topic with non-...

1

FINAL EXAM TOPIC ASSIGNMENT

There are 50 questions altogether.

32 questions on the non-calculator section &

18 questions on the calculator section.

TOPIC With

Calculator

Non-

Calculator

Trigonometry

Transformations

Parametric Equations

Summation Notation

Binomial Expansion/Specific Term

Sequence/Series

Exponential Graphs

Exponential/ Banking Applications

Solving Exponential Equations

Properties of Logs

Log Graphing

Solving Log Equations

Polynomial Function and Graphs

Zeros of Polynomials

Rational Functions and Graphs

The above chart is subject to slight modification.

A calculator may be used for questions indicated with an “*”;

do all other questions by hand – no calculator!.

2

Review for Spring Exam 2014

For questions 1 and 2, consider the pair of parametric equations: 4

2 3

x t

y t

______1. Find the rectangular form of the parametric equations above.

(A) 22 5y x

(B) 22 11y x

(C) 5

2

yx

______2. Find the restrictions placed on t, x, and y.

(A) 4, 0, 5t x y

(B) 4, 0, 5t x y

(C) 4, 0, 5t x y

______3. Identify the curve for the pair of parametric equations: cosθ

cos2θ

x

y

(A) parabola opening up

(B) a portion of a parabola opening up

(C) vertically-oriented hyperbola

(D) a portion of a vertically-oriented hyperbola

______4. Which graph best illustrates the parametric equations 2sinθ 1

3cosθ 1

x

y

(A) (B) (C)

x

y

x

y

x

y

3

______5. Identify the curve for the parametric equations: 2 23 , 1 2x t y t

(A) (B) (C) (D)

______6. Evaluate 77

8

3n

(A) 207

(B) 210

(C) 231

______7. Evaluate 5

0

!

2n

n

(A) 77

(B) 77.5

(C) 154

______8. Find the sum: 6

2

1 2k

k

k

(A) 40

(B) -4

(C) 6

(D) 8

x

y

x

y

x

y

x

y

4

______9*. 400!

398! 2!=

(A) impossible

(B) 79,800

(C) 159,600

______10. ( 1)!

( 1)!

n n

n

=

(A) 2n n

(B) 2

1

n n

(C) 1

1n

______11. 2 !

(2 3)!

n

n=

(A) 2

2 3

n

n

(B)

2

1 2n n

(C) 2 1 2n n n

(D) 2 2 1 2 2n n n

______12. Which of the following is the definition of e?

(A) 1

2

!n

n

n

(B) 1

1

!n n

(C) 0

1

!n n

5

______13*. Evaluate: 16

14

(A) 8/7

(B) 120

(C) 224

______14. Which of the following is not equal to 1 if x is any whole number?

(A) x xC

(B) 0xC

(C) 1xC

______15. Find a value of x (other than 50) for which the following is true: 500 500

50 x

(A) 450

(B) 250

(C) 10

______16. Expand 4

5 2i without a calculator.

(A) –41–840i

(B) 41 +840i

(C) 41–840i

______17*. Find the middle term in the expansion of

10

2

4

xy

.

(A)

510263

256

x y

(B) 5 5252x y

(C) 5 1063

256

x y

6

______18. Find the term containing x6 in the expansion of

83x y .

(A) 6 228x y

(B) 5 628x y

(C) 6 628x y

(D) 6 256x y

______19. Use the Binomial Theorem to expand 3

2 .x y

(A) 3 2 2 32 6 6x x y xy y

(B) 3 2 2 38 4 2x x y xy y

(C) 3 2 2 32 3 3x x y xy y

(D) 3 2 2 38 12 6x x y xy y

______20*. Given the explicit definition, find the 30th

term: ( 1) 2

4 5

n

n

na

n

.

(A) 12

25

(B) 12

23

(C) 12

23

______21. Find the tenth term of the sequence whose nth term is defined as

2 1

5 3 1n

na

n

(A) 21

32

(B) 21

72

(C) 22

32

(D) 19

29

7

______22. Which of the following is the recursive definition for the sequence shown below?

1

120, 40, 13 ,...3

nd

(A)

11

1203

n

nd

(B) 1 1

1120,

3n nd d d

(C) 1

1

3n nd d

(D) 1 1120, 3n nd d d

______23. Which of the following is an arithmetic sequence?

(A) 2, 4, 8, 16, 32,... (B) 2, 4, 8, 16, 32,...

(C) 3, 6, 9, 12, 15,... (D) 2, 4, 6, 10, 16,...

______24. In an arithmetic sequence, 5 38a and 9 21a . Which is the 25th

term in the sequence?

(A) –47

(B) 165.5

(C) –17.75

______25. Which of the following is a geometric sequence?

(A) 1 1 1 1

2, , , , ,...2 4 6 8

(B) 2, 4, 8, 16, 32,...

(C) 2, 0, 2, 4, 6,... (D) 2, 7, 3, 8, 4,...

______26*. In a geometric sequence, 2 80000g and 6 32768g . Which is the 7th

term in the sequence?

(A) 100000

(B) 26214.4

(C) 20971.52

(D) 16777.216

______27. Rewrite the following definition explicitly: 1 n n-1A 9, A 4 A

(A) n 1nA 9(4) (B) nA 9 4n (C)

n 1

n

1A 9

4

(D) nA 5 4n

8

______28*. Find the sum of the finite arithmetic sequence: 5,9.5,14,...,68}

(A) 543

(B) 547.5

(C) 552

(D) 556.5

______29*. Find the sum: 500

1

3 5n

n

(A) 756, 500

(B) 376,250

(C) 752,500

(D) 378,250

______30*. Find the sum of the finite geometric sequence: 1,3,9,...,6561

(A) 9841

(B) 11327

(C) 18336

(D) 29524

______31*. Find the sum of the expression: 10

0

32

5

n

n

to four decimal places.

(A) 4.9698

(B) 5.0000

(C) 4.9819

(D) 55.0000

______32*. Determine whether the infinite geometric series converges and if so, find the sum:

500 100 20 4 ...

(A) diverges (B) converges; 624

(C) converges; 625 (D) converges; 626

9

______33*. Evaluate: 0

25

3

n

n

(A) 6

(B) 3

(C) 1

(D) 0

______34. Solve for x:

2 1

5127

9

x

x

(A) x = 4/3

(B) x = –17

(C) x = 13/7

_____35*. The population of Bedrock is 14,500. If it decreases at a rate of 2½ % per year, what will the

population be in 10 years?

(A) 816.55

(B) 1462.31

(C) 11256.78

(D) 18561.22

_____36*. The population of Smallville is 50,000. It increases at a rate of 3.12% per year. In how many

years will it reach 60,500?

(A) 0.16 years

(B) 0.7 years

(C) 4.5 years

(D) 6.2 years

10

_____37*. A substance weighing 10 grams has a half-life of 36 days. After how many days will the

substance weigh only 2 grams?

(A) 63.14 days

(B) 75.68 days

(C) 83.59 days

(D) 92.34 days

_____38. Which of the following is the graph of 24 3xy ?

(A) (B) (C)

For questions 39-42, match each function with the correct graph.

______39. 14 3xy (A) (B) (C)

______40. 34 3xy

______41. 22 4 3xy (D) (E)

______42. 24 1xy

______43. Which of the following is the graph of 1 1xy e ?

(A) (B) (C)

(3, -2)

(-1, -4)

(2, 0)

(-2, -1)

(1, -4)

x

y

(2, -2)

x

y

(-2, -2)

x

y

(-2, -2)

x

y

(1, 2)

x

y

(-1, 2)

x

y

(-1, -2)

11

______44. The domain of 3 xy e is:

(A) 3, (B) 0, (C) , (D) ,3

______45. The range of 3 xy e is:

(A) ,3 (B) ,3 (C) 3, (D) ,

_____46. Determine the x-intercept: 22 3 5xy

(A) 3log 2.5 2

(B) ln2.5 2ln3

ln3

(C) 2.5log 3 2

(D) 2log3 log2.5

log3

_____47. Which of the following is not equivalent to 21(2) 2

2

xy ?

(A) 21(2) 2

2

xy

(B) ( 2)1(2) 2

2

xy

(C)

21 1

22 2

x

y

(D)

21 1

22 2

x

y

(E) ( 2)1

2 22

xy

_____48*. Determine how much money must be deposited at 9% interest compounded monthly in order to

have a balance of $35,000 after 20 years.

(A) $5824.45

(B) $6914.23

(C) $9470.02

(D) $12500.00

12

_____49*. If $9200 is invested at 9.5% interest compounded continuously, find the balance in the account

after 10 years.

(A) $17940.00

(B) $22628.35

(C) $23788.53

(D) $25040.56

For questions 50-53, match each function with one of the graphs shown on the right.

_________50. 1

2 3x

y

(A) (B)

_________51.

11

32

x

y

_________52. 212 3

xy

(C) (D)

_________53.

211

2 32

x

y

__________54. Identify the CP’ for

21

5 42

x

y

(A) (-2, 4)

(B) (-2, -1)

(C) (-2, 9)

__________55. Which functions have a point that is a “cusp” at the CP’?

(A) x

y b (B) 2xy b

__________56. Which functions have a smooth, rounded shape at the CP’?

(A) x

y b (B) 2xy b

x

y

xy

x

y

x

y

13

_____57. Evaluate: 7ln 7

(A) 1 (B) 0 (C) 2 (D) 49

_____58. Evaluate: 1ln xe

(A) 1 xe

(B) e

(C) 1 x

(D) ln 1 x

_____59. 4log 20 is equivalent to

(A) log 5 (B) 20 log 4 (C) log20

log4 (D)

log4

log20

______60. Write in logarithmic form: 34 64

(A) 4log3 64 (B) 3log 64 4 (C) 3log 4 64 (D) 4log 64 3

______61. Which of the following represents the condensed form of the log expression given below?

1

log 3log log2

x y z

(A) 3

logx z

y

(B)

3log

x

y z (C)

3

log

log

x

y z (D)

2

3log

x z

y

______62.Which of the following represents the expanded form of the log expression shown?

22 3

log10

a b

(A) 2log 3log 2a b (B) 1

4log log 13

a b

(C) 1

2log log 13

a b (D) 2

4log log 23

a b

14

_____63. Solve for x: 82log ( ) 5 1x

(A) 6561 (B) 1

64 (C) 262144 (D) 512

_____64*. Determine the y-intercept: 4log 3 1y x

(A) –0.21 (B) –1.79 (C) –0.88 (D) –1.12 (E) none

_____65. Determine the x-intercept: 1

2

log 5 2y x

(A) 4.75

(B) 5.25

(C) 1

(D) 1.25

(E) none

______66. Solve for x: 14 9x x

(A) log9

log4 log9

(B) log9

log9 log4

(C) log4

log4 log9

______67. Solve for x: 2 1ln 9xe

(A) 1 ln9

2

(B)9 1

2ln 2e

(C) 23

(D) 4

15

______68. Solve for x: 2

6010

4 xe

(A) 2

ln2 (B)

ln 20

2

(C) ln1 (D) ln2

2

______69*. Solve for x: ln 2 ln 5 2ln2x x [Do NOT solve graphically]

(A) 2.53, -5.53

(B) 2.53

(C) 5.53

(D) { }

70. Matching: Write the letter of the graph which best illustrates each function.

_______i. log 1 2y x A. E.

_______ii. 22 1

xy

_______iii. log 1 2y x

_______iv. ln 1 2y x B. F.

_______v. 15 2 2x

y

_______vi. 20.5 1

xy

_______vii. 22 1

xy

C. G.

_______viii. 10.5 2x

y

D. H.

(-1, 3)

(-2, 0)

16

______71. Which of the following best illustrates the graph of lny x ?

(A) (B) (C)

______72. Which of the following best illustrates the graph of 7

4

log ( ) 1y x ?

(A) (B) (C) (D)

______73. The domain of ln 3 1y x is:

(A) 1

,3

(B) , (C)

1 1, ,

3 3

(D) 0,

______74. The range of 3 xy e is:

(A) , 3 (B) ,3 (C) 3, (D) ,0

______75. Which function(s) will have a “double hockey stick?”

I. logy x II. logy x III. 2

logy x

(A) I only (B) II only (C) III only (D) none

(E) all (F) I and II (G) II and III

______76. Find the translation (not the T.P.) for: log 10 50 2y x .

(A) right 5, up 2

(B) left 50, up 2

(C) right 50, up 3

(D) right 5, up 3

x

y

x

y

x

y

x

y

x

y

x

y

x

y

17

______77. Find all the real zeros of the polynomial function: 4 25 36f x x x

(A) 3, 2

(B) 3

(C) 3, 2

(D) 2

______78. Find a polynomial function with the given zeros: –2, –2, 1, 3

(A) 1 3 2f x x x x

(B) 2

1 3 2f x x x x

(C) 2

1 3 2f x x x x

(D) 1 3 2f x x x x

______79. Determine the correct function for the given graph.

(A) 3 22 3f x x x

(B) 4 33 2f x x x

(C) 3 22 3f x x x

(D) 2 33 2f x x x

______80. Find a fourth degree polynomial with real coefficients that has zeros: 2, 3, 2i

(A) 4 3 25 8 10 12f x x x x x

(B) 4 25 6f x x x

(C) 4 3 25 6f x x x x

(D) 4 3 25 8 10 12f x x x x x

x

y

18

______81. Find a quadratic polynomial with real coefficients that has zeros: 2 5 3

4

i

(A) 216 16 79f x x x

(B) 216 16 29f x x x

(C) 24 16 79f x x x

(D) 216 16 79f x x x

______82. Determine the correct function for the given graph.

[assume least multiplicity]

(A) 2 33

2 1 34

f x x x x

(B) 2 31

2 1 34

f x x x x

(C) 2 31

2 1 34

f x x x x

(D) 2 31

2 1 34

f x x x x

______83. Which of the following is the graph of 2 23 2 4 2f x x x x

(A) (B) (C) (D)

______84. Use synthetic division to divide: 3 8x by 2x

(A) 2 2 4x x

(B) 2 4x

(C) 2 2 4x x

(D) 2 2 4x x

x

y

x

y

x

y

x

y

x

y

19

______85. Divide: 4 3

2

3 2 3 1

1

x x x

x

(A) 2

2

5 23 2 3

1

xx x

x

(B) 2

2

5 43 2 3

1

xx x

x

(C) 3 2

2

53 4

1x x x

x

(D) 2

2

4 53 1

1

xx x

x

______86. Which of the following is not a possible rational zero of 2 33 5 2f x x x

(A) 2

3

(B) 2 (C)

2

5 (D)

1

5

______87. Find all the real zeros of the function 3 22 14 24f x x x x

(A) 0, 3, 4

(B) 3, 4

(C) 4, 3, 0

(D) 0, 1, 6

______88. Find all the real zeros of the function 3 2 3 1f x x x x

(A) 1, 2

(B) 1, 1 2

(C) 1, 2

(D) 1, 1 2

______89. Simplify: 3

25

(A) 125

(B) 125i

(C) 125i

(D) 125

20

______90. Divide, then write the result in standard form: 4

1 4

i

i

(A) 8

17i

(B) i

(C) i

(D) 8

17i

______91. Simplify: 37 726 4i i

(A) 6 4i

(B) 4 6i

(C) 6 4i

(D) 4 6i

______92. Solve for x: 23 4 2x x

(A) 2 2 2

3

i

(B) 2 2 10

3

(C) 2 2

3

i

(D) 2 10

3

______93. Use the fact that 2 3i is a zero of f to find the remaining zeros:

4 3 26 12 2 21f x x x x x

(A) 2, 2, 2 3i

(B) 1, 3, 2 3i

(C) 1, 3, 2 3i

(D) 1, 3, 2 3i

______94. Find the domain: 2

2

3 2

xf x

x x

(A) all reals (B) all reals except 2, 1, 2x

(C) all reals except 2x (D) all reals except 1, 2x

21

______95. Find the equation of any horizontal asymptote(s): 5 3

2 5

xf x

x

(A) 5

2y

(B)

3

2y

(C)

3

5y

(D)

3

2y (E) none (Egyptian)

______96. Find the equation of any vertical asymptote(s) and whether each has a ‘jump’ or ‘stay’:

3 2

1

1 3

xf x

x x

(A) 1 , 3J Sx x (B) 1 , 3J Sx x (C) 1 , 3S Jx x (D) 1 , 3S Jx x

______97. Find the location of any crossing(s):

2

2 1 6

3

x xf x

x

(A) no crossings (B) 24

, 223

(C)24

, 123

(D) 24

, 223

______98. Find the location of any crossing(s):

3 2

2

3 3

4

x x xf x

x

(A) 3, 0 (B) 3, 6 (C) 3, 6 (D) 5, 5 (E) no crossings

______99. Determine the end behavior of the rational function:

2 3

2

2 1 2 4

4

x x xf x

x

(A) even-positive (B) odd-positive (C) even-negative (D) odd-negative

______100. Determine the location of any hole(s):

2

2

1 2 3

1 2 3

x x xf x

x x x

(A) no holes (B) 1, 2 (C) 3, 0

(D) 1, 2 and 3, 0 (E) 4

1, and 3, 03

22

______101. Which of the following function describes the graph shown:

(A)

2

2 4

3

xy

x

(B) 2 4

3

xy

x

(C) 3 6

3

xy

x

(D) 2 4

3

xy

x


(A) 2

10

4y

x

(B) 2

8

4y

x

(C)

2

10

2y

x

(D) 2

10

4y

x


(A) 2

2

4

9

xy

x

(B) 2 2

2

4

9

x xy

x

(C) 2

2

4

9

x xy

x

(D) 2

2

4

9

x xy

x

x

y

x

y

x

y

23


(A)

22

2

2 2

1

x x xy

x

(B)

22

2

2 2

1

x x xy

x

(C)

22 2 2

1

x x xy

x

(D)

22

2

2 2

1

x x xy

x


(A) 2

1

x xy

x

(B) 2

1

x xy

x

(C) 2

1

x xy

x

(D) 3 2

1

x xy

x

x

y

x

y

24

106. Find tan if sec = 13

5 and sin 0.

a. 12

5 b.

5

12 c.

12

5 d.

5

12 e.

13

12

107. Which of the following best represents one cycle of the graph of 3

2cos 3 14

y x

?

a. b. c.

d. e.

y

x

y

x

y

x

4

7

12

11

12

y

x

12

5

12

3

4

12

5

12

3

4

12

4

5

12

y

x

12

5

12

3

4

25

108. Which equation is best represented by the graph shown?

a. 2cot 28

y x

b. 2tan 28

y x

c. 2tan 28

y x

d. 2cot 28

y x

e. 5

2tan 28

y x

109. Find the radian solutions for x over the interval [0, 2).

24sin 1 0x

a. π 5π

,6 6

b. π 3π 5π 7π

, , ,4 4 4 4

c. π 3π

,4 4

d. π 2π 4π 5π

, , ,3 3 3 3

e. π 5π 7π 11π

, , ,6 6 6 6

110. Simplify the trigonometric expression: 2 2 2cot csc sinx x x

a. -1 b. csc2 x c.

2cot 1x d. 1 e. sin(2x)

111. Evaluate: arcsec 2 =

a. 5π

6 b.

11π

6 c.

π

6 d.

π

3 e.

2π

3

112. * Which of the following is not coterminal with an angle of 45o .

a. 9π

4 b.

7π

4

c. 2565 d.

7π

4 e. 1755o

y

x

4

26

113. * Which of the following is the reference angle for -147

114. * An observer is 250ft from a flagpole. The angle of depression from the top of the flag pole

to the observer is 47o. Find the height of the flagpole.

a. 233.12 b. 268.09 c. 318.31 d. 172.65 e. 293.01

115. * Find two values of over the interval [0, 360): sinθ = -0.258

a. 14.951, 110.916 b. 14.951, 249.084

c. 194.951, 345.049 c. 165.049, 345.049

116. Find the values of 2

cos(2 )2

x , over the interval 0 360ox

a. 45o, 315

o b. 22.5

o, 157.5

o c. 22.5

o, 157.5

o, 202.5

o, 337.5

o

d. 45o, 135

o, 225

o, 315

o

117. * In ABC, a = 6, b = 12, and c = 7. Find the measure of the largest angle to the nearest

tenth of a degree.

a. 43.5 b. 100.3 c. 36.2 d. 134.6

a. 213 b. -213 c. 0.26 d. 33 e. 0.56

27

118. * Determine the period of the function: 1

cot2 6

xy

.

a. 1

6 b. c. 6 d. 12 e. 2

119. The equations of 3 consecutive asymptotes of 1

csc(4 4π)2

y x are:

a. 0 and and 2

b. and

4 2

c. and and

4 4 2

d. 5 3

and and 4 2

e. 0 and and 2

For the following questions, find the area of ABC and match it with the answers provided.

120. * a = 19, b = 8, c = 15

a. 60.00

b. 31.44

121. * C = 109, a = 7, b = 9.

c. 27.16

d. 6468

e. 57.24

122. What is the equation of the following graph?

a. 2

12

( 1)y

x

b. 1

2( 1)

yx

c. 2

12

( 1)y

x

d. 1

2( 1)

yx

e. 2

12

( 1)y

x

x

y

28

The following three questions are based on the formula: 39 6

5 310 7

y x , compared to a graph of

3y x

123. The 9/10 on the outside produces a:

a. Horizontal compression by a factor of 9/10 b. Horizontal stretch by a factor of 10/9

c. Vertical compression by a factor of 9/10 d. Vertical stretch by a factor of 10/9

124. The 6/7 on the inside produces a:

a. Horizontal compression by a factor of 6/7 b. Horizontal stretch by a factor of 7/6

c. Vertical compression by a factor of 6/7 d. Vertical stretch by a factor of 7/6

125. This graph exhibits:

a. A Vertical reflection only

b. No reflection

c. A Horizontal reflection only

d. Both a Horizontal and Vertical reflection

29

ANSWERS TO PRECALCULUS

HONORS EXAM REVIEW

1. A 31. C 61. B 84. A 114. B

2. C 32. C 62. D 85. B 115. C

3. B 33. B 63. D 86. A 116. C

4. A 34. B 64. B 87. C 117. D

5. A 35. C 65. C 88. D 118. C

6. B 36. D 66. A 89. C 119. D

7. A 37. C 67. D 90. B 120. E

8. D 38. B 68. D 91. D 121. B

9. B 39. E 69. B 92. C 122. C

10. C 40. A 70i. F 93. D 123. C

11. D 41. D ii. D 94. D 124. B

12. C 42. C iii. A 95. D 125. D

13. B 43. B iv. H 96. B

14. C 44. C v. B 97. D

15. A 45. B vi. E 98. A

16. C 46. A vii. G 99. C

17. A 47. C viii. C 100. D

18. C 48. A 71. B 101. B

19. D 49. C 72. C 102. D

20. C 50. C 73. A 103. C

21. A 51. B 74. B 104. A

22. B 52. D 75. G 105. B

23. C 53. A 76. D 106. C

24. A 54. B 77. B 107. A

25. B 55. A 78. C 108. B

26. B 56. B 79. D 109. E

27. D 57. A 80. D 110. B

28. B 58. C 81. D 111. E

29. D 59. C 82. D 112. D

30. A 60. D 83. C 113. D

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