Download 2011 GHSGT Math Practice Questions

GHSGT – Mathematics Review
1. A quadratic function has this domain and range.


domain: {all real numbers}
range: {all real numbers greater than 1}
How many real zeroes does the function have?
a. at least 1
6. The vertex of y = (x – 6)2 + 3 is:
a. (-6, 3)
b. (6, 3)
c. (6, -3)
d. (-6, -3)
b. 0
7. The graph of y = -2(x + 1)2 + 4 will open:
c. exactly 2
d. exactly 1
2. The vertex of the quadratic function g(x) is
located at (4,2). An x-intercept is located at (5,0).
What is the y-intercept of g(x)?
a. (0,3)
b. (0,-30)
c. (0,-4)
d. (0,-14)
a. up
b. down
c. right
d. left
8. Which type of graph would be the BEST
representation for the data in the table?
3. What is the vertex of the parabola:
y = x2 – 6x + 12?
a. a cubic with leading coefficient positive
a. (1, -2)
b. (1,12)
c. (2,-3)
d. (3,3)
b. a parabola with leading coefficient negative
c. a line with a positive slope
d. a parabola with leading coefficient positive
4. Which of the following is the vertex form of :
y = 3x2 – 24x + 38?
9. Which could be the graph of: y – 2 = ½(x + 3)2
a. y = (3x – 8)2 + 38
b. y = (3x – 12)2 - 10
c. y = 3(x – 6) - 38
d. y = 3(x – 4) - 10
2
a.
b.
2
5. To reflect a parabola over the x-axis, change:
a. the sign of the vertex
b. the sign of the y-intercept
c. the sign of the leading coefficient
d. the sign of the x-intercept(s)
c.
d.
10. A steady rate of change is represented by what
type of function?
a. quadratic
b. cubic
c. linear
d. constant
11. If g(x) = - f(x), then the graph of g(x) will be
15. Inverses of functions reflect over:
a. f(x) = x
b. themselves
c. f(x) = -x
d. f(x) = f-1(x)
16. The inverse of a quadratic function has a
domain that is:
a. upside down
a. always negative
b. always positive
b. a reflection over the x-axis
c. restricted in some way
d. all real numbers
c. a reflection over the y-axis
17. Which system of equations is equivalent to the
1 - 4  x   9
matrix equation: 
    
2 3   y  12 
d. sideways
12. Use the graph below to determine for what x
values is f(x) < 0
a. x – 2y = 9
b. x + 4y = 12
-4x – 3y = 12
c. x – 4x = -9
2x - 3y = 9
d. x – 4y = -9
2y + 3y = 12
a. x < -2
b. -2 < x < 0
c. x < -2 or 1.5 < x < 5
d. x < 2
18. The inverse of the function f(x) = x2 – 10 is:
a. f
c. f
13. For the function y = 2x2 – 7, for which of these
values of x does y = 1?
a. -1
b. -2
c. -3
d. -4
14. The inverse of f(x) =
2
is:
x
a. –f(x)
b. f(-x)
c. -f(-x)
d. f(x)
2x + 3y = 12
1
( x)   x  10
b. f
1
( x)   x  10
d. f
1
( x)   x 2  10
1
( x)  x 2  10
19. Solve: (x – 3)(x + 2) > 0
a. x > 3
b. x < -2
c. -2 < x < 3
d. x < -2 or x > 3
20. A graph representing exponential growth is
always:
a. linear
b. increasing
c. horizontal
d. decreasing
21. Which expression is equivalent to:
a.
81 y 3
16 x
3y3
c.
2x
b.
81 y 12
16 x 4
3 xy 2
2
 3x 3 y 5
d.  4 2
 2x y



4
22. A geometric sequence contains which of the
26. Given the following piecewise function,
evaluate f(-3)
 x 2  4 x , x  0 or x  4

f ( x)    3 x
,0  x  4
 2
 x 1
a.
9
10
c.
3
b. 2
1
4
d.
21
following?
a. ratio
b. difference
c. last term
d. sum
27. In the graph below, for what value of x is the
function NOT defined?
23. The population in a city in 1990 was 213,426.
The population increased at a rate of about 3.1%
each year. What was the approximate population
in the city in 2000?
a. 220,042
b. 298,602
c. 289,624
d. 155,770
24. You deposit $825 into an account that earns
7.95% interest compounded monthly. What is the
balance in the account after 16 years?
a. $2931.26
b. $2805.54
c. $936.87
d. $2231.87
a. infinity
b. 3
c. 1
d. 0
28. A triangle has a height twice its base; its area
is 64 square units. What is the size of the base?
a. 4
b. 8
c. 32
d. 2
25. Negative exponents indicate:
a. fractions
b. values of 0
c. negative numbers
d. reciprocals
29. The length of a rectangle is 4 inches more than
twice its width. The area is 30 square inches. Find
the dimensions (length and width).
a. 3 x 10
b. 5 x 14
c. 2 x 15
d. 5 x 6
30. The length of a rectangle is twice its width.
The area is 32 square inches. Find the dimensions
(length and width).
a. 8 x 16
b. 2 x 16
c. 4 x 8
d. 6 x 12
34. What is the range of the function in #33?
a. x ≤ 4
b. x ≥ 4
c. all real numbers
d. y ≤ 4
35. What is the equation of the axis of symmetry
of the graph of y = 3x2 + 12x - 2?
31. Logan works in a factory. Logan uses the
formula y = x2 + x to determine how many
impurities(y) are in a sample of water at any
temperature (x) in degrees Celsius. For one
sample of water, Logan found 20 impurities.
Which are the possible temperatures for the sample
of water?
a. 2 or -10
b. -5 or 4
c. -2 or 10
d. 5 or -4
a. x = -2
b. x = 2
c. y = -2
d. y = 2
36. Find the roots of the function:
f(x) = x2 - 1
a. 1
b. 1, -1
c. I
d. i, -i
32. What are the zeros of the function:
37. On what interval is the function shown below
increasing?
f(x) = x2 + 5x - 24?
a. 6, -4
b. -6, 4
c. -3, 8
d. 3, -8
33. What is the domain of the function below?
(assume the function has “arrows” on each end)
a. x ≤ 4
b. x ≥ 4
a. (-∞, -3)
b. (3, ∞)
c. (2, ∞)
d. (-∞, 2)
38. What is the interval of increase of the
following function:
y = x2 + 3
c. all real numbers
d. y ≤ 4
a. x > 0
b. x < 0
c. x < 3
d. x > 3
39. Which of the following is the graph of
2x  5  3
a.
44. f(x) = x2 + 4 is
a. odd
b. even
c. not symmetrical
d. rotated 360 degrees
b.
45. f(x) = -|x| has symmetry across
c.
d.
a. x-axis
b. y-axis
c. origin
d. y = 0
40. Solve: 3x  12
a. no solution
b. x = -4
c. x = 4
d. x = 0
41. Which of the following functions is always
increasing?
a. f ( x)  x 2
c. f ( x ) 
1
x
b. f ( x)  x
d. f ( x)  x
46. What is the value of i 75 ?
a. i
b. 1
c. –i
d. -1
47. Simplify: (4 – 7i)2
a. 33 – 56i
b. -33 – 56i
c. -33 + 56i
d. 33 + 56i
48. The complex conjugate of 3i + 2 is:
42. What is the first step in solving the following
equation:
3x  2  4  12
a. -3i
b. 3i
c. 3i - 2
d. -3i - 2
a. square both sides
b. subtract four from both sides
c. subtract seven from both sides
d. taking the square root of both sides
49. The factored form of the expression
2x2 + 3x + 1 is:
a. (2x + 1)(x – 1)
b. (2x – 1)(x – 1)
c. (2x – 2)(x - .5)
d. (2x + 1)(x + 1)
43. An odd function contains the point (-1, -3).
What other point is on the graph?
a. (1, 3)
b. (-1, 3)
c. (1, -3)
d. (-1, -3)
50. Which is a factor of: x2 – 2x – 15?
a. (x – 3)
b. (x – 15)
c. (x + 3)
d. (x + 5)
51. Exponents change when polynomials are:
a. added
b. subtracted
c. multiplied and divided
d. divided
a.
c.
52. Simplify: 4x2 + x – 5 – (5x2 – 1)
a. -x2 + x – 6
b. 9x2 + x – 6
c. 9x2 + x – 4
d. -x2 + x – 4
53. A cardboard box has a length of x, width of 3x
and height of x + 2. Which expression represents
the volume of the box?
a. 3x3 + 2
3
c. 3x + 6x
b. 5x3 + 2
2
3
54. Which is equivalent to the following
expression:
x 2  6 x  27
x9
b. x - 3
c. x + 2
d. x + 3
55. Which is equivalent to the following
7 a 2b

expression:
15b 5
a.
a
5
b.
a
2
c.
7 a  6b 2
15b
d.
7 a  4b
5
25  4 3
28
3
5
5 3
b.
25  5 3
22
d. 5  3
57. Given the hypotenuse of a 30°-60°-90°
triangle is 16, what is the value of the short leg?
a. 8 3
b. 16
c. 16 3
d. 8
58. Given the long leg of a 30°-60°-90° triangle is
2
d. 5x + 6x
a. x - 2
56. Simplify:
11 3 , find the value of the hypotenuse.
a. 22 3
b. 11
c. 22 2
d. 22
59. The diagonal of a square is 6 2 cm long. Find
the length of a side of the square.
a. 12 2
b. 12
c. 24
d. 6
60. Calculate the missing angle to the nearest
degree.
a. 32
b. 52
c. 30
d. 38
61. Sam is trying to calculate the height of a tower. He
is standing 95 meters from the base of a tower. The
angle of elevation from Sam's position on the ground to
the top of the tower is 35°. Calculate the height of the
tower to the nearest tenth of a meter.
66. Given circle B, what is the m ADC ?
a. 23°
b. 46°
a. 66.5 meters
b. 77.8 meters
c. 77°
c. 62.7 meters
d. 54.5 meters
d. 80°
62. A 5'6" person walking down the street notices his
shadow. If the angle of elevation from the tip of the
shadow to the sun is 60°, what is the length of the
shadow (round to 2 decimal places)?
67. In the given diagram, what is the m ABD ?
a. 32°
a. 3.23 feet
b. 11.00 feet
b. 114°
c. 3.18 feet
d. 17.18 feet
c. 46°
d. 100°
63. A boat is spotted in the water with an angle of
depression of 25° from the top of a lighthouse that is 89
feet tall. To the nearest foot, how far away is the boat
from the base of the lighthouse?
a. 42 feet
b. 37 feet
c. 211 feet
d. 191 feet
68. Given the diagram, find x.
a. 3
b. 4
c. 5
64. Given a circle with a radius of 16 ft, and a central
angle of 135°, find the length of the arc created by the
angle.
a. 20  ft
b. 10  ft
c. 12  ft
d. 6  ft
d. 6
69. In the circle below, if CE = 3, ED = 18, AE = 6,
then EB = ?
65. Find the length of the minor arc:
a. 9
b. 1
a. 361  ft
b. 150.4  ft
c. 36
c. 15.8  ft
d. 38  ft
d. 3
70. In circle C, What is the measure of angle ACD?
a. 134°
75. Given the following properties, classify the
polygon: two pair of parallel sides, diagonals are
perpendicular bisectors, has four congruent sides,
and the diagonals are perpendicular.
b. 76°
c. 75°
d. 105°
71. If the radius of a sphere is doubled, by what
factor does the surface area increase?
a. 8
b. 4
c. 16
d. 2
a. rectangle
b. rhombus
c. parallelogram
d. square
76. Which statement is true about all
parallelograms?
a. The diagonals are perpendicular to each other.
b. The opposite angles are congruent.
c. The diagonals are congruent.
72. If the radius of a sphere is doubled, by what
factor does the volume area increase?
a. 8
b. 4
c. 16
d. 2
73. A sphere has a volume of 322 cubic cm. What
is the approximate diameter of the sphere?
a. 8.5 cm
b. 5.1 cm
c. 4.3 cm
d. 17.5 cm
d. The area is the product of two adjacent sides.
77. If an exterior angle is 22.5 degrees, how many
sides does the regular polygon have?
a. 16
b. 17
c. 18
d. 15
78. What is the measure of one interior angle in a
regular pentagon?
a. 120°
b. 540°
c. 90°
d. 108°
74. Identify the radius of the circle:
(x-1)2 + (y-3)2 = 4
a. (1, 3)
b. 16
c. 4
d. 2
79. In parallelogram ABCD, what is m C ?
a. 120°
b. 540°
c. 90°
d. 108°
80. What is the most specific name for the given
figure?
a. rhombus
b. parallelogram
c. quadrilateral
85. Your friend is visiting and only brought one
suitcase. In her suitcase is 4 different t-shirts, 3
pairs of pants, and 2 pairs of shoes. How many
different outfits can she wear?
a. 12
b. 24
c. 48
d. 15
d. kite
81. Points P(2, 9) and Q (8, 7) are on a coordinate
grid. What are the coordinates of the midpoint of
PQ?
a. (10, 16)
b. (6, 2)
c. (5, 8)
d. (3, 1)
82. Find the perimeter of the quadrilateral
whose vertices are these points: (-2, 1), (-2, 6),
(4, 6), and (4, 1).
a. 25
b. 20
c. 22
d. 19
83. State the contrapositive of the statement:
"If p, then q."
86. How many different arrangements are there of
the digits 5641?
a. 30
b. 16
c. 24
d. 20
87. Pete's Pizza has 12 different pizza toppings.
How many different combinations can be made
with three toppings?
a. 36
b. 144
c. 220
d. 110
88. You have a normal number cube with the digits
1-6 painted on each face of the cube. What is the
probability that if you throw the cube 3 times, you
will get the number 2 each time?
a. If not p, then q
b. If not p, then not q
a. 1/6
b. 1/8
c. If q, then p
d. If not q, then not p
c. 1/18
d. 1/216
84. State the inverse of the statement:
"If p, then q."
a. If not p, then q
b. If not p, then not q
c. If q, then p
d. If not q, then not p
89. There are 8 red socks, 4 yellow socks, and 6
green socks in a drawer. Maria will choose two
socks at random without replacement. What is the
probability that she will choose a pair of yellow
socks?
a. 1/153
b. 1/9
c. 12/153
d. 2/51
90. A pair of dice is rolled. What is the probability
that the sum of the dice rolled is either a 7 or a 2?
95. In a normal curve ___% of the data is within 2
standard deviations from the mean
a. 1/36
b. 3/36
a. 50
b. 95
c. 5/36
d. 7/36
c. 68
d. 99.7
96. Calculate the population standard deviation for the
following set of numbers: 12, 10, 8, 19, 6
91. You are rolling a fair die and you have rolled
for the last 10 times an even number. What is the
probability that you will roll another even number?
a. 1/2
b. 1/4
c. 1/3
d. 1/6
92. When the standard deviation is small, it means
the data is __________
a. more spread out
a. 5
b. 4.47
c. 11
d. 15
97. Calculate the sample standard deviation for the
following set of numbers: 12, 10, 8, 19, 6
a. 5
b. 4.47
c. 11
d. 15
b. large
c. bunched closely together d. small
98. A teacher wants to know how many books were
read by students in his school during summer vacation.
Melissa says she will survey the students in the book
club. What type of sampling is this?
93. Find the median for the data in the table
a. self-selected
b. systematic
c. random
d. convenience
a. 15
b. 15.5
c. 16
99. When the data points are graphed, which has a
negative correlation?
d. 14
a. When the points form a vertical line
94. A supply of hex nuts is produced and the
production records indicate a mean mass of 7.8 g
with a standard deviation of 0.3 g. Assuming a
normal distribution, estimate the percent of hex nuts
with mass less than 7.5 g.
a. 84%
b. 66%
c. 34%
d. 16%
b. When the points fall from left to right
c. When the points form a horizontal line
d. When the points rise from left to right
100. Sprayberry High School will do better than all
other Cobb County Schools on the math GHSGT
a. true
b. true
