Acc. Pre-Calculus Final Exam Revie...2 ____ 6. Find the domain of the function. f(x) = 2x2 + 4x - 5...

Name: ______________________ Class: _________________ Date: _________ ID: A

1

Acc. Pre-Calculus Final Exam Review

____ 1. Evaluate the function f x( ) = 13x - 8 at f 1( ) .

a. 3b. 4c. 6d. 7e. 5

____ 2. Evaluate the function f x( ) = 9x - 4 at f -4( ) .

a. –36b. –38c. –37d. –39e. –40

____ 3. Evaluate the function g yÊËÁÁˆ¯̃̃ = 5 - 7y at g s + 6( ) .

a. 5 - 7sb. -37 - 7sc. 37 - 7sd. 37 + 7se. -37 + 7s

____ 4. Evaluate the function g t( ) = 5t2 - 8t + 6 at g t( ) - g 4( ) .

a. 5t2 - 48t - 8b. 5t2 - 8t - 48c. 8t2 - 48t + 5d. 5t2 - 48 + 8te. 8t2 + 5t - 48

____ 5. Evaluate the function f x( ) = x + 6 + 10 at f -2( ) .

a. 13b. 12c. 14d. 10e. 11

2

____ 6. Find the domain of the function.

f x( ) = 2x2 + 4x - 5

a. Non-negative real numbers x such that x π 0b. All real numbers xc. All real numbers x such that x < 0d. All real numbers x such that x > 0e. Non-negative real numbers x


h t( ) =2

t

a. All real numbers t such that t > 0b. Non-negative real numbers tc. All real numbers t except t π 0d. Negative real numbers t e. All real numbers t such that t < 0


f x( ) =x - 5

x

a. Non-negative real numbers x such that x π 0b. Non-negative real numbers xc. All real numbers x such that x < 0d. All real numbers xe. All real numbers x such that x > 0


f x( ) =x + 3

3 + x

a. All real numbers xb. All real numbers x such that x < 3c. All real numbers x such that x > -3d. Non-negative real numbers xe. Non-negative real numbers x such that x π 3

3

____ 10. Find the value(s) of x for which f (x) = g (x).

f x( ) = x2 + 3x - 2 g x( ) = 8x + 4

a. -2, - 5, - 12

b. -2, 3, - 12

c. -1, - 12

d. 6, - 1e. -6, 1

____ 11. Find the zeros of the function algebraically.

f x( ) = 6x2 - 3x - 45

a. -5

2, 3

b. -2

5, 3

c. -5

2, -3

d.5

2, 3

e.5

2, -3

4


f x( ) = 3x2 + 19x - 14

a.2

3, 7

b.2

3, -7

c.3

2, -7

d. -2

3, -7

e. -2

3, 7


f x( ) =x

8x2 - 2

a. 2b. 9c. 8d. 7e. 0


f x( ) =x2 - 11x + 24

8x

a. -8, 0,3b. 0,8, 3c. 0,3, 8d. -8,- 3,0e. -3, 0,8

5

____ 15. Find (f + g)(x).

f(x) = x + 7, g(x) = x - 7

a. 2xb. –2xc. 2x + 14d. 7xe. –7x

____ 16. Find (f - g)(x).

f(x) = x + 5, g(x) = x - 5

a. 10b. 2xc. 2x - 5d. 2x - 10e. 2x + 10

____ 17. Find (fg)(x).

f(x) = x2 , g(x) = 5x - 5

a. 5x - 5x2

b. 5x2 + 5x3

c. 5x3 + 5x2

d. 5x2 - 5x3

e. 5x3 - 5x2

6

____ 18. Find (f / g)(x). What is the domain of f / g?

f(x) = x2 , g(x) = 6x - 4

a. -x2

6x - 4; all real numbers x .

b.x2

6x - 4; all real numbers x except x = 2

3

c.x2

6x + 4; all real numbers x except x = 3

2

d.6x - 4

x2; all real numbers x except x = 0

e.6x + 4

x2; all real numbers x except x = 0

____ 19. Evaluate the indicated function for f(x) = x2 + 2 and g(x) = x - 3.

(f + g)(2)

a. 3b. –5c. 7d. 6e. 5


(f - g)(-2)

a. –17b. –7c. 13d. 17e. 8

7


(f - g)(0)

a. 1b. 28c. –28d. 8e. 36

____ 22. Find fog.

f(x) = x4 , g(x) = x - 1

a. x - 1( )4

b. x4 + 1Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

c. x + 1( )4

d. x4 - 1Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

e. x4

____ 23. Find go f.

f(x) = x2 , g(x) = x - 3

a. x2 + 3Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜

b. x - 3( )2

c. x2 - 3d. x2

e. x + 3( )2

8

____ 24. Find fog and the domain of composite function.

f(x) = x + 3 , g(x) = x

a. x + 3Domain of fog: all real numbers x

b. x - 3( )Domain of fog: all real numbers x

c. - x + 3( )Domain of fog: all real numbers x

d. x + 3( )Domain of fog: all real numbers x

e. x - 3( )Domain of fog: all real numbers x

____ 25. Find gof and the domain of composite function.

f(x) = x2 + 5, g(x) = x

a. x - 5( )5

Domain of gof: all real numbers xb. x - 5( )

5

Domain of gof: all real numbers xc. x + 5( )

5

Domain of gof: all real numbers x

d. x2 + 5Domain of gof: all real numbers x

e. x + 5( )5

Domain of gof: all real numbers x

____ 26. Determine the x-intercept(s) of the quadratic functionf x( ) = x2 - 4x + 5.a. 3, 0Ê

ËÁÁˆ¯̃̃ , 1, 0Ê

ËÁÁˆ¯̃̃

b. -3, 0ÊËÁÁ

ˆ¯̃̃ , -1, 0Ê

ËÁÁˆ¯̃̃

c. -3, 0ÊËÁÁ

ˆ¯̃̃ , -5, 0Ê

ËÁÁˆ¯̃̃

d. no x-intercept(s)e. 5, 0Ê

ËÁÁˆ¯̃̃ , -1, 0Ê

ËÁÁˆ¯̃̃

9

____ 27. Determine the x-intercept(s) of the quadratic functionf x( ) = x2 + 4x + 3.a. no x-intercept(s)b. 5, 0Ê

ËÁÁˆ¯̃̃ , 2, 0Ê

ËÁÁˆ¯̃̃

c. 1, 0ÊËÁÁ

ˆ¯̃̃ , 3, 0Ê

ËÁÁˆ¯̃̃

d. -5, 0ÊËÁÁ

ˆ¯̃̃ , -2, 0Ê

ËÁÁˆ¯̃̃

e. -1, 0ÊËÁÁ

ˆ¯̃̃ , -3, 0Ê

ËÁÁˆ¯̃̃

____ 28. Select from the following which is the polynomial function that has the given zeros.

0, 6

a. f x( ) = x - 6

b. f x( ) = x2 + 6xc. f x( ) = x + 6

d. f x( ) = x3 + x2 - 6x

e. f x( ) = x2 - 6x____ 29. Select from the following which is the polynomial function that has the given zeros.

2,- 7

a. f x( ) = -x2 - 5x - 14

b. f x( ) = x2 + 5x - 14

c. f x( ) = x2 + 5x + 14

d. f x( ) = -x2 + 5x - 14

e. f x( ) = x2 - 5x + 14____ 30. Select from the following which is the polynomial function that has the given zeros.

0, -6,- 4

a. f x( ) = x3 - 10x2 + 24x

b. f x( ) = x3 + 10x2 + 24x

c. f x( ) = x3 - 10x2 - 24x

d. f x( ) = -x3 + 10x2 + 24x

e. f x( ) = x3 + 10x2 - 24x

10

____ 31. Select from the following which is the polynomial function that has the given zeros.

1 + 5 ,1 - 5

a. f x( ) = -x2 - 2x - 4

b. f x( ) = x2 - 2x + 4

c. f x( ) = x2 - 2x - 4

d. f x( ) = -x2 - 2x + 4

e. f x( ) = x2 + 2x - 4____ 32. Use long division to divide.

x4 + 7x3 + 12x2 - x - 4Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ ∏ x + 4( )

a. x3 + 3x2 + 1b. x3 + 3x2 - 1c. x3 + 3x2 + 1d. x3 - 3x2 + 1e. x3 - 3x2 - 1

____ 33. Use long division to divide.

x3 + 4x2 + 25x + 100Ê

Ë

ÁÁÁÁÁÁˆ

¯

˜̃̃˜̃̃ ∏ x + 4( )

a. x2 + 8x + 37 - 133x + 4

b. x2 + 25

c. x2 + 8x + 57 + 72x + 4

d. x2 - 20

e. x2 + 8x + 37

11

____ 34. Use long division to divide.

x3 + 125Ê

Ë

ÁÁÁÁÁÁˆ

¯

˜̃̃˜̃̃ ∏ x + 5( )

a. x2 - 5x + 25

b. x2 + 5x - 25

c. x2 - 25 + 5x + 5

d. x2 + 25

e. x2 - 25____ 35. Use long division to divide.

x4 - 2x2 - 4Ê

Ë

ÁÁÁÁÁÁˆ

¯

˜̃̃˜̃̃ ∏ x2 - 3x - 2

Ê

Ë

ÁÁÁÁÁÁˆ

¯

˜̃̃˜̃̃

a. x2 + 3x - 3

b. x2 + 3x - 3 - 4

x2 + 3x - 3

c. x2 - 3x + 3 + x - 2

x2 - 3x - 2

d. x2 - 3x + 3

e. x2 + 3x + 9 + 33x + 14

x2 - 3x - 2____ 36. Use synthetic division to divide.

3x3 + 17x2 + 18x - 8Ê

Ë

ÁÁÁÁÁÁˆ

¯

˜̃̃˜̃̃ ∏ x + 4( )

a. 3x2 + 10x + 8

b. 3x2 + 11x - 3

c. 3x2 + 5x - 2

d. 3x2 + x + 6

e. 3x2 + 7x - 4

12

____ 37. Using the factors x - 5( ) and x - 2( ) , find the remaining factor(s) of f x( ) =x3 - 4x2 - 11x + 30 and write the polynomial in fully factored form.a. f x( ) = x - 5( ) x - 2( ) x + 3( )

b. f x( ) = x - 5( ) x - 2( ) 2

c. f x( ) = x - 5( ) 2 x - 2( )

d. f x( ) = x - 5( ) x - 2( ) x + 7( )

e. f x( ) = x - 5( ) x - 2( ) x - 3( )

____ 38. Using the factors 5x + 2( ) and x - 1( ) , find the remaining factor(s) of

f x( ) = - 10x4 + 61x3 - 54x2 - 7x + 10 and write the polynomial in fully factored form.a. f x( ) = 5x + 2( ) 5x + 2( ) 2x - 1( ) x - 1( )

b. f x( ) = 5x + 2( ) -x - 5( ) 2 x + 1( )

c. f x( ) = 5x + 2( ) 2 2x - 1( ) x + 1( )

d. f x( ) = 5x + 2( ) -x + 5( ) 2x - 1( ) x - 1( )

e. f x( ) = 5x + 2( ) 2 x - 1( ) 2

____ 39. Use the Remainder Theorem and synthetic division to find the function value. Verify youranswer using another method.

f(x) = 3x3 - 7x + 3, f(1)

a. –1b. ––1c. 0d. –4e. 1


f(x) = 5x3 - 6x + 5, f(-3)

a. –111b. –115c. –112d. 115e. –110

13


f(x) = 4x3 - 9x + 6, f1

2

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

a. 3b. –1c. 4d. 2e. 0


f(x) = 4x6 - 9x4 - 5x2 + 6, f 4( )

a. 18677b. 18679c. –18674d. 18674e. 18678

____ 43. Perform the addition or subtraction and write the result in standard form.

8 - i( ) - 5 - i( )

a. 3b. 4c. 5d. 6e. 7


13i - 14 - 3i( )

a. -14 + 19ib. -14 - 16ic. -14 + 16id. 14 - 16ie. 14 + 16i

14


27 + -13 + 12i( ) + 11i

a. -14 + 23ib. 14 + 25ic. -14 - 23id. 14 + 23ie. 14 - 23i

____ 46. Perform the operation and write the result in standard form.

1 + i( ) 3 - 2i( )

a. 5 + ib. 7 + ic. 9 + id. 6 + ie. 8 + i


14i 1 - 7i( )

a. 100 + 14ib. 102 + 14ic. 98 + 14id. 99 + 14ie. 101 + 14i


19 + 20i( )2

a. 39 + 760ib. -39 + 760ic. 39 - 760id. -760 + 39ie. -39 - 760i

15


11 - 10i( )2

a. 21 - 220ib. 21 + 220ic. -21 + 220id. -21 - 220ie. 23 - 220i

____ 50. Write the quotient in standard form.

3

1 - i

a.3

2+

3

2i

b.3

2 + i

c.3

2-

3

2i

d.3

2 - i

e.3

2i

16

____ 51. Write the quotient in standard form.

5 + i

5 - i

a. 1312

+ 135

i

b. 1213

+ 135

i

c. 1312

+ 513

i

d. 1213

- 513

i

e. 1213

+ 513

i

____ 52. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

ln 8x

a.ln 8

ln xb. ln 8 + ln xc. ln 8 ¥ ln xd. ln 8 - ln xe. None of these


log3 9x

a. log3 9 ¥ log3 xb. log3 9 - log3 x

c.log3 9

log3 x

d. log3 9 + log3 xe. None of these

17


log4x2 y

a. log4 + 2 logx + logy

b.log4

2 logx + logyÊËÁÁ

ˆ¯̃̃

c. log4 + 2 logx - logyd. log4 + logx + 2 logye. log4 ¥ 2 logx ¥ logy


logx2

y4

5

a.2

5logx +

4

5logy

b.5

2logx +

10

4logy

c.1

10logx +

1

20logy

d. 10 logx + 20 logy

e.2

5logx -

4

5logy

18


log5

x4

y4 z 3

a. 4 log5 x + 4 log5 y - 3 log5 zb. 4 log5 x + 4 log5 y + 3 log5 z

c.4 log5 x

4 log5 y ¥ 3 log5 z

d. 4 log5 x - 4 log5 y - 3 log5 ze. 4 log5 x - 4 log5 y + 3 log5 z

____ 57. Solve for x.

6 x = 7, 776

a. 6b. -6c. 11d. 5e. -5


5 x = 625

a. 4b. 9c. -4d. 5e. -5

19


1

3

Ê

Ë

ÁÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃˜

x

= 81

a. -4b. 4c. 3d. 7e. -3

____ 60. Solve the exponential equation algebraically. Approximate the result to three decimal places.

26x = 1200

a.ln 1200

6 ln 2ª 1.979

b.ln 1200

6 ln 2ª 1.705

c.ln 1200

6 ln 2ª 0.016

d.ln 1200

6 ln 2ª -1.705

e.ln 1200

6 ln 2ª 0.126

20


6-6x = 0.10

a. -ln 0.10( )

6 ln 6ª 0.214

b.ln 0.10( )

6 ln 6ª 0.13

c. -ln 0.10( )

6 ln 6ª 0.214

d. -ln 0.10( )

6 ln 6ª 0.13

e. -ln 0.10( )

6 ln 6ª -0.214


2 x- 4 = 64

a. 12b. -10c. 13d. 10e. 11

21


2 5 x- 4Ê

ËÁÁÁÁ

ˆ

¯˜̃̃˜ = 16

a. 4 +ln 8

ln 5ª 5.292

b. 4 +ln 8

ln 5ª 7.292

c. 4 +ln 8

ln 5ª 8.292

d. 4 +ln 8

ln 5ª 9.292

e. 4 +ln 8

ln 5ª 6.292


2 53 - xÊ

ËÁÁÁÁ

ˆ

¯˜̃̃˜ = 8

a. 3 -ln 4

ln 5ª 3.139

b. 3 -ln 4

ln 5ª 6.139

c. 3 -ln 4

ln 5ª 4.139

d. 3 -ln 4

ln 5ª 5.139

e. 3 -ln 4

ln 5ª 2.139

22

____ 65. Find (if possible) the complement of the following angle.

p

4

a. Complement: -p

4

b. Complement: 2

pc. Complement: p

d. Complement: p

4

e. Complement: p

2____ 66. Find (if possible) the supplement of the following angle.

p

5

a. Supplement: p

b. Supplement: -p

5

c. Supplement: 5

4p

d. Supplement: 4p

5

e. Supplement: p

5

23

____ 67. Find angle 7p

4 in degree measure.

a. 158∞

b. 320∞

c. 315∞

d. 290∞

e. 168∞

____ 68. Find angle p

2 in degree measure.

a. 95∞

b. 45∞

c. 125∞

d. 90∞

e. 50∞

____ 69. Convert the angle measure from degrees to radians. Round your answers to three decimal places.

80∞

a. 80∞ ª 1.296 radians

b. 80∞ ª 0.08 radian

c. 80∞ ª 8.488 radians

d. 80∞ ª 1.696 radians

e. 80∞ ª 1.396 radians

24

____ 70. Convert the angle measure from degrees to radians. Round to three decimal places.

-202.2∞

a. -202.2∞ ª -3.429 radians

b. -202.2∞ ª 3.429 radians

c. -202.2∞ ª -3.829 radians

d. -202.2∞ ª 3.529 radians

e. -202.2∞ ª -3.529 radians____ 71. Find the exact values of the three trignometric functions of the angle q (sinq, cosq, tanq) shown in

the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)

a = 8, b = 15

a. sin q =17

8, cosq =

15

17, tanq =

15

8

b. sin q =15

17, cosq =

8

17, tanq =

8

15

c. sin q =8

17, cosq =

15

17, tanq =

8

15

d. sin q =15

17, cosq =

8

17, tanq =

15

8

e. sin q =17

8, cosq =

17

15, tanq =

8

15

25

____ 72. Find the exact values of the three trignometric functions of the angle q cot q, secq, cscqÊËÁÁ

ˆ¯̃̃ shown in


a = 5, b = 13

a. cot q =5

12, secq =

1

5, cscq =

1

13

b. cot q =5

12, secq =

1

12, cscq =

1

5

c. cot q =5

12, secq =

13

5, cscq =

13

12

d. cot q =12

5, secq =

13

12, cscq =

13

5

e. cot q =12

5, secq =

13

5, cscq =

13

12

26

____ 73. Find the exact values of the three trignometric functions of the angle q sin q, cos q, tan qÊËÁÁ

ˆ¯̃̃ shown in


a = 9, b = 41

a. sin q =9

41, cosq =

40

41, tanq =

9

40

b. sin q =41

9, cosq =

41

40, tanq =

9

40

c. sin q =41

9, cosq =

41

40, tanq = 1

d. sin q =41

9, cosq =

41

40, tanq =

40

9

e. sin q =9

41, cosq =

40

41, tanq =

40

9____ 74. Use the Pythagorean Theorem to determine the third side and then find the three trignometric

functions of q: sin q, cot q , and cscq

tan q =24

7

a. sin q =7

25, cot q =

7

24, cscq =

25

7

b. sin q =24

25, cot q =

7

24, cscq =

25

24

c. sin q =25

24, cot q =

7

24, cscq =

24

25

d. sin q =24

25, cot q =

24

7, cscq =

25

24

e. sin q =24

7, cot q =

7

25, cscq =

7

24

27

____ 75. Use the Pythagorean Theorem to determine the third side and then find the two trignometric functions of q: cotq and cscq

sin q =1

6

a. cot q = 6 , cscq = 35b. cot q = 35 , cscq = 35c. cot q = 35 , cscq = 35d. cot q = 35 , cscq = 6e. cot q = 35 , cscq = 6

____ 76. Find the period and amplitude.

y = -5 sin x

a. Period: 2p; Amplitude: 1b. Period: 2p; Amplitude: 5c. Period: p; Amplitude: -5

d. Period: 2p; Amplitude: -1

5

e. Period: p; Amplitude: 1

5____ 77. Find the period and amplitude.

y = 8 sin 20x

a. Period: p; Amplitude: -8

b. Period: p

10; Amplitude: -

1

8

c. Period: p

10; Amplitude: 8

d. Period: 2p; Amplitude: 1

e. Period: p; Amplitude: 1

8

28

____ 78. Select the graph of the function. (Include two full periods.)

y = sin 4x

a. d.

b. e.

c.

30

____ 79. Select the graph of the function. (Include two full periods.)

y = cosx

6

31

a. d.

b. e.

c.

32

____ 80. Find the exact value of cos arctan 815

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜.

a. 815

b. 158

c. 3215

d. 1732

e. 1715

____ 81. Find the exact value of cot sin-1 725

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜.

a. 247

b. 725

c. 257

d. 317

e. 2431

____ 82. Use the fundamental identities to simplify the expression.

cotq secq

a. cosqb. cscqc. tan qd. secq cotqe. cot q

33

____ 83. Use the fundamental identities to simplify the expression.

cotq

cscq

a. secqb. sinqc. cscqd. cosqe. cot q

____ 84. Which of the following expression is equivalent to

cot 5x

sec 5x

a. csc5x + sin 5xb. -5cscx + sin xc. -cscx - 5 sin xd. -5 sec x - sin xe. csc5x - sin 5x

____ 85. Evaluate the following expression.

secq - 1

1 - cos q

a. secq - cos qb. -cos qc. secqd. -secqe. cos q


csc2x - sin 2x

a. sin 2x csc2xb. cos 2x cot 2xc. 2 sin x cot xd. -2 sin 2x cot 2xe. -2 cos 2x cot 2x

34


3

sin 5x-

3

csc5x

a. 3 csc5x + sin 5x( )b. 5 csc5x - sin 5x( )c. -3 csc5x - sin 5x( )d. 5 csc5x + sin 5x( )e. 3 csc5x - sin 5x( )

____ 88. Solve the following equation.

4 cos x + 2 = 0

a.7p

6+ 2np,

11p

6+ 2np

b.2p

3+ 2np,

4p

3+ 2np

c.p

3+ np,

p

3+ np

d.4p

3+ np,

2p

3+ np

e.p

2+ np,

2p

5+ np

35


2 3 csc x - 4 = 0

a.p

4+ 2np,

2p

4+ 2np

b.p

2+ 2np,

2p

3+ 2np

c.p

3+ 2np,

2p

3+ 2np

d.p

3+ p,

2p

3+ 2np

e.p

3+ 2np,

2p

3+ p


6 cot x2 - 2 = 0

a.4p

3+ np,

2p

3+ np

b.p

3+ np,

2p

3+ np

c.p

2+ np,

2p

5+ np

d.2p

3+ np,

2p

3+ np

e.p

3+ np,

p

3+ np

36


2 sin x - 1 = 0

a. x = p6+ 2np and x = 7p

6+ 2np, where n is an integer

b. x = p6+ 2np and x = 5p


c. x = p3+ 2np and x = 5p


d. x = p4+ 2np and x = 5p


e. x = 2p3

+ 2np and x = 4p3

+ 2np, where n is an integer


cos 2 x + cos x = 0

a. x = p + np and x = 5p4

+ np, where n is an integer

b. x = 2np and x = 3p2


c. x = p2+ np and x = p + 2np, where n is an integer

d. x = np and x = p2+ 2np, where n is an integer

e. x = 2p3

+ 2np and x = 5p3



4 cos 4 x - 1 = 0

a. x = p2+ np, where n is an integer

b. x = np and x = p2+ np, where n is an integer

c. x = np and x = 3p4

+ np, where n is an integer

d. x = np and x = 3p2


e. x = p4+ np

2, where n is an integer

37

____ 94. Find the expression as the cosine of an angle.

cosp

9cos

p

4- sin

p

9sin

p

4

a. cos13p

36

b. sin13p

36

c. cosp

36

d. cos36p

13

e. sin36p

13____ 95. Find the expression as the sine of an angle.

sin 50∞ cos 20∞ + cos 50∞ sin 20∞

a. cos 70∞b. sin 50∞c. cos 30∞d. sin 70∞e. sin 30∞

____ 96. Find the expression as the sine or cosine of an angle.

cos 100∞ cos 40∞ - sin 100∞ sin 40∞

a. sin 140∞b. cos 100∞c. cos 140∞d. sin 60∞e. cos 60∞

38

____ 97. Find the expression as the tangent of an angle.

tan 70∞ - tan 20∞

1 + tan 70∞ tan 20∞

a. tan-1 50∞b. tan 70∞c. tan 20∞d. tan 50∞e. tan-1 90∞

____ 98. Find the expression as the tangent of an angle.

tan 4x + tan x

1 - tan 4x tan x

a. tan 5xb. tan 4xc. tan-1 5xd. tan-1 3xe. tan 3x

39

____ 99. Use the figure to find the exact value of the trigonometric function.

cos 2q

a = 1,b = 2

a.5

4

b.3

5

c.4

5

d.5

3

e.3

4

40


sin 2q

a = 1,b = 4

a.8

9

b.9

17

c.8

17

d.17

9

e.17

8

41


tan 2q

a = 1,b = 8

a.63

65

b.16

63

c.63

16

d.16

65

e.65

63

42


sec 2q

a = 1,b = 6

a.36

37

b.35

37

c.35

36

d.37

36

e.37

35

43


csc 2q

a = 1,b = 2

a.5

4

b.5

5

c.4

5

d.4

5

e.5

5____ 104. Use the Law of Sines to solve the triangle. Round your answer to two decimal places.

A = 25∞,B = 45∞, c = 13

a. C = 110∞,a ª 6.85,b ª 9.78b. C = 110∞,a ª 3.72,b ª 11.78c. C = 110∞,a ª 5.85,b ª 9.78d. C = 110∞,a ª 7.85,b ª 11.78e. C = 110∞,a ª 9.78,b ª 10.78

____ 105. Use the Law of Sines to solve the triangle. Round your answer to two decimal places.

A = 110∞,B = 30∞, c = 10

a. C = 40∞,a ª 3.72,b ª 7.78b. C = 40∞,a ª 16.62,b ª 9.78c. C = 40∞,a ª 14.62,b ª 7.78d. C = 40∞,a ª 8.78,b ª 7.78e. C = 40∞,a ª 9.78,b ª 15.62

44

____ 106. Use the Law of Sines to solve (if possible) the triangle. Round your answers to two decimal places.

A = 76∞,a = 34, b = 21

a. B ª 73.2∞,C ª 30.8∞,c ª 32.3b. B ª 36.82∞,C ª 67.18∞,c ª 32.3c. B ª -67∞,C ª 37∞,c ª 32.3d. B ª 67.18∞,C ª 36.82∞,c ª 32.3e. No Solution

____ 107. Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places.

A = 60∞,a = 13.9, b = 15.3

a. B ª 47.59∞,C ª 72.41∞,c ª 15.3b. B ª 91∞,C ª 29∞,c ª 11.85c. B ª 29∞,C ª 91∞,c ª 13.9d. B ª 72.41∞,C ª 47.59∞,c ª 11.85e. No Solution

____ 108. Because of prevailing winds, a tree grew so that it was leaning 2∞ from the vertical. At a point 41 meters from the tree, the angle of elevation to the top of the tree is 30∞ (see figure). Find the height a of the tree.

where c = 41 m

B = 92∞

(Round your answer to two decimal places.)

a. 22.17 mb. 25.17 mc. 23.17 md. 26.17 me. 24.17 m

45

____ 109. Given A = 60∞, B = 73∞, and c = 8, use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

a. b = 7.24b. b = 9.47c. b = 8.83d. b = 6.76e. b = 6.12

____ 110. Given A = 55∞, B = 64∞, and a = 5.10, use the Law of Sines to solve the triangle for the value of b. Round answer to two decimal places.

a. b = 4.96b. b = 5.45c. b = 5.60d. b = 4.65e. b = 4.78

46

____ 111. Use the law of Cosines to solve the given triangle. Round your answer to two decimal places.

a = 9, b = 11,c = 15

a. A ª 36.58∞,B ª 96.67∞, C ª 46.75∞b. A ª 46.75∞,B ª 46.75∞ , C ª 86.5∞c. A ª 36.58∞,B ª 46.75∞ , C ª 96.67∞d. A ª 46.75∞,B ª 36.58∞, C ª 96.67∞e. A ª 96.67∞,B ª 46.75∞, C ª 36.58∞


a = 8,b = 4,c = 9

a. A ª 62.72∞,B ª 90.9∞,C ª 26.38∞b. A ª 90.9∞,B ª 62.72∞,C ª 26.38∞c. A ª 26.38∞,B ª 62.72∞,C ª 90.9∞d. A ª 62.72∞,B ª 26.38∞,C ª 90.9∞e. A ª 90.9∞,B ª 26.38∞,C ª 62.72∞

47


A = 33∞ ,b = 18, c = 33

a. a ª 33, B ª 30.7∞ ,C ª 116.3∞b. a ª 20.41, B ª 118.3∞ ,C ª 28.7∞c. a ª 33, B ª 28.7∞ ,C ª 118.3∞d. a ª 20.41, B ª 28.7∞ ,C ª 118.3∞e. a ª 18, B ª 28.7∞ ,C ª 118.3∞


a = 14, b = 7, C = 111∞

a. A ª 49.4∞, B ª 49.4∞, c ª 7b. A ª 19.6∞, B ª 19.6∞, c ª 7c. A ª 49.4∞, B ª 19.6∞, c ª 7d. A ª 19.6∞, B ª 17.76∞, c ª 17.76e. A ª 47.4∞, B ª 21.6∞, c ª 17.76

____ 115. Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle. Round your answer to two decimal places.

a = 18,b = 20,c = 14

a. Law of Sines;A ª 60.94∞,B ª 42.83∞,C ª 76.23∞b. Law of Sines;A ª 60.94∞,B ª 76.23∞,C ª 42.83∞c. Law of Cosines; A ª 60.94∞,B ª 76.23∞,C ª 42.83∞d. Law of Cosines; No solutione. Law of Sines; No solution

48

____ 116. Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle. Round your answer to two decimal places.

a = 165,B = 14∞, C = 9∞

a. Law of Sines; A = 157∞,b ª 102.16, c ª 66.06b. Law of Cosines; No solutionc. Law of Cosines; A = 157∞,b ª 102.16, c ª 66.06d. Law of Sines;A = 157∞,b ª 66.06, c ª 102.16e. Law of Sines; No solution

ID: A

1

Acc. Pre-Calculus Final Exam ReviewAnswer Section

1. ANS: E PTS: 1 REF: 1.4.37a 2. ANS: E PTS: 1 REF: 1.4.37b 3. ANS: B PTS: 1 REF: 1.4.38c 4. ANS: B PTS: 1 REF: 1.4.41c 5. ANS: B PTS: 1 REF: 1.4.44a 6. ANS: B PTS: 1 REF: 1.4.71 7. ANS: C PTS: 1 REF: 1.4.73 8. ANS: E PTS: 1 REF: 1.4.81 9. ANS: C PTS: 1 REF: 1.4.80 10. ANS: D PTS: 1 REF: 1.4.68

OBJ: Find values that equate two functions 11. ANS: A PTS: 1 REF: 1.5.23 12. ANS: B PTS: 1 REF: 1.5.24 13. ANS: E PTS: 1 REF: 1.5.25 14. ANS: C PTS: 1 REF: 1.5.26 15. ANS: A PTS: 1 REF: 1.8.9a 16. ANS: A PTS: 1 REF: 1.8.9b 17. ANS: E PTS: 1 REF: 1.8.11c 18. ANS: B PTS: 1 REF: 1.8.11d 19. ANS: E PTS: 1 REF: 1.8.17 20. ANS: D PTS: 1 REF: 1.8.18 21. ANS: D PTS: 1 REF: 1.8.19 22. ANS: A PTS: 1 REF: 1.8.37a 23. ANS: C PTS: 1 REF: 1.8.37b 24. ANS: A PTS: 1 REF: 1.8.41a 25. ANS: D PTS: 1 REF: 1.8.43b 26. ANS: D PTS: 1 REF: 2.1.26

OBJ: Determine x-intercepts of quadratic function 27. ANS: E PTS: 1 REF: 2.1.25

OBJ: Determine x-intercepts of quadratic function 28. ANS: E PTS: 1 REF: 2.2.55 29. ANS: B PTS: 1 REF: 2.2.57 30. ANS: B PTS: 1 REF: 2.2.59 31. ANS: C PTS: 1 REF: 2.2.63 32. ANS: B PTS: 1 REF: 2.3.15 33. ANS: B PTS: 1 REF: 2.3.16

OBJ: Divide polynomials using long division

ID: A

2

34. ANS: A PTS: 1 REF: 2.3.18 OBJ: Divide polynomials using long division

35. ANS: E PTS: 1 REF: 2.3.21 OBJ: Divide polynomials using long division

36. ANS: C PTS: 1 REF: 2.3.27 OBJ: Divide polynomials using synthetic division of polynomial

37. ANS: A PTS: 1 REF: 2.3.67b OBJ: Factor polynomial given factor(s)

38. ANS: D PTS: 1 REF: 2.3.70 OBJ: Factor polynomial given factor(s)

39. ANS: A PTS: 1 REF: 2.3.55a 40. ANS: C PTS: 1 REF: 2.3.55b 41. ANS: D PTS: 1 REF: 2.3.55c 42. ANS: A PTS: 1 REF: 2.3.56a 43. ANS: A PTS: 1 REF: 2.4.23 44. ANS: C PTS: 1 REF: 2.4.27 45. ANS: D PTS: 1 REF: 2.4.28 46. ANS: A PTS: 1 REF: 2.4.31 47. ANS: C PTS: 1 REF: 2.4.33 48. ANS: B PTS: 1 REF: 2.4.37 49. ANS: A PTS: 1 REF: 2.4.38 50. ANS: A PTS: 1 REF: 2.4.52 51. ANS: E PTS: 1 REF: 2.4.53 52. ANS: B PTS: 1 REF: 3.3.45 53. ANS: D PTS: 1 REF: 3.3.46 54. ANS: A PTS: 1 REF: 3.3.54 55. ANS: E PTS: 1 REF: 3.3.60 56. ANS: D PTS: 1 REF: 3.3.63 57. ANS: D PTS: 1 REF: 3.4.13 58. ANS: A PTS: 1 REF: 3.4.14 59. ANS: A PTS: 1 REF: 3.4.16 60. ANS: B PTS: 1 REF: 3.4.40 61. ANS: A PTS: 1 REF: 3.4.42 62. ANS: D PTS: 1 REF: 3.4.44 63. ANS: A PTS: 1 REF: 3.4.49 64. ANS: E PTS: 1 REF: 3.4.50 65. ANS: D PTS: 1 REF: 4.1.31a 66. ANS: D PTS: 1 REF: 4.1.32a 67. ANS: C PTS: 1 REF: 4.1.61a 68. ANS: D PTS: 1 REF: 4.1.62b

ID: A

3

69. ANS: E PTS: 1 REF: 4.1.65 70. ANS: E PTS: 1 REF: 4.1.67 71. ANS: C PTS: 1 REF: 4.3.5 72. ANS: D PTS: 1 REF: 4.3.6 73. ANS: A PTS: 1 REF: 4.3.7 74. ANS: B PTS: 1 REF: 4.3.16 75. ANS: E PTS: 1 REF: 4.3.17 76. ANS: B PTS: 1 REF: 4.5.11 77. ANS: C PTS: 1 REF: 4.5.13 78. ANS: B PTS: 1 REF: 4.5.44 79. ANS: B PTS: 1 REF: 4.5.43 80. ANS: E PTS: 1 REF: 4.7.60

OBJ: Find the exact value of an expression involving inverse function 81. ANS: A PTS: 1 REF: 4.7.65

OBJ: Find the exact value of an expression involving inverse function 82. ANS: B PTS: 1 REF: 5.1.37 83. ANS: D PTS: 1 REF: 5.1.43 84. ANS: E PTS: 1 REF: 5.2.23 85. ANS: C PTS: 1 REF: 5.2.24 86. ANS: B PTS: 1 REF: 5.2.25 87. ANS: E PTS: 1 REF: 5.2.28 88. ANS: B PTS: 1 REF: 5.3.11 89. ANS: C PTS: 1 REF: 5.3.13 90. ANS: B PTS: 1 REF: 5.3.16 91. ANS: B PTS: 1 REF: 5.3.12 OBJ: Solve trig equations 92. ANS: B PTS: 1 REF: 5.3.17 OBJ: Solve trig equations 93. ANS: C PTS: 1 REF: 5.3.22 OBJ: Solve trig equations 94. ANS: A PTS: 1 REF: 5.4.30 95. ANS: D PTS: 1 REF: 5.4.31 96. ANS: C PTS: 1 REF: 5.4.32 97. ANS: D PTS: 1 REF: 5.4.33 98. ANS: A PTS: 1 REF: 5.4.35 99. ANS: B PTS: 1 REF: 5.5.11 100. ANS: C PTS: 1 REF: 5.5.12 101. ANS: B PTS: 1 REF: 5.5.13 102. ANS: E PTS: 1 REF: 5.5.14 103. ANS: A PTS: 1 REF: 5.5.15 104. ANS: C PTS: 1 REF: 6.1.13 105. ANS: C PTS: 1 REF: 6.1.14 106. ANS: B PTS: 1 REF: 6.1.28

ID: A

4

107. ANS: D PTS: 1 REF: 6.1.29 108. ANS: E PTS: 1 REF: 6.1.45 109. ANS: B PTS: 1 REF: 6.1.5

OBJ: Solve triangles using the Law of Sines (ASA) 110. ANS: C PTS: 1 REF: 6.1.6

OBJ: Solve triangles using the Law of Sines (AAS) 111. ANS: C PTS: 1 REF: 6.2.5 112. ANS: D PTS: 1 REF: 6.2.6 113. ANS: D PTS: 1 REF: 6.2.7 114. ANS: E PTS: 1 REF: 6.2.8 115. ANS: C PTS: 1 REF: 6.2.30 116. ANS: A PTS: 1 REF: 6.2.32

Acc. Pre-Calculus Final Exam Revie...2 ____ 6. Find the domain of the function. f(x) = 2x2 + 4x - 5...

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Transcript of Acc. Pre-Calculus Final Exam Revie...2 ____ 6. Find the domain of the function. f(x) = 2x2 + 4x - 5...