Indiana Academic Super Bowl
Math Round
2017 – 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
The following series is ____________.
1 + ½ + ¼ + 1/8 + 1/16 + …..
A.
B.
C.
D.
indeterminate
convergent
divergent
Both A and B
SD-CP-M-2
The series
Sn = 1 + ½ + ¼ + 1/8 + …1/2n-1 is ___.
A.
B.
C.
D.
bounded above
bounded below
unbounded
bounded above and below
SD-CP-M-3
Joseph-Louis LaGrange found that the
volume of a regular tetrahedron is
, where a is the length of an
edge.
Find the area of one face of the solid.
Find the total surface area of the solid.
SD-CP-M-4
Write the equation for the least squares
regression line for the given data points.
(-2, -1), (1, 1), (3, 2)
SD-CP-M-5
The sales (in millions) of a company are
given below. Estimate the 2018 sales.
X (year)
Y (sales
in
millions)
2011
12
2012
19
2013
29
2014
37
2015
45
SD-CP-M-6
Expand (x –
3
2)
SD-CP-M-7
Use Pascal’s Triangle of the Binomial Theorem to
expand the following:
(x +
5
3)
SD-CP-M-8
A stone bridge is to be constructed over the Seine
and modeled after a parabolic arch. The bridge is
constructed at a strategic military point which
happens to be the widest portion of the river, 200
meters from bank to bank. If the peak of the
bridge’s arch is 25 meters above the river, how far
above the water is the bridge’s arch 65 meters
from the river bank?
SD-CPM-9
Determine the equation of a line tangent to the
given parabola at its vertex.
y = x2 + 2x + 10
SD-CP-M-10
Determine the equation of the line tangent to the
given circle at the given point.
(x + 2)2 + (y – 4)2 = 25; (1, 8)
A.
B.
C.
D.
y – 8 = 4/3(x – 1)
y – 8 = -¾(x – 1)
y – 1 = 4/3(x – 8)
y – 1 = -¾(x – 8)
SD-CP-M-11
The Arc de Triomphe has two separate sized
vaults. The smaller vault is 18.68 meters tall and
roughly 8 meters wide. The vault is created by
placing a parabolic arch atop two vertical supports.
If you are to estimate the legs to be 16.68 meters
tall, determine the focus and directrix of the arch
based on the estimated width and height of the
space.
SD-CP-M-12
Determine the center and estimate the radius of the
given circle.
x2 – 8x + y2 + 10y = 72.
SD-CP-M-13
An ellipse is centered on a Cartesian
coordinate grid. Its domain varies from
-7 to 7 inclusive, with its range covering
-3 to 3 inclusive. Create an equation for this
shape.
SD-CP-M-14
Given the following function,
f (x) = 5x4 -2x2 + 7
how many possible positive and negative
solutions exist?
SD-CP-M-15
Notre Dame cathedral has a vaulted ceiling
measuring roughly 33.5 meters tall. How tall is it
in decimeters?
SD-CP-M-16
There are 0.6213 miles in a kilometer. If the
average human walks at a rate of 3.1 miles per
hour, what would the average human’s rate be in
centimeters per second?
SD-CP-M-17
Given the following function
f(x) = x3 – 5x2 – 14x + 12,
what are possible x-intercepts of the graph?
A. it will not cross the x-axis
B. it will cross 1 time below zero
C. it will cross 1 time below zero and 1
time above zero
D. it will cross 1 time below zero and 2
times above zero
SD-CP-M-18
What type of graph is represented by the
equation
x2 – y2 + 5x – 4y = 56
A.
B.
C.
D.
parabolic
hyperbolic
elliptical
circular
SD-CP-M-19
During the French Revolution, what
units were proposed as the new standard
units of measure?
SD-CP-M-20
During the time of the French Revolution, French
mathematicians attempted the decimalization of
all units, including time. This system consisted of
a day where there were 10 hours in a day, with
100 minutes in an hour and 100 seconds in a
minute. If your favorite television show airs at
9:00 p.m., what time would your show air under
this system?
End of Math Round
Senior Academic Super Bowl
Area Contest – April 18, 2017
SD Math Coaches Practice Answer Key:
1.
B
2.
A
SD Math Coaches Practice Answer Key:
3. Area of one face:
Total surface area of the solid:
SD Math Coaches Practice Answer Key:
4.
x
y
xy
x2
-2
1
-2
1
1
1
1
1
3
2
6
9
2
4
5
11
Slope =
Y – int =
Y=
N = 3 pts
SD Math Coaches Practice Answer Key:
5.
SD Math Coaches Practice Answer Key:
6.
(x – 2) (x – 2) (x – 2)
(x2 – 4x + 4) (x – 2)
x3 – 6x + 12x - 8
7.
(x + 3)0 =
1
(x + 3)1 =
1
(x + 3)2 =
1
(x + 3)3 =
(x + 3)4 =
1
1
1
2
3
4
1
3
6
1
4
1
(x + 3)5 = 1x5 + 5x4 . 3 + 10x3 . 32 + 10x2 . 33 + 5x34 + 1.35
= x5 + 15x4 + 90x3+ 270x2 + 405x + 243
SD Math Coaches Practice Answer Key:
8.
SD Math Coaches Practice Answer Key:
9.
SD Math Coaches Practice Answer Key:
10.
SD Math Coaches Practice Answer Key:
11.
SD Math Coaches Practice Answer Key:
12.
SD Math Coaches Practice Answer Key:
13.
SD Math Coaches Practice Answer Key:
14.
SD Math Coaches Practice Answer Key:
15.
SD Math Coaches Practice Answer Key:
16.
SD Math Coaches Practice Answer Key:
17.
18.
D
SD Math Coaches Practice Answer Key:
19.
20.