to find the exact value of the expression. Do not use a calculator.22) cot 930° 22)

A) -3

3B) - 3 C) 3

3D) 3

Use transformations to graph the function.

23) y = 3 sin 13

x 23)

A) B)

MAC 1147 - Summer 2015 5

Final Exam - CC) D)

Graph the function.24) y = 4 tan(2x) 24)

A) B)

MAC 1147 - Summer 2015 6

Final Exam - CC) D)

Find the exact value of the expression.25) cos-1(1) 25)

A)2

B) C) - D) 0

Find the inverse function f-1 of the function f.26) f(x) = 6 tan(8x) 26)

A) f-1(x) = 6 tan-1(8x) B) f-1(x) =16

tan-1 x8

C) f-1(x) =1

6 tan(8x)D) f-1(x) =

18

tan-1 x6

Write the trigonometric expression as an algebraic expression in u.27) cos (cot-1 u) 27)

A) u2 + 1u2 + 1

B) u2 - 1 C) u u2 + 1u2 + 1

D) u2 + 1u

Find the exact value of the expression.

28) tan 1312

28)

A) 2 + 3 B) -2 - 3 C) 2 - 3 D) 3 - 2

Use the information given about the angle , 0 2 , to find the exact value of the indicated trigonometric function.

29) csc = -32

, tan > 0 Find cos(2 ). 29)

A) -4 59

B) 19

C) 4 59

D) -19

30) tan = 3, < <32

Find tan2

. 30)

A) 10 - 13

B) 10 + 13

C) 10 + 1-3

D) 10 - 1-3

MAC 1147 - Summer 2015 7

Final Exam - CSolve the equation on the interval 0 < 2 .

31) 2 cos2 - 3 cos + 1 = 0 31)

A) 0,6

, 16

B) 0,3

, 53

C)3

,2

, 53

D) 0,3

, 23

32) sin2 - cos2 + cos = 0 32)

A) 0, 56

, 76

B) 0,3

, 53

C) 0, 23

, 43

D) 0, 23

, , 43

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

33) a = 4, A = 40°; Find b, c, and B. 33)A) b = 4.77

c = 6.23B = 60°

B) b = 4.77c = 6.23B = 50°

C) b = 4.77c = 7.23B = 60°

D) b = 4.77c = 7.23B = 50°

34) b = 3, c = 7; Find a, B, and A. 34)A) a = 7.62

B = 25.38°A = 64.62°

B) a = 6.32B = 64.62°A = 25.38°

C) a = 7.62B = 26.38°A = 63.62°

D) a = 6.32B = 25.38°A = 64.62°

Solve the triangle.35)

100°3 4

35)

A) c = 4.4, A =46.8°, B = 33.2° B) c = 6.4, A = 33.2°, B = 46.8°C) c = 5.4, A = 33.2°, B = 46.8° D) c = 5.4, A = 46.8°, B = 33.2°

36)

86

4

36)

A) A = 46.6°, B = 28.9°, C = 104.5° B) A = 104.5°, B = 46.6°, C = 28.9°C) A = 46.6°, B = 104.5°, C = 28.9° D) A = 104.5°, B = 28.9°, C = 46.6°

MAC 1147 - Summer 2015 8

Final Exam - CFind the area of the triangle. If necessary, round the answer to two decimal places.

37)

1

10°7

37)

A) 0.61 B) 3.45 C) 2.43 D) 1.22

38) (sec u - tan u)(sec u + tan u) = 38)A) sec u - tan u B) sec u · tan u C) 1 D) 0

MAC 1147 - Summer 2015 9