Mathematics Exam #2
2014 – High School - Practice Questions
Student Instructions:
· Write your complete ID code on your answer sheet.
· For each question, choose the BEST answer. If you change your answer, erase well.
1. There are 120 distinct four digit numbers that can be formed using the digits 1, 2, 3, 4, and 5 with no repeat digits in any one number. What is the sum of this set of numbers?
A. 402,160
B. 399,960
C. 399,900
D. 360,000
2. Which of the following choices is equivalent to xpy2q-2x3pypq?
A. x3q2y4p
B. x3q2py2q
C. x3q-2py4q-2
D. xp(3q-2)yq(4-p)
3. Let i, j, and k be unit vectors in the x, y, and z directions respectively. Calculate the magnitude of the following vector: a = 3i – j + 2k.
A. 4
B. 12
C. 14
D. 14
4. What are the eigenvalues of the matrix 2412?
A. 0, 4
B. 0, -4
C. 2, 2
D. 2, -2
5. Convert 12, -32 into polar coordinates.
A. 1, π3
B. 12, π3
C. 12, -π3
D. 1, -π3
6. Which statement below correctly identifies the gray region in the Venn diagram shown to the right?
A. X∩Y∩Z
B. X∩Y∪Z
C. X∩Y∪Zꞌ
D. X∩Y∩Zꞌ
7. The sum of the first 4 terms of an arithmetic sequence is 98 and the sum of the first 5 terms is 150. What is the common difference of the sequence if the first term of the sequence is 8?
A. 11
B. 10
C. 9
D. 8
8. How many times does the graph of the following equation cross the x-axis on the interval [0, π2]?
x2 + sin2 x – 1 = y
A. 0
B. 1
C. 2
D. 3
9. Solve the following equation in terms of x: y = ln(3 + e2x).
A. x=y2 ln3
B. x=y-ln22
C. x=lney-3
D. x=ey-32
10. The following inequalities define a specific region on the Cartesian coordinate system. Which of the choices given can be removed without changing the region?
I / x ≥ 0II / y ≥ 0
III / x + y ≤ 20
IV / -x + y ≤ 10
V / x – 2y ≥ 8
A. V
B. IV
C. III
D. II
11. Let y vary jointly as x and w and inversely as the square of z. When y = 100, x = 2, w = 4, and z = 20. Solve for y when x = 1, w = 5, and z = 4.
A. 2125
B. 2450
C. 30752
D. 31252
12. Which statement below best describes the solutions of the following equations containing rational expressions?
I / 3x+3-1x=-9x(x+3)II / 5x2+8x-43x2+11x+6-1x+3=x3x+2
A. Equation I has one regular solution and equation II has two regular solutions.
B. Both equation I and equation II have one regular solution.
C. Equation I has an extraneous solution and equation II has two regular solutions.
D. Equation I has an extraneous solution and equation II has one regular and one extraneous solution.
13. The following function can be used to determine the height above the ground of a person riding a Ferris wheel at a particular amusement park. The height, in meters, is denoted by h and the time, in seconds, is denoted by t. How long does it take the Ferris wheel to complete one rotation and what is the lowest point of the Ferris wheel during its rotation?
h=-5 costπ60+6
A. time for one rotation = 60 seconds; lowest point = 6 meters above ground
B. time for one rotation = 60 seconds; lowest point = 1 meter above ground
C. time for one rotation = 120 seconds; lowest point = 6 meters above ground
D. time for one rotation = 120 seconds; lowest point = 1 meter above ground
14. Find the inverse function of fx= (x-8)23 for x ≥ 8.
A. f-1x=(x+8)32;x ≥8
B. f-1x=x32+8;x ≥0
C. f-1x=x23+8;x ≥0
D. f-1x=1(x-8)23;x ≥8
15. Which of the following statements is true regarding the domain and range of the following functions?
I / fx=7x+4II / gr=r3+1
III / hs=s-2+1
A. The domains of functions II and III are all real numbers.
B. The ranges of functions I and III are all real numbers greater than or equal to zero.
C. Functions I and III have the same range.
D. The domains of functions I and II are all real numbers greater than or equal to zero.
16. Solve for x: log x = 2 – log(x – 15).
A. 20
B. -5 or 20
C. -5
D. {∅}
17. Solve for x: 3xe-x – 12e-x = 0.
A. 0
B. 2
C. 4
D. 8
18. Angle θ is an angle in standard position. If sec θ and tan θ are both less than zero in which quadrant of the Cartesian coordinate system does angle θ lie?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
19. Which of the following is equivalent to tan θ – cot θ?
A. cos2θ-sin2θ
B. cos2θ-sin2θsinθcosθ`
C. sin2θ-cos2θsinθcosθ
D. sin2θ-cos2θ
20. Express the complement of an angle that has a measure of π30 as a fraction. What is the value of the numerator?
A. 22π
B. 13π
C. 7π
D. π
2014 KAAC – High School Mathematics –Practice Questions 2 - Page 9
21. According to the Rational Root Theorem what are the possible zeroes of the following polynomial function?
Q(x) = 2x3 – 5x2 + 4x – 3
A. 0,±1,±3
B. ±12,±1,±32,±3
C. 0,±12,±1,±32
D. ±12,±1,±3
22. Use Descartes’ Rule of Signs to determine the number of positive and negative real solutions for the following function.
R(x) = 5x4 + x3 + 3x2 – 3x – 1
A. 1 positive root, 1 or 3 negative roots
B. 1 positive root, 3 negative roots
C. 1 or 3 positive roots, 1 negative root
D. 1 or 3 positive roots, 1 or 3 negative roots
23. In the drawing to the right, first reflect triangle ABC in the x-axis and second, reflect triangle AꞌBꞌCꞌ in the y-axis. What is the distance between points B and Bꞌꞌ?
A. 12 units
B. 122 units
C. 15 units
D. 261 units
24. Given point D (3, 4), which of the following pairs of translations would map point D to coordinates (-2, -3)?
A. 90o clockwise rotation about the origin followed by a reflection in x = -1
B. 90o counterclockwise rotation about the origin followed by a reflection in x = 1
C. 90o clockwise rotation about the origin followed by a reflection in x = 1
D. 90o counterclockwise rotation about the origin followed by a reflection in x = -1
25. Triangle ABC has the following coordinates: A (-7, -2), B (-5, -5), and C (-4, -2). Triangle ABC undergoes a vector translation of 3, 8. In what quadrant of the Cartesian coordinate system is triangle AꞌBꞌCꞌ located?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
26. Triangle ABC shown to the right is equilateral. The intersection of the three altitudes of the triangle meets at point O. If AB = 2, what is the length of AO?
A. (23)3
B. 33
C. 32
D. (33)4
27. Which of the following statements best describes the triangles formed given the following parameters?
I / ΔABC: m∠A = 30o, a = 9, b = 8II / ΔDEF: m∠D = 35o, d = 7, e = 10
III / ΔGHI: m∠I = 40o, GH = 8, GI = 10
A. I and II will form two triangles whereas III will only form one triangle.
B. I will only form one triangle whereas II and III will form two triangles.
C. I and III will form two triangles whereas II will only form one triangle.
D. I, II, and III will form two triangles.
28. Find the measure of angle ABD in the regular pentagon ABCDE shown to the right.
A. 72o
B. 63o
C. 60o
D. 54o
29. Which of the following polyhedrons is classified as a cantellated cubic honeycomb?
A. B. C. D.
30. What is the perimeter of the kite shown to the right?
A. 62 units
B. 58 units
C. 54 units
D. 48 units
2014 KAAC – High School Mathematics –Practice Questions 2 - Page 9
31. All of the solids pictured below have the same height. The solid pictured at choice A is a square base pyramid, the solid pictured at choice B is a right circular cone, the solid pictured at choice C is a right circular cylinder, and the solid pictured at choice D is equilateral triangular based prism. Which of the following solids has the greatest volume?
A. B. C. D.
32. The cube shown to the right has a volume of 125 u3. What is the perimeter of the triangle ABC?
A. 15 u
B. 610u
C. 152u
D. 153u
33. To the nearest hundredth radian, calculate the measure of the central angle of a circle with radius 3 that corresponds to an arc length of 11 units.
A. 0.27 rad
B. 3.67 rad
C. 5.50 rad
D. 7.33 rad
34. The circle shown to the right has a diameter of 10 units. To the nearest hundredth square unit calculate the area of the shaded regions in the circle.
A. 56.72 u2
B. 42.16 u2
C. 30.54 u2
D. 21.82 u2
35. The diameter of circle O shown to the right is 12 units. Vertex O of square OPRS is located at the center of the circle and vertex R of square OPRS is located on the circle. Find the length of RS.
A. 32 units
B. 3 units
C. 4 units
D. 23 units
36. In the drawing to the right the equation for AB is y = 2x – 8. As shown, AB and CD are perpendicular and their intersection occurs on the x-axis. What is the y-intercept of CD? (Graph not drawn to scale.)
A. (0, 1)
B. (0, 2)
C. (0, -8)
D. not enough information to determine the y-intercept of line segment CD
37. An equilateral triangle is inscribed in the parabola y2 = 4x. One vertex of the triangle is at the vertex of the parabola. What is the length of the sides of the equilateral triangle?
A. 83
B. 102
C. 103
D. 82
38. Twenty red marbles, 20 blue marbles, 20 green marbles, and 20 white marbles are placed in a large cloth bag and thoroughly mixed. If four marbles are drawn from the bag without replacement, what is the probability that all four marbles are different colors?
A. 0.42%
B. 1.69%
C. 3.37%
D. 10.12%
39. Consider the set of numbers {1, 2, 3, 4, 5}. If this set of numbers is used to create 5-digit numbers where each member of the set can only be used once, how many of the 5-digit numbers have the first digit larger than the second digit?
A. 30
B. 50
C. 60
D. 90
40. Use the partially filled two-way table to calculate the percentage of 8th graders, who are boys that ride their bike to school.
Results of 8th Grade School Transportation Survey at Gilroy Junior High
8th Grade Boys / 8th Grade Girls / TotalsWalk to school / 46
Ride in car / 28 / 45
Ride school bus / 12 / 27
Ride bike / 17 / 69
Totals / 129 / 92
A. 7.69%
B. 23.53%
C. 31.22%
D. 40.31%
2014 KAAC – High School Mathematics –Practice Questions 2 - Page 9
2014 KAAC – High School Mathematics –Practice Questions 2 - Page 9
41. In a production process, one out of every five items produced has a minor defect. Ten items from the production line are randomly selected and inspected. Let the random variable X, the number of defective items, be modeled by a binomial distribution. What are the mean and variance of X?
A. mean = 1.6, variance = 1.60
B. mean = 1.6, variance = 1.26
C. mean = 2.0, variance = 1.60
D. mean = 2.0, variance = 1.26
42. A fair coin is tossed 50 times. Which of the following is the best approximation for the distribution of the number of heads?
A. N (50, 12)
B. N (50, 12.5)
C. N (25, 12.550)
D. N (25, 12.5)
43. For six pairs of observations the least squares regression line is y = 0.5 – 0.5x and 81% of the variation in y is explained by regression on x. What is the correlation coefficient of this set of data?
A. -0.9
B. 0.9
C. 0.81
D. -0.81
44. A car manufacturer claims a certain model car in their fleet averages 45 miles per gallon on the highway. Consumer Watchdog, an independent consumer organization, sets up a hypothesis test to evaluate the car manufacturer’s claim. Which of the following sets of hypotheses would be used by Consumer Watchdog to perform their hypothesis test?
A. Ho:μ=45
Ha:μ<45
B. Ho:μ=45
Ha:μ≠45
C. Ho:μ=45
Ha:μ>45
D. Ho:μ≤45
Hao:μ>45
45. The following measurements were taken with a special instrument for the expansion of sections of railway track in southern Texas on days when the temperature exceeded 95o F. What would be the best description for the graph of this data?
Expansion in mm / FrequencyLess than 0.1 / 3
[0.1, 0.2) / 5
[0.2, 0.3) / 10
[0.3, 0.4) / 8
[0.4, 0.5) / 6
[0.5, 0.6) / 4
[0.6, 0.7) / 3
[0.7, 0.8) / 2
A. uniform
B. symmetrical
C. skewed left
D. skewed right
46. Let f(x) = 2x5 – 3x4 + 2x2 -17x + 31. Which of the following statements about this function at x = -1 is true?
A. the graph of the function bends downward and the slope of the tangent line at x = -1 is positive
B. the graph of the function bends upward and the slope of the tangent line at x = -1 is positive
C. the graph of the function bends downward and the slope of the tangent line at x = -1 is negative
D. the graph of the function bends upward and the slope of the tangent line at x = -1 is negative