35
Math 12 Multiple Choice Final Exam Review 1. What mapping rule describes the transformation of graph 1 onto graph 2? a) b) c) d) 2. The function has: a) a minimum value of -12 b) a minimum value of 2 c) a maximum value of -12 d) a maximum value of -2 3. A parabola has a minimum value at its vertex (1,3). The domain and range of the function represented by this parabola are: a) and b) and c) and d) and 4. Given . The value of represents a) the minimum or maximum value b) the “x” value of the vertex c) the coordinates of the vertex d) the y-intercept 5. A function is represented by the following graph: Which of the following is true? a) c > 0 b) c = 0 c) c < 0 d) c is an imaginary number 6. The discriminant of the equation is: a) equal to zero b) greater than zero c) less than zero d) equal to 3 –10 –5 –5 5 10 x y x y Graph 1 Graph 2

Math 12 Multiple Choice Final Exam Review - ednet.ns.cahrsbstaff.ednet.ns.ca/pirving/Class Pages/Math 12/Multi…  · Web viewlinear quadratic. logarithmic. exponential ... Quadratic

Embed Size (px)

Citation preview

Math 12 Multiple Choice Final Exam Review

1. What mapping rule describes the transformation of graph 1 onto graph 2?

a)

b)

c) d)

2. The function has:

a) a minimum value of -12 b) a minimum value of 2c) a maximum value of -12 d) a maximum value of -2

3. A parabola has a minimum value at its vertex (1,3). The domain and range of the function represented by this parabola are:

a) and b) and c) and d) and

4. Given . The value of represents

a) the minimum or maximum value b) the “x” value of the vertexc) the coordinates of the vertex d) the y-intercept

5. A function is represented by the following graph:

Which of the following is true?

a) c > 0b) c = 0c) c < 0d) c is an imaginary number

6. The discriminant of the equation is:

a) equal to zero b) greater than zeroc) less than zero d) equal to 3

–10 –5

–5

5

10

x

y

x

y

Graph 1

Graph 2

7. The function describes the height of a baseball “h” in metres, as a function of time “t” in seconds, from the instant the ball is hit. Mark solved the equation

and its positive root represents:

a) the initial height of the ballb) the maximum height of the ballc) the time it takes for the ball to reach a maximum height of 2 metresd) the time it takes fo the ball to hit the ground.

8. Given the quadratic function , which of the following statements is true?

a) The function Is increasing for all x-valuesb) The function is decreasing for all x-valuesc) Its graph is symmetric about the y-axisd) Its graph has 2 distinct x-intercepts

9. Select the correct graph for the equation , if m > o and n > 0.

a) b)

c) d)

10. What type of function would best model the data in the table below?

a) linearb) quadraticc) logarithmicd) exponential

X Y1 21.42 45.63 72.64 102.45 135

–3 –2 –1 1 2 3 4 5

–3–2–1

12345

x

y

–5 –4 –3 –2 –1 1 2 3 4 5 6

–5–4–3–2–1

123456

x

y

–1 1 2 3 4 5 6 7 8 9 10

–4–3–2–1

123456789

10

x

y

–6 –5 –4 –3 –2 –1 1 2 3 4–1

123456789

10

x

y

11. Which of the following sequences could be generated by a quadratic function?

a) {1, 2, 3, 4, …} b) {-5, -3, 3, 13, …}c) {2, 4, 8, 12, …} d) {2, 6, 18, 54, …}

12. Which of the following is true about a quadratic function?

a) The graph always increasesb) The graph always crosses the x-axisc) The graph is always symmetric about the y-axisd) The equation is always considered a second degree equation

13. The graph of the equation is the image of after:

a) a horizontal translation of 7 and a vertical translation of 4b) a horizontal translation of -7 and a vertical translation of 4c) a horizontal translation of 7 and a vertical translation of -4d) a horizontal translation of -7 and a vertical translation of -4

14. If the roots of an equation are -2 and 4, then the discriminant is:

a) an imaginary number b) 0c) a positive number d) a negative number

15. Which quadratic equation best represents the following graph? (a, h, and k are positive real numbers).

a) b) c) d)

16. When deriving the quadratic formula, a student starts with , then solves . Why?

a) The student wants to determine the y-intercept of its graphb) The student wants to determine the x-intercept(s) of its graphc) Quadratic equations always equal zerod) Zero is easier to work with than any other number

17. The function is represented by the following graph. Which of the following statements is true?

a) a>0 and c> 0b) a>0 and c<0c) a<0 and c<0d) a<0 and c>0

–6 –4 –2 2 4 6

–10–8–6–4–2

246

x

y

–4 –2 2 4 6 8

–10–8–6–4–2

2468

10

x

y

18. Given the equation , the domain and range can be written as:

a) domain , range b) domain , range c) domain , range d) domain , range

19. David wants to find the minimum value of the function . He should:

a) state the value for b) make , then factor

c) state the x-coordinate of the vertex d) state the y-coordinate of the vertex

20. Which formula generates the sequence represented by the graph below?

a) b) c) d)

21. The equation of the axis of symmetry of the parabola represented by the function is:

a) x = -2 b) x = 2 c) x -= 0 d) y = 2

22. What is the nature of the roots of a quadratic equation having a discriminant equal to 0?

a) two equal real roots b) two unequal real rootsc) two imaginary roots d) no real roots

23. Given the equation , then “x” is equal to:

a) b) c) d)

1 2 3 4 5 6 7

123456789

10

x

y

24. Which graph has a vertical stretch factor of when compared to the graph of ?

a) b)

c) d)

25. For the function , the y-intercept is always:

a) b) c c) d)

26. The function representing a parabola with a vertex at (3, 2) and passing through the point (4, 4) is:

a) b)

c) d)

27. The domain and range of the function represented by the graph below are:

a) and b) and c) and d) and

–5 –4 –3 –2 –1 1 2 3 4 5

5

10

x

y

–5 –4 –3 –2 –1 1 2 3 4 5

5

10

x

y

–5 –4 –3 –2 –1 1 2 3 4 5

5

10

x

y

–5 –4 –3 –2 –1 1 2 3 4 5

5

10

x

y

–5 –4 –3 –2 –1 1 2 3 4 5

–5–4–3–2–1

12345

x

y

28. An Olympic diver dives from the high diving board. The distance, d, in metres, from the surface of the water varies with the time, t, in seconds, that have passed since she left the board, according to the equation . What is her maximum elevation above the water during the dive? (rounded to the nearest unit)

a) 3 metres b) 10 metres c) 11 metres d) 12 metres

29. The function is used to generate a quadratic sequence. What is the value of D2?

a) 1 b) 2 c) d) 4

30. The mapping rule that describes how to map onto is:

a) b)

c) d) 31. What are the coordinates of the vertex of the quadratic function having a maximum value of 20 and x-intercepts located at (5, 0) and (-1, 0).

a) (3, 20) b) (2, 0) c) (2, 20) d) (3, 0)

32. The graph of a quadratic function is given below:When solving for the “x” in the equation

, the solution (s)represent:

a) the “x” coordinate of the vertexof the quadratic function

.b) the maximum or minimum value

of “x”c) the x-intercepts of d) the “x” coordinate of the y-intercept

of the quadratic function

x

y

33. In which of the following quadratics is the discriminant equal to zero?

a) b)

c) d)

34. The vertex of the parabola represented by is:

a) (1, -6) b) (1, -5) c) (-1, 2) d) (-1, 6)

35. The axis of symmetry for the parabola defined by :

a) x = -4 b) x = 4 c) x = 8 d) x = 12

34. A cannon ball is shot into the air and its height in meters is represented by where “t” is time in seconds. How high does the cannon ball go?

a) 23.10 m b) 4.78 m c) 28.73 m d) 2.36 m

35. A basketball player is trying to increase her shot accuracy. She stays in the same position on the court and increases the arc of the flight path of the ball.

Her coach graphs the quadratic function

to model parabolic

Path I of the basketball. The coach then Changes certain values in the given Equation to graph path II. Which value(s)Did the coach NOT change?

a) a b) hc) k d) h and a

–4 –3 –2 –1 1 2 3 4

123456789

10

x

y

–2 –1 1 2 3 4 5 6

123456789

10

x

y

–4 –3 –2 –1 1 2 3 4

5

10

x

y

–4 –3 –2 –1 1 2 3 4

–10

–5

x

y

36. If in a sequence the second difference is constant, then the sequence is:

a) arithmetic b) linear c) quadratic d) cubic

37. The equation of the axis of symmetry of the parabola represented by the function is:

a) x = 2 b) x = -2 c) y = 2 d) x = 0

38. Given the equation , then “x” is equal to:

a) b) c) 6.9 d) No possible Value

39. Which mapping rule describes how to map function onto the function ?

a) b) c)

d)

40. For the function , the y-intercept is always:

a) b) c) d)

41. If the equation has two equal roots (double root), then the value of k is:

a) k = 0 b) k > 0 c) k = 2 d) k > 2

42. Which function has an axis of symmetry at ?

a) b) c) d)

43. What value of “b” makes the expression a perfect square?

a) b) c) d)

44. A cannon ball is shot into the air and its height, in metres, is represented by the function where “t” is time in seconds. Which of the following best

approximates how long it will take for the ball to hit the ground?

a) 1.34 sec b) 1.50 sec c) 2.78 sec d)10.25 sec

45. If the roots of are , then the graph of the function :

a) has no x-intercept b) has no y-interceptc) is not parabolic d) has 2 distince x-intercepts46. The value of “c” that will make the expression a perfect square is:

a) 36 b) 4 c) 81 d) 16

47. Given , for what values of “k” will there be no real roots?

a) k<1 b) k>1 c) k< 0 d) k> -1

48. has the same value as:

a) b) c) d)

49. What is half of ?

a) b) c) d)

50. Select a graph that best represents the following situation:

“A car depreciates at a rate of 30% per year”

a) b)

c) d)

51. Marla is trying to determine the value for x in the equation . Which one of the following will she use to obtain the value of x?

x

y

x

y

10 20x

y

10x

y

a) b) c) d)

52. Which equation is the same as ?

a) b) c) d)

53. The price of a particular product doubles every 35 years. If the price of the product was $16.40 on January 1, 1996, then the price of the product will be $36.50 in the year:

a) 2028 b) 2031 c) 2036 d) 2040

54. can be expressed as:

a) b) c) d)

55. expressed as a single logarithm is:

a) b) c) d)

56. If then x is equal to:

a) 0.04 b) 32 c) d) 147

57. Which of the following table of values is an exponential function?

a) b) X 2 3 4 5Y 9 16 25 36

c) d) X 2 4 6 8Y 1 7 13 19

58. Joey has been collecting antique toy cars as an investment. The value “V”, in dollars, of a toy car with respect to its age “t” in years, can be modeled using the function . Which of the following is true?

a) The car’s initial value was 2 dollars and it tripled in value every 4 years.b) The car’s initial value was 3 dollars and it doubled in value every 4 years.c) The car’s initial value was 4 dollars and it tripled in value every 2 years.d) The car’s initial value was 2 dollars and it quadrupled in value every 3 years.

X 2 6 8 15Y 6 12 24 48

X 2 5 8 11Y 24 12 6 3

59. Given , the value of “x” is:

a) b) c) d)

60. Which of the following is equal to ?

a) b) c) d)

61. The expression is equivalent to:

a) b) c) d)

62. is equal to:

a) b) c) d)

63. If , then x is equal to:

a) 3 b) 4.5 c) 18 d) 81

64. Which graph best describes the growth of bacteria that doubles every three hours (t is time in hours, A is amount of bacteria per square mm).

a) b)

c) d) 1 2 3 4 5 6 7 8 9 10

123456789

10

x

y

1 2 3 4 5 6 7 8 9 10

123456789

10

x

y

1 2 3 4 5 6 7 8 9 10

123456789

10

x

y

1 2 3 4 5 6 7 8 9 10

123456789

10

x

y

65. Two exponential functions, and , of the form are graphed. How do the two values of “a” compare in the two functions?

a) The value of “a” for is greater that theValue of “a” for .

b) The value of “a” for is less than the valueOf “a” for

c) The value of “a” for is equal to the value of “a” for .

d) For the function , and for the Function , a>1.

66. Given . Which of the following statements if false?

a) b) c) d)

67. The students of East High School are planning a surprise party for the principal. One students tells two other students who in turn each tell two other people and so on as indicated in the following diagram. What type of sequence is depicted by this situation?

a) cubicb) geometricc) quadraticd) arithmetic

68. can also be expressed as:

a) b) c) d)

69. Which of the following expressions is equivalent to ?

a) b) c) d)

70. The graph below shows the growth, in square millimeters, of a rare fungus, F, in a petrie dish after each day (t). The equation of the function is:

a) b) c) d)

0 1 2 3 4 5

2000

4000

6000

8000

10000

x

y

(0,2000)

(2,4500)

(3, 6750)

(4, 10125)

71. If a person earns an annual interest if 7% compounded annually on an investment of $50.00, which functions shows how much money the investor has at time t, in years?a) b) c) d)

72. The function has a horizontal asymptote at:

a) y = -5 b) y = -3 c) y = 3 d) y = 5

73. An exponential equation that is equivalent to is:

a) b) c) d)

74. The table given shows how two dollars invested over a period of years grows in value when interest is compound annually. What is the approximate annual interest rate?

a) 1.03%b) 3%c) 6%d) 9.7%

75. Which one of the following tables of values was generated by an exponential function?

a) b)

c) d)

76. The value of is:

a) b) c) d)

77. Which of the following is equal to if ?

a) b) c) d)

X years 1 2 3 4Y $ 2.06 2.12 2.18 2.25

X -1 2 3 5Y 1 2 4

X -1 1 3 5Y 1 3 9 27

X -1 0 1 2Y

31 1

X 1 2 3 4Y 1 4 9 16

78. Which graph represents , where and ?

79. A particular bacteria population doubles every 7 days. Which equation determines the number of bacteria “N” after “t” days, given the initial amount of 500 bacteria?

a) b) c) d)

80. What could be the next correct step in solving this equation ?

a) b) c) d)

81. can also be expressed as:a) b) c) d)

82. The value of “x” in the equation is:

a) 0 b) c) d)

83. The expression is equal to:

a) -4 b) 3 c) 5 d) 32

84. Which of the following is NOT a geometric sequence?

a) b) 24, 18, 13.5, …

c) 0.8, 0.08, 0.008, … d)

85.Which of the following expressions is equivalent to ?

a) b) c) d)

86. If then “x” is equal to:

a) 16 b) 8 c) d)

87. Which of the following relationships cannot be modeled as an exponential function?

a) Growth of a Population b) Compound Interestc) Half-life of radioactive elements d) tidal cycles

88. Which of the following is FALSE?

a) b)

c) d)

89. The value of “x” in the equation is:

a) 4 b) c) 8 d)16

90. Choose the converse of the following statement:

“If two chords on a circle are equidistant from the centre of the circle, then they are congruent.”

a) Therefore chords on a circle are equidistant from the centre of the circle.b) If the centre of a circle is equidistant from two chords, then they are congruent.c) If two chords on a circle are congruent, then they are equidistant from the centre of

the circle.d) Two chords on a circle are congruent if they are equidistant from the centre.

91. What are the coordinates of the centre of the circle that has the points (a, b) and (c, d) as endpoints of a diameter?

a) b)

c) d)

92. Given with midpoint M(2, -3) and endpoint Q(-5, 1), what are the coordinates of P?

a) (-1.5, -1) b) (-1, -4) c) (3.5, -2) d) (9, -7)

93. The segment below is to be cut into 4 equal pieces. What are the coordinates of B?

a) (2, 1) b) (-1, 2)

c) d) (-1, 3)

94. If two chords of a circle intersect, then their perpendicular bisectors:

a) don’t intersect b) are parallelc) bisect each other d) intersect at the center of the circle

95. Given the following figure:

a) AB = DC

b) The midpoint of is

c) The diagonals and Are of equal lengths

d) The diagonals and bisect each other

96. Given the points A and B on the diagram as indicated, AB is equal to:

a)

b)

c)

d)

97. To prove that a quadrilateral ABCD is a rectangle, John showed that the opposite sides are congruent. Which of the following statements would complete his proof?

a) Opposite sides are parallel. b) The diagonals bisect each other.c) and are perpendicular d)

x

y

(5,-2)

(1,6)

98. A chord in a circle is 10 cm long. If the radius is 7 cm, what is the distance between the chord and the centre of the circle.

a) 7 b) c) d)

99. In which diagram is there enough evidence to conclude that the segment AB passes through the centre of the circle?

100. Two dice are tossed. What is the probability that the will land on different numbers?

a) b) c) d)

101. A bag contains 12 green marbles, 10 red marbles and 18 white marbles. Bill removes 1 marble from a bag. The probability that Bill removes a red marble from the bag is:

a) b) c) d)

102. If an event can succeed in “s” ways and fail in “f” ways, then the probability of success is:

a) b) c) d)

103. In a school of 200 students, 80 have blood type O. If 5 students are chosen at random, what is the probability of selecting five students with type O blood?

a) b) c) d)

104. Consider the following Venn diagram. Which of the following is correct?

a) P(K or L) = P(K) + P(L)b) P(K and L) = P(K) + P(L)c) P(K or L) = P(K) x P(L)d) P(K and L) = P(K) x P(L)

105. Your math teacher gives your class a list of eight questions to study. Five of the eight questions will be randomly selected for the next test. If you study only the first five questions from the list, the probability that all of those five questions will be on the test is:

a) b) c) d)

106. The value of is:

a) 1 b) 1.002 c) 500 d) undefined

107. A bag contains 9 marbles, 4 of which are red. What expression represents the probability of selecting three red marbles when three marbles are drawn at random?

a) b) c) d)

108. Some students were asked whether they watch hockey or football. The results are shown in the following Venn Diagram. What is the probability that a person chosen at random watches hockey?

a) b) c) d)

109 Given the following tree diagram. What is the probability of staying home and inviting friends?

a) 0.50b) 0.70c) 0.90d) 0.56

110. Tim and Rebecca are the first and second students in a line of 7 students waiting to buy tickets for a concert. The number of different orders in which the remainder of the students can line up behind them is:

a) 5! b) 7! c) (5!)(2!) d)

111. Two coins and one die are simultaneously tossed on a table. What is the probability of obtaining two heads and a 6?

a) b) c) d)

112. If we shuffle a standard deck of 52 cards and randomly select one card, what is the probability of selecting a king or a queen?

a) b) c) d)

113. Two boxes contain marbles. The first contains five red marbles and three white marbles. The second box contains four black marbles and seven green marbles. One marble is chosen at random from each box. What is the probability that a white and a black marble will be chosen?

a) b) c) d)

114. Mr. Smith has 3 pairs of black pants and 2 pairs of grey pants in the first drawer of his dresser. In the second drawer, he has 1 white shirt and 4 multi-colored shirts. He gets up late one morning and without looking quickly grabs a pair of pants from the first drawer and a shirt from the second drawer. What is the probability that he grabs a pair of black pants and a white shirt?

a) b) c) d)

115. You want to put 8 different books on a shelf, side by side. In how many ways can these books be arranged?

a) 8! b) c) d)

116. Peter, Mary, and Susan are part of a group of 10 people. An executive consisting of Peter as the President, Mary as the Treasurer, and Susan as the Secretary could be formed from this group. What is the probability this executive will be formed?

a) b) c) d)

117. 40 people were surveyed and asked whether they use a mechanical pencil or a wooden pencil when writing a test. The results are shown in the Venn Diagram below. If one person is randomly chosen, what is the probability that this person does not use a wooden pencil when writing a test?

a) b)

c) d)

Answers: 1) d 2) a 3) d 4) b 5) b 6) a 7) d 8) c 9) c 10) b 11) b 12) d 13) b 14) c 15) a 16) b 17) d 18) c 19) d 20) c 21) b 22) a 23) c 24) d 25) b 26) a 27) b 28) c 29) d 30) d 31) c 32) c 33) b 34) a 35) b 34) c 35) b 36) c 37) d 38) b 39) a 40) b 41) c 42) a 43) c 44) c 45) a 46) b 47) b 48) b 49) c 50) d 51) c 52) b 53) c 54) b 55) d 56) b 57) d 58) a 59) b 60) a 61) d 62) b 63) a 64) b 65) b 66) a 67) b 68) c 69) b 70) d 71) a 72) c 73) a 74) b 75) b 76) a 77) b 78) b 79) d 80) b 81) d 82) c 83) a 84) d 85) c 86) a 87) d 88) a 89) c 90) c 91) d 92) d 93) d 94) d 95) c 96) c 97) c 98) c 99) d 100) a 101) a 102) b 103) d 104) a 105) a 106) c 107) b 108) b 109) d 110) a 111) b 112) d 113) a 114) a 115) a 116) a 117) d