Honors Pre-Calculus Summer Assignment
2017-18 School Year
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 on 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 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?: Starting July 13th
Ms. Mullen will be in the IMC on Thursdays from 10am to noon if you need
extra help. If you have further questions, also try emailing your teacher or math department dean.
Mrs. Brogan => [email protected]
Mrs. Clements => [email protected]
Mr. Pineault => [email protected]
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
3025x
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
A. 3
8
q
q B.
3
7
q
q C. 8q D.
152
3622
2
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 # 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
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. Consider the following piecewise function:
Carefully graph the function. Identify whether or not he graph is a function. Then, evaluate the graph
at any specified domain value. You may use your calculators to help you graph, but you must sketch it carefully on the
grid!
212
25)(
xx
xxxf
Function? Yes or No
3
4
2
f
f
f
5. Consider the following piecewise function:
Carefully graph the function. Identify whether or not he graph is a function. Then, evaluate the graph
at any specified domain value. You may use your calculators to help you graph, but you must sketch it carefully on the
grid!
243
224)(
xx
xxxf
Function? Yes or No
4
8
2
f
f
f