Honors Precalculus Summer Assignment

Welcome to Honors Precalculus! This summer review assignment is designed to refresh your Algebra 2

skills. It includes information that was taught in Honors Algebra 2 and will be used throughout the

Precalculus course.

Assignment Requirements: You MUST show all work in order to receive credit! This includes the

multiple choice problems. All work must be done on a separate sheet of paper in a neat and organized

manner. No work, no credit! Please fill in the correct multiple choice answers on the provided bubble

sheet. The majority of the questions should be completed without the use of a calculator.

Due Date: This packet must be completed by the first day of school. Ten points will be deducted for each

day that the packet is late.

Grading: This assignment will be collected and graded upon completion and correctness. It will count as

an assessment grade for Term I. During the first week of school, a test on this material will be given during

class.

About Honors Precalculus: Honors Precalculus is a rigorous and fast-paced course. This standards based

course that meets every other day emphasizes the use and application of polynomial, rational, radical,

logarithmic and trigonometric functions and their application and the concept of theory of limits. There will

be extensive use of the graphing calculator, which is required for this course.

Questions?: If you have any questions about the Precalculus course or if you are having difficulty with this

packet, there will be help available in the IMC on Wednesdays from 10:00 am to noon (starting July 6th).

Part I: Multiple Choice: Bubble the correct answer on the bubble sheet. Show all work on separate piece

of paper. Work must support answer chosen to receive credit.

1. Determine the slope of the line .1247 yx

A. 7 B. 7

4 C. -3 D.

4

7

2. Find the slope-intercept form of a line passing through the points (-4, 1) and (5, 2).

A. 3

31

3

5 xy C. 133 xy

B. 9

23

9

1 xy D.

9

13

9

1 xy

3. Write the slope-intercept form of the equation of a line passing through the point (2, 1) and perpendicular

to the line .324 yx

A. 32 xy B. 22

1 xy C. xy

2

1 D. 52 xy

4. In the figure below, the perimete is yxx 284 2 units and the length is .2 2 yxx What is the

width?

A. yxxw 372 2 B. 282 2 xxw C. yxw 46 D. yxw 23

5. Simplify: 2535 3 xxx

A. 652535 234 xxxx C. 6252535 234 xxxx

B. 625285 23 xxx D. 65225 23 xxx

6. Factor completely: xxx 4022 23

A. 452 xxx C. 245 xxx

B. 524 xxx D. 542 xxx

7. Factor completely: 8103 2 tt

A. 463 tt B. 243 tt C. 243 tt D. prime

8. Factor completely: 278 3 x

A. 36232 2 xxx C. 36232 2 xxx

B. 96432 2 xxx D. 96432 2 xxx

9. Factor completely: 14425 24 xx

A. 234 xxx C. 3344 xxxx

B. 3344 xxxx D. no solution

10. Which of the following is a factor of the polynomial ?10134 2 xx

A. 5x B. 24 x C. 54 x D. 2x

11. Which of the following is a factor of the polynomial ?2835810 tymyxtmx

A. tm 34 B. yx 72 C. tx 72 D. tm 34

12. The imaginary number 47i is equivalent to

A. i B. 1 C. i D. -1

13. Simplify: ii 15311

A. i1414 B. i44 C. i1212 D. i1614

14. Simplify: i76

3

A. i85

21

85

18 B. i

85

7

85

6 C. i

13

21

13

18 D. i

85

21

85

18

15. Simplify: ii 85108

A. 801440 i B. i14120 C. 2801440 ii D. i5088

16. Given ,18162)( 2 xxxf find the value of k if the function is written in vertex form.

A. 9k B. 4k C. 14k D. 7k

17. Which function is represent by the graph?

A. 633

1)( xxxf

B. 63)( xxxf

C. 63)( xxxf

D. 633)( xxxf

18. Graph 33)( 2 xxxf

A. C.

B. D.

19. Which of the following does not represent the parabola with a vertex at (1, 4) and x-intercepts (-1, 0) and

(3, 0).

A. 4)( 2 xxxf C. 32)( 2 xxxf

B. 41)( 2 xxf D. 31)( xxxf

20. Compare the two functions represented below. Determine which of the following statements is true.

A. The functions have the same vertex.

B. The minimum value of )(xf is the same as the minimum value of ).(xg

C. The functions have the same axis of symmetry.

D. The minimum value of )(xf is less than the minimum value of ).(xg

21. Solve: 024132 2 xx

A. 3x or 8x C. 2

3x or 8x

B. 2

3x or 8x D.

3

2x or 8x

22. Solve: 120152x

A. 23x C. 5

3025 x

B. 63x or 6 D. 621x

23. What are the solutions to the quadratic equation ?605213 2 xxx

A. 3

2948 ix

C.

3

6128 ix

B. 3

2928 ix

D.

2

618 ix

24. Simplify:

2

209

1018

16

32

yx

yx

A. 2092 yx B. 10

94

y

x C.

20

184

y

x D. 20184 yx

25. Simplify:

46

32

4

2

nm

mn

A. 10

5

32n

m B.

n

m92 C.

10

3

32n

m D.

m

n8

26. Simplify:

7

1

7

3

7

4

x

xx

A. 7

6

x B. 8

7

x C. 6

7

x D. 7

8

x

27. Determine which expression would make the following statement true:

10374

4?

16yx

yx

A. 34 xy B. 3112 yx C. 1774 yx D. 17764 yx

28. Which is equivalent to 2

3

49

A. 21 B. 98 C. 294 D. 343

29. Simplify: 3

1

3

1

93

A. 9 B. 3 3 C. 3 D. 3

30. Simplify: 12572 yx

A. 56 26 xx B. 12526 yx C. xyx 626 D. xyx 26 62

31. Simplify: 3 121348 ba

A. 342 aba B. 344 26 aba C. 344 62 aba D. none of these

32. Simplify: 103102

A. 10616 B. 1064 C. 104 D. 10515

33. Simplify: 777 xx

A. xx 497 B. xx 497 C. 497 xx D. x42

34. Simplify: x

x

2

90 18

A. xx 53 8 B. 1718x C.

835 xx D. none of these

35. Simplify: 37

37

A. 4

2124 B.

2

215 C.

4

214 D. -1

36. Solve the equation: 5109 x

A. 34 B. 25 C. 16 D. 14

37. Simplify:

mm

mmm

m

168

12684

123

2

2

2

A. 216

292

mm

m B.

2

42

m

mm C. 2m D. 23 m

38. Simplify: 55

2

1

12

xx

x

A. 115

67

xx

x B.

15

7

x C.

1

3

x D.

15

72 x

39. Simplify: 3

1

152

3522

2

qqq

qq

A. 3

8

q

q B.

3

7

q

q C. 8q D.

152

3622

2

qq

qq

40. Simplify. State any restrictions on the variables: 82

45

65

162

2

2

2

xx

xx

xx

x

A.

;

13

42

xx

x 1,3 x C.

;

32

142

2

xx

xx 4,2,3 x

B.

;

13

42

xx

x 4,1,2,3,4 x D.

;

13

1

xx 4,1,2,3,4 x

41. Simplify the complex fraction:

yy

yy

2

31

2

4

3

A. 3

20 B.

2

1 C. -2 D.

20

3

42. If each of the following expressions is defined, which is equivalent to ?1x

A.

1

11

x

xx C.

2

2

2

21

x

x

x

xx

B. 2

1

2

1

x

x

x

x D.

2

1

1

21

x

x

x

xx

43. Solve the equation: 2

5

4

7

d

d

d

d

A. 3

1d B.

9

17d C.

5

17d D.

5

17d

44. Solve the equation: 31

3

5

kk

A. 3

8k B.

9

16k C.

9

8k D.

2

1k

45. Solve: 1

4

1

7

1

12

xx

x

x

x

A. ,2x 1 B. ,1x 1 C. 2x D. no solution

46. Describe the vertical asymptote)s) and hole(s) for the graph of 42

25

xx

xxy

A. vertical asymptote: 4x and hole: 2x C. vertical asymptote: 5x and hole: 4x

B. vertical asymptotes: 4x and 2x D. vertical asymptote: 4x and hole: 2x

47. Let .712

5)(

2

2

x

xxf Which ONE of the following statements is true?

A. )(xf has exactly two vertical asymptotes. C. The domain of )(xf is all real numbers.

B. 0y is a horizontal asymptote. D. )(xf has a slant asymptote.

E. )(xf has exactly one vertical asymptote.

48. Find the slant asymptote of .3

72)(

2

x

xxf

A. 62 xy B. 12 xy C. 2y D. 102 xy

49. Find )6( tf for .192)( 2 xxxf

A. 125332 2 tt C. 125332 2 tt

B. -125 D. 125332 2 tt

50. Let 6)( 2 xxf and .8

)(x

xxg

Find 7fg .

A. 7

55 B.

7

384 C.

49

295 D.

55

63

51. Find the inverse of 10

115)(

xxf

A. 11

105)(1 x

xf C. 5

1110)(1 x

xf

B. 11

105)(1 x

xf D. 5

1110)(1 x

xf

52. Divide using synthetic division: 428554418 234 xxxxx

A. 416810 23 xxx C. 411018 23 xxx

B. 71214 23 xxx D. 14712 23 xxx

53. What is the remainder in the division ?32946 23 xxxx

A. 15 B. -3 C. 3 D. -15

54. Use the graph below to identify the y-intercepts and zeros.

A. y-intercept: 20; zeros: No zeros C. y-intercept: 20; zeros: -2.24, -2, 2, 2.24

B. y-intercepts: -2.24, -2, 2, 2.24; zero: 20 D. y-intercept: -20; zeros: -2.24, -2, 2, 2.24

55. Which polynomial is graphed below?

A. 31)( xxxf

B. 311)( xxxxf

C. 31)( xxxxf

D. 31)( xxxxf

56. What are the values of the relative maxima and/or minima of the function graphed below?

A. relative maxima: 0 C. relative maxima: 3.3 and 4.7

relative minima: -4 and 4 relative minima: 0

B. relative maxima: 10 D. relative maxima: 2 and 10

relative minima: -1 and 2 relative minima: -1

57. For the given graph below, describe the end behavior, determine whether it represents an odd-degree or

even degree polynomial function, and state the number of real zeros.

A. The end behavior of the graph is )(xf as x and )(xf as x .

It is an odd-degree polynomial function that has five real zeros.

B. The end behavior of the graph is )(xf as x and )(xf as x .

It is an odd-degree polynomial function that has five real zeros.

C. The end behavior of the graph is )(xf as x and )(xf as x .

It is an odd-degree polynomial function that has four real zeros.

D. The end behavior of the graph is )(xf as x and )(xf as x .

It is an even-degree polynomial function that has five real zeros.

58. Find the zeros of the function .1052 23 xxxy

A. -5, -2, 5 B. 5,2,5 C. -5, 5, 2 D. 2,5,5

59. Write a polynomial function in standard form with zeros at -4, 2, and -5

A. 4027)( 23 xxxxf C. 627)( 23 xxxxf

B. 61203)( 23 xxxxf D. 2740)( 23 xxxxf

60. Find a third-degree polynomial equation with rational coefficients that has roots -5 and .6 i

A. 0237 23 xxx C. 0185237 23 xxx

B. 037127 23 xxx D. 03712 23 xxx

61. Graph the function 1210383)( 2345 xxxxxf .

A. C.

B. D.

62. State the domain and range for the graph below.

A. Domain: (-5, 4); Range: [-2, 4) C. Domain: (-5, 4]; Range: [-4, 4)

B. Domain: [-4, 4); Range: (-5, 4] D. Domain: [-5, 4]; Range: [-4, 4]

63. If )(xf is given below, then what is ?)2(f

A. 6 B. 4 C. 2 D. 1

64. Evaluate: 8log5

A. 0.2041 B. 0.7740 C. 1.0586 D. 1.2920

65. Rewrite 9ln2

13ln4 as a single logarithm,

A. 7.2ln B. 3ln C. 27ln D. 243ln

66. Solve for x: )2log(4log3log xx

A. -8 B. 7

8 C. 3 D. 8

67. Solve for x: 22ln 35 xe

A. 5

19 B. 5 C.

5

3

ln

22

e D.

5

22ln3

68. Solve for x: 1)1log(21log xx

A. 3

1 B.

3

2 C.

12

11 D. no solution

69. Solve for x: )563(log)2(loglog 444 xxx

A. -54 B. -7 C. -7 and 8 D. 8

Use the formulas

nt

n

rPA

1 and rtPeA to answer questions 70 and 71.

70. How much MORE money will you earn in an account that compounds interest continuously than in an

account that compounds interest quarterly if you invest $3,000 for 7 years at an interest rate of 11%?

A. $67.02 B. $59.37 C. $101.16 D. $35.52

71. Find the initial amount invested at 7.25% interest compounded quarterly if, after 6 years, it has grown to

$20,000.

A. $12,945.29 B. $12,995.82 C. $13,141.54 D. $30,779.14

72. Expressed in radian measure, 235 is

A. 235

B.

235 C.

36

47 D.

47

36

73. What is the value of 240sin ?

A. 2

1 B.

2

1 C.

2

3 D.

2

3

74. The value of 3

2cos

2

3sin

is

A. 2

1 B.

2

1 C.

2

3 D.

2

3

75. Find the exact value of .30csc45cot60sec

A. 1 B. 2 C. 2

3

2

3 D. 5

76. Use the angle 4.37 to determine the exact value of x in the figure below.

A. 4.37sin6.15x C. 4.37cot6.15x

B.

6.15

4.37tan

x D.

6.15

4.37cot

x

E. 4.37tan6.15x

77. In the unit circle shown below, what are the coordinates of B?

A.

2

3,

2

1 B.

2

1,

2

2 C.

2

1,

2

3 D.

2

2,

2

2

78. What is the value of ?2

2arcsin

A. 4

B.

4

C.

2

D.

2

79. What is the value of ?3tancos 1

A. 1 B. 2

1 C.

2

3 D.

2

2

80. Which expression is not equivalent to 150sin ?

A. 30sin B. 210sin C. 60cos D. 60cos

81. The expression

sec

tanis equivalent to

A.

sin

cos2

B.

2cos

sin C. cos D. sin

82. What value of x in the interval 1800 x satisfies the equation ?01tan3 x

A. 30 B. 30 C. 60 D. 150

83. The line of a sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 25 feet

above the water makes a 25 angle with the water. To the nearest foot, how far is the boat from the cliff?

A. 141 feet B. 129 feet C. 27 feet D. 75 feet

35ft

2525

o ft

Drawing is not to scale.

25

84. In XYZ , Y is a right angle and . In lowest terms, find cos X .

A. 4

3 B.

4

5 C.

5

3 D.

3

5

85. Find the exact value of .4

cos

A. 2

2 B.

2

2 C.

2

3 D.

2

3

X

Z

Y

2025

Part II: Matching: Match the following equations to their description.

Part III: Function Transformation: Use the graph of )(xfy below to sketch the following

transformations.

Part IV: Short Answer: Answer the questions on a separate piece of paper. Work must be shown in order

to receive credit. Use the attached graph paper to graph required functions.

1. Given the following quadratic equation 1582 xxy , find

a. direction of opening

b. the axis of symmetry

c. the vertex

d. the maximum/minimum value

e. the y-intercept

f. the x-intercepts/roots/zeros

g. Graph the parabola, finding at least 3 additional points. Use the graph paper included in the packet.

h. Write the equation in vertex form.

2. For 603815)( 24 xxxxh

a. How many zeros should this polynomial function have?

b. How many turns could the graph of the equation make?

c. What is the end behavior of the graph of the function?

d. State the number of positive, negative, and imaginary zeros using Descartes Rule of Signs.

e. Use the Rational Zero Theorem to find the possible rational zeros of the polynomial function.

f. Find all the zeros of the polynomial function (real and imaginary).

3. For 1284

127)(

2

2

xx

xxxf

a. State all the discontinuities.

b. Write the equations of any vertical asymptotes.

c. Write the equations of any horizontal asymptotes.

d. State the ordered pairs for any holes.

e. Write the ordered pairs for any x-intercepts.

f. Write the ordered pair for the y-intercept.

g. Graph the rational function, finding additional points. Use the graph paper included in the packet.

h. Using interval notation, state the domain and range of the rational function.

4. Find the six trigonometric ratios for the right triangle given below.