Indiana Academic Super Bowl
Math Round
2016 – Coaches Practice
A Program of the Indiana Association of School Principals
Students:
Throughout this round we will be
pronouncing mathematic symbols
and concepts as spoken words.
If there are any discrepancies
between what is said and what you
see on the screen, the screen
supersedes what is spoken.
The only calculators allowed during this
competition are the following models:
TI-30Xa and TI-30X IIS
SD-CP-M-1
30 seconds
Find the axis of symmetry of the graph
of x = y2 + 2y + 3.
A.
B.
C.
D.
x=1
x = -1
y=1
y = -1
SD-CP-M-2
The focus of a parabola is at (0, 3).
Which could be the equation of the
directrix for this parabola?
A.
B.
C.
D.
x=0
y=1
y=3
cannot be determined
SD-CP-M-3
What are the x-intercepts of the
graph of y = x2 – x – 20?
A.
B.
C.
D.
(5, 0) and (-4, 0)
(4, 0) and (-5, 0)
(-4, 0) and (-5, 0)
(4, 0) and (5, 0)
SD-CP-M-4
Which of the following is the equation
of a parabola?
A.
B.
C.
D.
x2 – 7x + y2 = 20
xy = -5
y2 = 2y + x + 4
x2 – y 2 = 1
SD-CP-M-5
What are the coordinates of the vertex of
the graph of y = - (x + 4)2 – 2?
A.
B.
C.
D.
(-4, -2)
(4, -2)
(-4, 2)
(4, 2)
SD-CP-M-6
The vertex of the parabola y = x2 – 8x + c
will be a point on the x axis if the value
of c is _________.
A.
B.
C.
D.
-4
4
-16
16
SD-CP-M-7
SD-CP-M-8
The coordinates of the foci of the ellipse with the
equation 3x2 + 7y2 = 63 are _____.
A.
B.
C.
D.
SD-CPM-9
The eccentricity of the ellipse with equation
12(x – 1)2 + 3 (y + 4)2 = 48 is _______.
A.
1/4
B.
C.
3/4
D.
SD-CP-M-10
SD-CP-M-11
The endpoints of the minor axis of the ellipse with
the equation
are _____.
A.
B.
C.
D.
(11, -4) & (-1, -4)
(5, -10) & (5, 2)
(2, -4) & (8, -4)
(5, -7) & (5, -1)
SD-CP-M-12
SD-CP-M-13
Find the center of the hyperbola with the
equation x2 – 4x – y2 - 4y – 5 = 0.
A.
B.
C.
D.
(2, 2)
(2, -2)
(-2, -2)
(-2, 2)
SD-CP-M-14
SD-CP-M-15
SD-CP-M-16
SD-CP-M-17
The graph of x2 – 4y2 = 0 is _______.
A.
B.
C.
D.
parabola
ellipse
hyperbola
none of these
SD-CP-M-18
The Oval Office of the President is an ellipse
31 ft. wide and 38 ft. long. The President and an
advisor can best hear each other using the rooms
acoustics if they each sit at the location of a focus
of the ellipse. Approximately how far apart will
they be sitting?
A. 21 ft.
B. 22 ft.
C. 23 ft.
D. 24 ft.
SD-CP-M-19
If logb16 = log2b, then the value of
b is _______.
A.
B.
C.
D.
1
2
4
8
SD-CP-M-20
SD-CP-M-21
SD-CP-M-22
SD-CP-M-23
Let n = x – yx-y. Find n when x = 2 and
y = -2.
A.
B.
C.
D.
256
18
1
-14
SD-CP-M-24
SD-CP-M-25
Write log4 x = 2 in exponential form.
A.
B.
C.
D.
4x = 2
2x = 4
42 = x
x4 = 2
SD-CP-M 26
SD-CP-M-27
Find the value of [log (5 log 100)]2
A.
B.
C.
D.
25
10
2
1
SD-CP-M-28
SD-CP-M-29
SD-CP-M-30
Which is the smallest number?
A.
B.
C.
D.
1.2 x 10-6
2.4 x 10-2
3.1 x 10-5
8.5 x 10-7
SD-CP-M-31
SD-CP-M-32
SD-CP-M-33
SD-CP-M-34
SD-CP-M-35
SD-CP-M-36
The expression
A.
C.
8
equals __.
B.
D.
SD-CP-M-37
If (x + x-1)2 = 16, then the value of x2 +
x-2 is _______.
A.
B.
C.
D.
12
14
16
20
SD-CP-M-38
Find the sum of the solutions of the equation
(4x - 8)(4x - 2) = 0.
A.
B.
C.
D.
1
log410
2
43
SD-CP-M-39
If
= 2 then the difference of the
solutions for x is ______.
A.
B.
C. 2
D.
SD-CP-M-40
The sum of the solutions for
is ________.
A.
B.
C.
D.
2
-2
-6
-8
SD-CP-M-41
The sum of the solutions for
___.
A.
B.
C.
D.
-34
-6
6
15
SD-CP-M-42
If
which of the following
could NOT be a value of n?
A.
B.
C.
D.
-4
-2
1
2
SD-CP-M-43
If x is a real number and
SD-CP-M-44
The set of x values satisfying the inequality
A.
B.
C.
D.
x < -1 or x > 3
-4 < x < -1 or 3 < x < 6
3 < x < 6 or -6 < x < -3
-6 < x < -4 or -1 < x < 3
SD-CP-M-45
The sum of the real values of x satisfying the
equality
is _______.
A.
B.
C.
D.
SD-CP-M-46
If
for all x such that
then the smallest possible
value of N is ______.
A.
B.
C.
D.
0.0301
0.0399
0.0401
0.0499
SD-CP-M-47
Which of the following statements about
derivatives is FALSE?
A. If the velocity of an object is constant,
then its acceleration is zero.
B. The second derivative represents the
rate of change of the first derivative.
C. If y = f(x)g(x), then dy/dx = f ′(x)g′(x)
D. If f ′(c) and g′(c) are zero and
h(x) = f(x)g(x), then h′(c) = 0
SD-CP-M-48
If
A.
B. -6
C. 4
D. 6
SD-CP-M-49
If f (x) = cos (x – 6), then f ′(x) = ____.
A.
B.
C.
D.
cos (sin(x – 6))
-sin (x – 6)
- 6 cos x
6 sin (x – 6)
SD-CP-M-50
If f (x) =
A.
B.
C.
D.
-14
1
14
28
, then
SD-CP-M-51
If y = 16x2 + 8x + 10, then y′ = ____.
A.
B.
C.
D.
32x + 18
8x + 8
16x + 4
32x + 8
SD-CP-M-52
If y =
A.
C.
B.
1
D.
2
SD-CP-M-53
A.
B.
C.
D.
SD-CP-M-54
Find
A.
2 – x-2
B.
C.
D.
2x2
x2 + x
SD-CP-M-55
A.
B.
C.
D.
-49x-8
-56x-8
-49x-6
-42x-6
SD-CP-M 56
If y = (2x – 3)(x +
A.
B.
C.
D.
2
1) ,
6x2 – 2
2(2x – 3)(x + 1)
12x2 – 4x – 2
2(x + 1)(3x – 2)
then y′ = ___.
SD-CP-M-57
If y =
? = _______.
A.
B.
C.
D.
4x3 + 4x
2x
4x
8x
SD-CP-M-58
If y =
? = _______.
A.
B.
C.
D.
2x
2x2 + 2
4x3 + 2x
4x2 + 2x
SD-CP-M-59
If y = (x2 – 1)(x + 2), then y′ = _____.
A.
B.
C.
D.
2x
2
-x – 4x + 1
3x2 + 4x – 1
2x2 - 2
SD-CP-M-60
If f (x) = sec x tan x,
then f′(x) = sec3 x + ____.
A.
B.
C.
D.
tan2 x sec x
tan x sec2 x
tan x sec x
tan3 x
SD-CP-M-61
If f (x) = 5x csc x, then f ′(x) = _______.
A.
B.
C.
D.
5x cot x
-5 csc2 x + 5 cot x
-5 csc x cot x + 5
5 csc x (1 – x cot x)
SD-CPM-62
A.
B.
C.
D.
sec2 u
-csc2 u
sec u tan u
-csc u cot u
SD-CP-M-63
A particle moves on a line according to the
equation s = 2t3 – 3t2. What is the velocity of
the particle at t = 3?
A. 72
B. 36
C. 27
D. 21
SD-CP-M-64
Let f (x) = 4x5 – 5x4 – 40x3. Which of the
following statements is TRUE?
A.
B.
C.
D.
There is a relative max at x = -2
There is a relative max at x = 3
There is a relative min at x = 0
There is a relative min at x = 6
SD-CP-M-65
Find the equation of the tangent line at the
point (2, 8) on the graph of y = x3.
A.
B.
C.
D.
y = 12x + 6
y = 12x + 3
y = 12x – 16
y = 12x - 32
SD-CP-M-66
Find the equation of the line tangent to the
graph of y = 3x2 – 4 at the point (1, -1).
A.
B.
C.
D.
6x – y = 7
6x – y = 0
12x – y = 13
9x – y = 10
SD-CP-M-67
A population of 500 bacteria is introduced into a
culture and grows in number according to the
equation
where t is
measured in hours.
Find the rate at which the population is growing
when t = 2.
A. 31.6 bacteria per hour
B. 36.8 bacteria per hour
C. 38.4 bacteria per hour
D. 42.2 bacteria per hour
SD-CP-M-68
The volume V in cubic feet of water in a tank
follows the equation V = 3(t – 12)2 for t in
seconds with t > 0. Which of the following is
FALSE?
A.
B.
C.
D.
The rate of change of V at t = 0 is 432
The volume decreases until t = 12
The rate of change of V at t = 3 is -54
The rate of change of V at t = 5 is -42
SD-CP-M-69
A coin is thrown straight up from the top of a
building which is 300 ft. tall. After t seconds, its
position is described by s = -16t2 + 24t + 300,
where s is its height above the ground in feet.
When does the coin begin to descend?
A.
B.
C.
D.
¼ sec
½ sec
¾ sec
1 sec
SD-CP-M-70
One-fourth of a short ton is how many
ounces?
A.
B.
C.
D.
8000
7250
6000
4000
SD-CP-M-71
Which of the following is NOT equal to
the other three?
A.
B.
C.
D.
1 acre
160 sq rods
43,000 sq ft
1 rod wide by ½ mile long
SD-CP-M-72
If Emmett picked 4 bushels and 2 pecks
of peaches, how many gallons did he
pick?
A.
B.
C.
D.
40
38
36
34
SD-CP-M-73
Which of the following is NOT
equal to one chain?
A.
B.
C.
D.
0.1 furlong
4 rods
792 inches
64 feet
SD-CP-M-74
Which of the following units of length
is in order from smallest to longest?
A.
B.
C.
D.
inch, hand, chain, rod
hand, rod, chain, furlong
hand, yard, furlong, rod
rod, chain, mile, furlong
SD-CP-M-75
Which is longest?
A.
B.
C.
D.
1 rod
1 foot
1 hand
1 yard
SD-CP-M-76
About how heavy (in pounds) is a
5-gallon bucket of water, if full?
A.
B.
C.
D.
30
40
50
60
SD-CP-M-77
Which is the smallest?
A.
B.
C.
D.
174 tablespoons
75 ounces
15 cups
3 quarts
SD-CP-M-78
The Ordinance of 1785 provided for the
scientific surveying of the territory’s land
and for a systematic subdivision of them.
The basic unit of land was the township.
How large was a township?
A. 6 square miles
B. 640 acres
C. 1920 acres
D.
36 square miles
End of Math Round
Senior Academic Super Bowl
Area Contest – April 19, 2016
SD Math Coaches Practice Answer Key:
1.
D
11.
C
21. A
31. D
41. A
2.
B
12.
C
22. A
32. A
42. B
3.
A
13.
B
23. D
33. C
43. D
4.
C
14. A
24. B
34. C
44. B
5.
A
15. A
25. C
35. D
45. D
6.
D
16. A
26. D
36. C
46. C
7.
D
17.
D
27. D
37. B
47. C
8.
B
18.
B
28. B
38. C
48. C
9.
D
19. C
29. A
39. B
49. B
20.
30. D
40. B
50. D
10. C
D
SD Math Coaches Practice Answer Key:
51.
D
61.
D
71. C
52.
C
62. A
72. C
53.
B
63.
B
73. D
54.
B
64. A
74. B
55.
A
65.
C
75. A
56.
D
66. A
76. B
57.
D
67. A
77. B
58.
A
68. A
78. D
59.
C
69.
60. A
C
70. A