Indiana Academic Super Bowl
Math Round
2017 – Senior Division Invitational 1
A Program of the Indiana Association of School Principals
Emcee:
Please ask Proctors to check student
calculators at this time. The only
calculators allowed during this
competition are the following models:
TI-30Xa and TI-30X IIS
If someone at your table has a different
model, raise your hand for a
procedural official.
SD-I1-M-1
20 seconds
Which scientist(s) served on the initial
committee charged with the decimalization
of France?
A.
B.
C.
D.
Jean-Charles de Borda
Pierre-Simon Laplace
de Borda and Laplace
none of the above
SD-I1-M-1
Which scientist(s) served on the initial
committee charged with the decimalization
of France?
C.
de Borda and Laplace
SD-I1-M-2
Expand: (x + 1)3
A.
B.
C.
D.
x3 +3x2 + 3x + 1
x3 + 2x + 1
x3 + 2x2 + x
x3 + 2x2 + 1
SD-I1-M-2
Expand: (x + 1)3
A. x3 +3x2 + 3x + 1
20 seconds
SD-I1-M-3
40 seconds
An ellipse is centered on the point (-3, 2).
Its domain is from -5 to -1 inclusive, and its
range is from -4 to 8 inclusive. Given the
following points, which best estimates the
ellipse’s foci?
A. (-3, -3.5), (-3, 7.5)
B. (-3, -2.5), (-3, 6)
C. (-3.5, 2), (-2.5, 2)
D. (-3.75, 2, (-1.25, 2)
SD-I1-M-3
An ellipse is centered on the point (-3, 2).
Its domain is from -5 to -1 inclusive, and its
range is from -4 to 8 inclusive. Given the
following points, which best estimates the
ellipse’s foci?
A. (-3, -3.5), (-3, 7.5)
SD-I1-M-4
Given the following function
f(x) = -3x5 + 2x4 – 12x3 -3x2 – 5x
Which of the following is NOT a
combination of possible roots?
A. 1 zero, 2 positive, 2 negative
B. 1 zero, 1 positive, 2 negative
C. 1 zero, 2 positive, 2 complex
D. 1 zero, 2 negative, 2 complex
SD-I1-M-4
Given the following function
f(x) = -3x5 + 2x4 – 12x3 -3x2 – 5x
Which of the following is NOT a
combination of possible roots?
B. 1 zero, 1 positive, 2 negative
SD-I1-M-5
Use Pascal’s Triangle or the Binomial
Theorem to expand (x + y)3
A.
B.
C.
D.
x3 + 3x2y + 3xy2 + y3
x3 + y3
x3 + x2y + xy2 + y3
x3 + xy + y3
SD-I1-M-5
Use Pascal’s Triangle or the Binomial
Theorem to expand (x + y)3
A. x3 + 3x2y + 3xy2 + y3
SD-I1-M-6
20 seconds
Which of the following is closest to the edge
length of a tetrahedron with a volume of
20 cm3, if
, where a is the length of
an edge?
A. 5.54 cm
B. 6.21 cm
C. 13.03 cm
D. 15.49 cm
SD-I1-M-6
Which of the following is closest to the edge
length of a tetrahedron with a volume of
20 cm3, if
, where a is the length of
an edge?
A. 5.54 cm
SD-I1-M-7
40 seconds
What is the slope for the least
squares regression line for the given
data points. (-2, -1), (1, 1), (3, 2)
A. 23/38
B. 15/38
C. 5/19
D. 8/19
SD-I1-M-7
What is the slope for the least
squares regression line for the given
data points. (-2, -1), (1, 1), (3, 2)
A. 23/38
SD-I1-M-8
20 seconds
Use Pascal’s Triangle or the Binomial
Theorem to expand (x + 1)5
A.
B.
C.
D.
x5 + 1
x5 + 4x4 + 6x3 + 4x2 + x
x5 + 4x4 + 6x3 + 4x2 + 1
x5 + 5x4 + 10x3 + 10x2 + 5x + 1
SD-I1-M-8
Use Pascal’s Triangle or the Binomial
Theorem to expand (x + 1)5
D. x5 + 5x4 + 10x3 + 10x2 + 5x + 1
SD-I1-M-9
20 seconds
In 1795, the French Revolutionary government
proposed all of the following as standard units
of measure EXCEPT the _______.
A.
B.
C.
D.
gramme
kilometer
franc
stère
SD-I1-M-9
In 1795, the French Revolutionary
government proposed all of the following as
standard units of measure EXCEPT the
_______.
B.
kilometer
SD-I1-M-10
20 seconds
Joseph-Louis Lagrange founded, or was a
member of, many famous European
academies throughout his life. Which
academy was he NOT a member of?
A. Prussian Academy of Sciences in Berlin
B. French Academy of Sciences
C. Royal Academy of Science of Turin
D. Spanish Royal Academy of Science in
Madrid
SD-I1-M-10
Joseph-Louis Lagrange founded, or was a
member of, many famous European
academies throughout his life. Which
academy was he NOT a member of?
D.
Spanish Royal Academy of Science in
Madrid
SD-I1-M-11
40 seconds
Determine the equation of a line tangent
to the given parabola at its vertex
y = 3x2 + 12x +8
A. y = -4
B. y = -2
C. x = -2
D. x = -4
SD-I1-M-11
Determine the equation of a line tangent
to the given parabola at its vertex
y = 3x2 + 12x +8
A. y = -4
SD-I1-M-12
30 seconds
Which of the following could NOT be a net
of a tetrahedron?
A.
B.
C.
D.
SD-I1-M-12
Which of the following could NOT be a net
of a tetrahedron?
B.
SD-I1-M-13
Expand: (x + i)2
A.
B.
C.
D.
-x2i2
x2 + i2
x2 – 1
x2 + 2xi – 1
SD-I1-M-13
Expand: (x + i)2
D. x2 + 2xi – 1
SD-I1-M-14
20 seconds
What type of graph is represented with the
equation 14x2 + 14y2 – 6x + 12y = 36?
A.
B.
C.
D.
circular
hyperbolic
elliptical
parabolic
SD-I1-M-14
What type of graph is represented with the
equation 14x2 + 14y2 – 6x + 12y = 36?
A.
circular
SD-I1-M-15
40 seconds
Write the equation for the least squares
regression line for the given data points.
(-1, 0), (0, 2), (1, 4), (2, 5)
A. Y = 3.2x + 0.6
B. Y = 1.7x + 1.9
C. Y = 2.5x + 2.0
D. Y = 0.7x + 0.9
SD-I1-M-15
Write the equation for the least squares
regression line for the given data points.
(-1, 0), (0, 2), (1, 4), (2, 5)
B. Y = 1.7x + 1.9
SD-I1-M-16
20 seconds
Given the following function
(f)x = 2x4 + 3x2 – 48, list the possible
positive and negative roots of the
function.
A. 0 positive, 0 negative
B. 1 positive, 1 negative
C. 2 positive, 0 negative
D. 0 positive, 2 negative
SD-I1-M-16
Given the following function
(f)x = 2x4 + 3x2 – 48, list the possible
positive and negative roots of the
function.
B. 1 positive, 1 negative
SD-I1-M-17
20 seconds
What type of graph is represented by the
equation x2 – y2 + 5x – 4y = 56
A.
B.
C.
D.
parabolic
hyperbolic
elliptical
circular
SD-I1-M-17
What type of graph is represented by the
equation x2 – y2 + 5x – 4y = 56
B. hyperbolic
SD-I1-M-18
20 seconds
Use Pascal’s Triangle or the Binomial
Theorem to expand (x + 3)4
A.
B.
C.
D.
x4 + 81
x4 + 4x3 + 6x2 + 4x + 1
x4 + 12x3 + 36x2 + 36x + 12
x4 + 12x3 + 54x2 + 108x + 81
SD-I1-M-18
Use Pascal’s Triangle or the Binomial
Theorem to expand (x + 3)4
D. x4 + 12x3 + 54x2 + 108x + 81
SD-I1-M-19
20 seconds
In his most famous publication,
Èlements de Géométrie, which
mathematician reorganized and
simplified many of Euclid’s Elements?
A. Adrien-Marie Legendre
B. Augustin-Louis Cauchy
C. Rene Descartes
D. Pierre-Simon Laplace
SD-I1-M-19
In his most famous publication,
Èlements de Géométrie, which
mathematician reorganized and
simplified many of Euclid’s Elements?
A. Adrien-Marie Legendre
SD-I1-M-20
Find the total surface area of a regular
tetrahedron if
, where a is the
length of an edge.
A. a2
B.
C.
D.
SD-I1-M-20
Find the total surface area of a regular
tetrahedron if
, where a is the
length of an edge.
C.
SD-I1-M-21
30 seconds
Name the center of the ellipse for
25x2 + 4y2 + 100x – 16y = 84
A.
B.
C.
D.
(2, 2)
(2, -2)
(-2, -2)
(-2, 2)
SD-I1-M-21
Name the center of the ellipse for
25x2 + 4y2 + 100x – 16y = 84
D. (-2, 2)
SD-I1-M-22
30 seconds
The Seine has been dredged to allow oceanic
vessels to dock up the river 64.79 nautical
miles from the sea at Rouen. If 1 meter is
0.0005399 nautical miles, and it took the ship
15 hours to enter the river and dock, how fast
was the ship traveling in kilometers per hour?
A. 7 km/hr
B. 7.5 km/hr
C. 8 km/hr
D. 8.5 km/hr
SD-I1-M-22
The Seine has been dredged to allow oceanic
vessels to dock up the river 64.79 nautical
miles from the sea at Rouen. If 1 meter is
0.0005399 nautical miles, and it took the ship
15 hours to enter the river and dock, how fast
was the ship traveling in kilometers per hour?
C.
8 km/hr
SD-I1-M-23
30 seconds
A tetrahedron of pure gold has an edge
length of 6.00 cm. What is the mass of
the solid? (The density of gold is
19.32 g/cm3)
A. 0.759 g
B. 1.32 g
C. 25.4 g
D. 492 g
SD-I1-M-23
A tetrahedron of pure gold has an edge
length of 6.00 cm. What is the mass of
the solid? (The density of gold is
19.32 g/cm3)
D. 492 g
SD-I1-M-24
40 seconds
This bridge over the Seine is 45 meters wide with a
maximum height of 16 meters above the river. The
arch is connected 9 meters above the water to the
stone embankments. Which equation would best
predict the height of the arch given a distance from
the bank?
A. y = 0.14(x - 22.5)2 + 16
B. y = 0.014(x - 22.5)2 + 16
C.
y = -0.014(x - 22.5)2 + 16
D.
y = -0.14(x - 22.5)2 + 16
SD-I1-M-24
This bridge over the Seine is 45 meters wide with
a maximum height of 16 meters above the river.
The arch is connected 9 meters above the water to
the stone embankments. Which equation would
best predict the height of the arch given a distance
from the bank?
C.
y = -0.014(x-22.5)2 + 16
SD-I1-M-25
A table showing U.S. traffic deaths (in
thousands) is shown below. How many
deaths would you project for 2017?
X (year)
2006
2007
2008
Y (deaths in
thousands)
42.7
41.3
37.4
A.
B.
C.
D.
5,800
13,600
35,700
44,200
SD-I1-M-25
A table showing U.S. traffic deaths (in
thousands) is shown below. How many
deaths would you project for 2017?
X (year)
2006
2007
2008
Y (deaths in
thousands)
42.7
41.3
37.4
B.
13,600
End of Mathematics Round
The Next Round will be English
2017 Academic Area Super Bowl Competition
Tuesday, April 18, 2017
Coach Reminder:
Team Rosters of up to 30 students eligible to
compete at the Area Competition (on April
18, 2017) must be submitted through the
online form by March 26.
For Contest Rules (including rules about
eligibility and roster submission) consult the
Academic Super Bowl Coach Handbook
http://www.iasp.org/pdf/coachhandbooksuper.pdf