Indiana Academic Super Bowl
Math Round
2017 – Senior Division Invitational 2
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-I2-M-1
Use Pascal’s Triangle or the Binomial
Theorem to expand the following:
(x – 1)5
A. x5 – 1
B. x5 – 4x4 + 6x3 – 4x2 + 1
C. x5 – 5x4 + 10x3 – 10x2 + 5x – 1
D. x5 + 5x4 + 10x3 + 10x2 + 5x + 1
SD-I2-M-1
Use Pascal’s Triangle or the Binomial
Theorem to expand the following:
(x – 1)5
C. x5 – 5x4 + 10x3 – 10x2 + 5x – 1
SD-I2-M-2
The Eiffel Tower measures 984 feet tall.
If 1 meter is equal to roughly 3.281 feet,
how tall is the tower in decameters?
A. 29.99 decameters
B. 299.93 decameters
C. 2,999.32 decameters
D. 29,993.24 decameters
SD-I2-M-2
The Eiffel Tower measures 984 feet tall.
If 1 meter is equal to roughly 3.281 feet,
how tall is the tower in decameters?
A. 29.99 decameters
SD-I2-M-3
20 sec
Joseph-Louis LaGrange found that the volume
of a regular tetrahedron is
where
a is the length of an edge. What is the volume
of a tetragon with an edge length of 2 cm?
A.
B.
C.
D.
SD-I2-M-3
Joseph-Louis LaGrange found that the volume
of a regular tetrahedron is
where
a is the length of an edge. What is the volume
of a tetragon with an edge length of 2 cm?
A.
SD-I2-M-4
40 sec
There are 0.9144 meters in 1 yard.
Convert 262 feet 9 inches into
decimeters.
A. 800.86
B. 80.09
C. 8.01
D. 0.80
SD-I2-M-4
There are 0.9144 meters in 1 yard.
Convert 262 feet 9 inches into
decimeters.
A. 800.86
SD-I2-M-5
Use Pascal’s Triangle or the Binomial
Theorem to expand the following:
(2x + 1)4
A. 16x4 + 1
B. x4 + 4x3 + 6x2 + 4x + 1
C. 2x4 + 12x3 + 36x2 + 36x + 1
D. 16x4 + 32x3 + 24x2 + 8x + 1
SD-I2-M-5
Use Pascal’s Triangle or the Binomial
Theorem to expand the following:
(2x + 1)4
D. 16x4 + 32x3 + 24x2 + 8x + 1
SD-I2-M-6
20 sec
Given the following function
f(x) = x3 - 5x2 – 14x + 12, which of the
following combinations lists a possible
set of solution types?
A. 1 zero, 2 complex
B. 2 positive, 2 complex
C. 2 positive, 1 negative
D. 2 positive, 1 zero
SD-I2-M-6
Given the following function
f(x) = x3 - 5x2 – 14x + 12, which of
the following combinations lists a
possible set of solution types?
C. 2 positive, 1 negative
SD-I2-M-7
Find the y-intercept for the best-fit line
through the given data points.
(0, 0), (1, 2), (2, 4)
A.
B.
C.
D.
(0, 0)
(0, 2)
(2, 0)
(2, 2)
SD-I2-M-7
Find the y-intercept for the best-fit line
through the given data points.
(0, 0), (1, 2), (2, 4)
A.
(0, 0)
SD-I2-M-8
20 sec
What type of graph is represented
by the equation
15x2 – 15y2 + x – 16y = 38
A. circular
B. parabolic
C. elliptical
D. hyperbolic
SD-I2-M-8
What type of graph is represented
by the equation
15x2 – 15y2 + x – 16y = 38
D. hyperbolic
SD-I2-M-9
40 sec
Find the slope for the best-fit line
through the following points.
(0, 0), (1, 1), (3, 2)
A.
B.
C.
D.
11/14
-11/14
9/14
-9/14
SD-I2-M-9
Find the slope for the best-fit line
through the following points.
(0, 0), (1, 1), (3, 2)
C. 9/14
SD-I2-M-10
40 sec
Determine the center and radius of
the given circle
x2 – 18x + y2 + 12y = 56
A. Center (9, -6) Radius 7.48
B. Center (6, -9) Radius 7.48
C. Center (-9, 6) Radius 13.15
D. Center (9, -6) Radius 13.15
SD-I2-M-10
Determine the center and radius of
the given circle
x2 – 18x + y2 + 12y = 56
D.
Center (9, -6) Radius 13.15
SD-I2-M-11
20 sec
For which of the following would a least square
analysis be a suitable way to project a value?
A. projected height of an adult at age 50, based
on the heights of his/her neighbors
B. projected sales of a company based on sales
over the past 10 years
C. projected population of bacteria in a petri
dish, based on the population in previous
minutes
D. projected October temperatures based on
average temperatures for February through
September of the same year
SD-I2-M-11
For which of the following would a least square
analysis be a suitable way to project a value?
B.
projected sales of a company based on sales
over the past 10 years
SD-I2-M-12
Which mathematician is commonly
referred to as “French”, but actually was
not born in France, and produced his
intellectual works in what became the
modern nations of Italy, Germany, and
France?
A. Leonhard Euler
B. Rene Descartes
C. Joseph-Louis Lagrange
D. Pierre-Simon Laplace
SD-I2-M-12
Which mathematician is commonly
referred to as “French”, but actually
was not born in France, and produced
his intellectual works in what became
the modern nations of Italy, Germany,
and France?
C. Joseph-Louis Lagrange
SD-I2-M-13
A tetrahedron of pure lead has an edge
length of 2.00 cm. What is the mass of the
solid? (The density of lead is11.34 g/cm3)
A.
B.
C.
D.
0.83 g
10.66 g
12.06 g
12.28 g
SD-I2-M-13
A tetrahedron of pure lead has an edge
length of 2.00 cm. What is the mass of the
solid? (The density of lead is11.34 g/cm3)
B.
10.66 g
SD-I2-M-14
Which famous mathematician is commonly
referred to as the “French Newton” or the
“Newton of France” due to his numerous
mechanics and astronomical works?
A. Joseph Fourier
B. Pierre-Simon Laplace
C. Augustin-Louis Cauchy
D. Joseph-Louis Lagrange
SD-I2-M-14
Which famous mathematician is commonly
referred to as the “French Newton” or the
“Newton of France” due to his numerous
mechanics and astronomical works?
B.
Pierre-Simon Laplace
SD-I2-M-15
Expand: (x – i)2
A.
B.
C.
D.
-x2 + 1
x2 – 1
x2 – 2xi – 1
x2 + 2xi – 1
SD-I2-M-15
Expand: (x – i)2
C. x2 – 2xi – 1
20 sec
SD-I2-M-16
20 sec
In 1795, the French Revolutionary
government proposed which unit as the
standard unit of mass?
A.
B.
C.
D.
pound
kilogramme
gramme
litre
SD-I2-M-16
In 1795, the French Revolutionary
government proposed which unit as the
standard unit of mass?
C. gramme
SD-I2-M-17
Expand: (x + 2)3
A.
B.
C.
D.
x3 + -6x2 + 6x - 8
x3 + 6x2 +12x + 8
x3 + 4x + 8
x3 + 4x2 + 8
SD-I2-M-17
Expand: (x + 2)3
B. x3 + 6x2 +12x + 8
20 sec
SD-I2-M-18
20 sec
What type of graph is represented
by the equation
-15x2 – 2x – y = 36
A. linear
B. parabolic
C. elliptical
D. hyperbolic
SD-I2-M-18
What type of graph is represented
by the equation
-15x2 – 2x – y = 36
B. parabolic
SD-I2-M-19
Which of the following is closest to the
edge length of a tetrahedron with a
volume of 10 cm3, if
where
a is the length of an edge?
A. 2.77 cm
B. 4.39 cm
C. 12.06 cm
D. 28.28 cm
SD-I2-M-19
Which of the following is closest to the
edge length of a tetrahedron with a
volume of 10 cm3, if
where
a is the length of an edge?
B. 4.39 cm
SD-I2-M-20
20 sec
Given the following function
f(x) = x6 + 5x4 – 3x3 + 9, choose the best
roots of the given function.
A.
B.
C.
D.
1 positive, 0 negative
2 positive, 0 negative
1 positive, 1 negative
0 positive, 2 negative
SD-I2-M-20
Given the following function
f(x) = x6 + 5x4 – 3x3 + 9, choose the best
roots of the given function.
B.
2 positive, 0 negative
SD-I2-M-21
Find the area of one face of a regular
tetrahedron if
where a is the
length of an edge, if a = 3 cm.
A. 27/2 cm2
B.
C.
D.
SD-I2-M-21
Find the area of one face of a regular
tetrahedron if
where a is the
length of an edge, if a = 3 cm.
D.
SD-I2-M-22
20 sec
Use Pascal’s Triangle or the Binomial
Theorem to expand the following:
(x - y)3
A. x3 – 3x2y – 3xy2 + y3
B. x3 – 3x2y + 3xy2 - y3
C. x3 + 3x2y + 3xy2 - y3
D. x3 – y3
SD-I2-M-22
Use Pascal’s Triangle or the Binomial
Theorem to expand the following:
(x - y)3
B. x3 – 3x2y + 3xy2 - y3
SD-I2-M-23
40 sec
SD-I2-M-23
Dimitri has the ball on the ground 27.5 meters away from
Oliver. Dimitri kicks the ball toward Oliver with an initial
upward velocity of 12.25 meters per second and Oliver heads
it into the net on its way back down at a height of 2.64
meters. Ignoring wind resistance, use the formula
h(t) = -4.9t2 + v0t + h0 where h(t) is the height of the ball, v0 is
the initial upward velocity, and h0 is the initial height of the
ball, to determine how long it took the ball to reach Oliver.
B.
2.3 seconds
SD-I2-M-24
Expand: (x – 4)3
A.
B.
C.
D.
x3 – 64
x3 – 4x2 + 16x – 64
x3 – 12x2 + 48x - 64
x3 – 4x2 – 16x - 64
SD-I2-M-24
Expand: (x – 4)3
C. x3 – 12x2 + 48x - 64
20 sec
SD-I2-M-25
40 sec
Estimate the area of the given circle
x2 – 18x + y2 + 12y = 56
A.
B.
C.
D.
640 sq units
600 sq units
540 sq units
500 sq units
SD-I2-M-25
Estimate the area of the given circle
x2 – 18x + y2 + 12y = 56
C. 540 sq units
End of Math Round
The Next Round will be English
2017 Academic Area Super Bowl Competition
Tuesday, April 18, 2017