review test 1 - paso robles high schoolprhs.pasoschools.org/jsteaffens/2007 files/algebra 2...28....

1. What are all the values for u that will makethe equation below true?

|3u − 9| = 3

A. 2 and 4

B. 2 and − 4

C. −2 and 4

D. −2 and − 4

2. What are all the possible roots for the equation 4|v + 4|+10 = 26?

A. −8 and 0

B. −13 and 5

C. 0

D. 5

3. Which expression is the solution of |z + 6| ≤ 5?

A. z ≤ − 1

B. −11 ≤ z

C. −11 ≤ z or z ≤ − 1

D. −11 ≤ z ≤ − 1

4. Which expression is the solution of |m − 13| > 6?

A. m < 7

B. m < 7 orm > 19

C. 7 < m < 19

D. m > 19

5. What are the coordinates of the point ofintersection of the graphs of the equationsbelow?

5x + y = 195x + y = 12

A. (10, 9)

B. (19, 12)

C. The lines are coincident.

D. The lines do not intersect; they are parallel.

6. The sum of three different numbers is 223.The largest number is 13 more than thesmallest number. The sum of the largestnumber and the smallest number is 7 morethan twice the middle number. What is thelargest of these numbers?

A. 59

B. 69

C. 72

D. 82

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7. The substitution method will be used to solvethe system of equations below.

{ x + 2y = 72x − 7y = 3

Which equation would lead to a correctsolution with this method?

A. (7 − 2y) + 2y = 7

B. (7 + 2y) + 2y = 7

C. 2(7 − 2y) − 7y = 3

D. 2(7 + 2y) − 7y = 3

8. The length of a rectangle can be represented by the expression 2x − 1. The width of the same rectangle can be represented by the expression x2 − x + 3. Which of the following

expressions can represent the area of therectangle?

A. x2 + x + 2

B. 2x3 − 2x2 − 3

C. 2x3 + x2 + 5x + 3

D. 2x3 − 3x2 + 7x − 3

9. What is the sum of ( − 9x4 + 6x3 + 2x5 + 6) and (3x5 + 3x4 + 7x3 + 8)?

A. 12x24 + 14

B. 5x5 − 6x4 + 13x3 + 14

C. 5x10 − 6x8 + 13x6 + 14

D. 6x5 − 27x4 + 42x3 + 48

10. For all x ≠ − 9, 5m3 + 43m2 − 14m + 36

m + 9 =

A. m2 + 2m + 5

B. m2 + 3m + 4

C. 5m2 − 2m + 4

D. 5m2 + 2m + 4

11. Jeremiah divided the two polynomials shownbelow.

What is the quotient?

A. 4x + 2 + −32x + 2

B. 4x + 2 + −40x + 2

C. 4x + 18

D. 4x − 18

12. When factored completely, 27x3 − 8y3 is equivalent to

A. (3x − 2y)(9x2 − 6xy − 4y2)B. (3x − 2y)(9x2 + 6xy + 4y2)C. (3x + 2y)(9x2 − 6xy − 4y2)D. (3x + 2y)(9x2 + 6xy + 4y2)

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13. Which expression represents a complete factorization of 16y4 − 81?

A. (2y − 3)(2y + 3)(4y2 + 9)B. (2y − 3)(2y − 3)(4y2 + 9)C. (4y2 + 9)(4y2 + 9)D. (4y2 − 9)(4y2 − 9)

14. Which polynomial is equivalent to 15z2 − 2z − 8 when factored completely?

A. (3z − 2)(5z − 4)

B. (3z − 2)(5z + 4)

C. (3z + 2)(5z − 4)

D. (15z + 2)(z − 4)

15. What is the solution set for (x + 1)2 − 4 = 0?

A. {−5, 3}

B. {−3, 1}

C. {−3, 5}

D. {−1, 3}

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16. The graph of y = a(x − b)2 is pictured below.

Which of the following could be the graph of y = a(x − b)2 + 3?

A. C.

B. D.

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17. Which of the following quadratic equations has a graph with a minimum at (−2, 5)?

A. y = x2 − 4x + 9

B. y = x2 + 4x + 9

C. y = x2 + 3

D. y = x2 + 5

18. The graph represents which of the followingfunctions?

A. f (x) = x2

B. f (x) = x2 + 1

C. f (x) = 2x2

D. f (x) = 2x2 + 1

19. What is the maximum of the quadraticfunction represented in the graph?

A. (0, − 4) and (0, 0)

B. (0, 0)

C. (−2, 4)

D. (0, 4) and (0, 0)

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20. Which graph describes f (x) = 3x2 − 6x − 4?

A. C.

B. D.

21. What is the value of x in the equation4 = log3 x?

A. 12

B. 34

C. 64

D. 81

22. What is the value of log5125?

A. 1

B. 3

C. 5

D. 25

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23. What is the radical expression ( 64 )3 written in exponential form?

A. 634

B. 61

C. 643

D. 612

24. What number is equal to ( − 27)13 ?

A. −9

B. −3

C. 3

D. 9

25. What happens to the value of y as x increases

in value in the equation y = 3x?

A. y approaches 0

B. y approaches 3

C. y approaches negative infinity

D. y approaches positive infinity

26. The value of log315 is equivalent to which of the following?

A. 15log 3

B. 3log15

C. log 3log15

D. log15log 3

27. Which of the following expressions is equivalent to 3log 2 + 4log 2?

A. 12log 4

B. log 24

C. log 48

D. log 128

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28. Which is the BEST description of the graph

of the equation x2 + 2x = 4y2?

A. a parabola that passes through (0, 0)

B. an ellipse centered at (−1, 0)

C. a parabola that passes through (−2, 0)

D. a hyperbola that passes through (−2, 0)

29. The graph of the equation 16x2 + 9y2 − 32x + 18y − 119 = 0 is which of the following conic sections?

A. circle

B. ellipse

C. hyperbola

D. parabola

30. The graph of the equation x2 + y2 + 8x − 10y − 40 = 0 is which of the following conic sections?

A. parabola

B. hyperbola

C. ellipse

D. circle

31. A club has 7 members. Elections are beingheld to fill the offices of president, vicepresident, and treasurer. Any of the7 members can hold one office. How manypossible ways can the offices be filled?

A. 21

B. 35

C. 210

D. 840

32. There are 10 students in Mr. Romero’sSpanish class. Only 4 students can go on a fieldtrip because of space. If all students areeligible, how many different groups of 4students are possible for the field trip?

A. 40

B. 210

C. 5040

D. 10,000

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33. Which graph BEST represents f (x) = 13

(x + 5)2 ?

A. C.

B. D.

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34. Which graph describes f (x) = x2 − 2x + 1?

A. C.

B. D.

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35. Janene is solving the equation, log3x 324 = 2, and does not have access to a log table. Which exponential equation can she

use to solve her log equation?

A. 3242 = 3x

B. 324 x = 23

C. (3x)2 = 324

D. 3x2 = 324

36. Use the following approximations to answer the question : log2 ≈ 0.30log3 ≈ 0.48log7 ≈ 0.85

Which number is the closest approximation of log14?

A. 0.26

B. 1.15

C. 1.70

D. 2.23

37. Which expression is equivalent to 3log 4 + log 6 − log 8?

A. 3log 2

B. 3log 3

C. log 48

D. log 1728

38. Which value or values of x will make thisalgebraic equation true?

xx + 2 − 1 − x

2 = x − 1

A. x = 0

B. x = − 1

C. x = − 1, 2

D. x = {all real numbers}

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39. Which is the BEST description of the graph

of the equation x2 + y2 − x = 0?

A. a circle of radius 12

B. a parabola that passes through (0, 0)

C. a parabola that passes through ( 12 , 0)

D. a pair of straight lines through the origin

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40. Which graph BEST represents the equation 4x2 + 4y2 + 20x − 16y + 37 = 0?

A. C.

B. D.

41. Which of the following is the equation of ahyperbola?

A. 25x2 + 4y2 = 100

B. x2

16 − y2

81 = 1

C. y2 − 36x = 0

D.(x − 5)2

49 +(y + 5)2

49 = 1

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42. Debbie is making a salad. She can choose from3 types of lettuce, 2 types of tomatoes, and5 types of cheese. How many different saladscan she make using 1 type of lettuce, 1 type oftomato, and 1 type of cheese?

A. 6

B. 10

C. 25

D. 30

43. What is the sum of the integers 1 through 220(including 220)?

A. 23,980

B. 24,090

C. 24,200

D. 24,310

44. What is the sum of the series 34 + 3

16 + 364 + 3

256 + . . . ?

A. 0.95

B. 1

C. 3

D. 3.25

45. Which of the following represents the inverse

f −1(x) of f (x) = x3 − 7?

A. f −1(x) = 7 − x3

B. f −1(x) = 1x3 − 7

C. f −1(x) = x3 + 7

D. f −1(x) = x + 73

46. Given f (x) = (x + 2) and g(x) = (4 − x)2, what is ( f − g)(x)?

A. − x2 + x + 18

B. − x2 + 9x − 14

C. x2 + x + 18

D. x2 − 9x + 18

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review test 1 - paso robles high schoolprhs.pasoschools.org/jsteaffens/2007 files/algebra 2...28....

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