Honors Precalculus Summer Assignment - Fall River Precalculus Summer Packet...Honors Precalculus...

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Transcript of Honors Precalculus Summer Assignment - Fall River Precalculus Summer Packet...Honors Precalculus...

  • 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: 12015 2 x

    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. 76

    x B. 87

    x C. 67

    x D. 78

    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 23

    49

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

  • 29. Simplify: 31

    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.

    157

    x C.

    1

    3

    x D.

    1572 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