Indiana Academic Super Bowl Math Round Team/2015...A Program of the Indiana Association of School...

transcript

Indiana Academic Super Bowl

A Program of the Indiana Association of School Principals

Math Round2016 – Coaches Practice

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. x = 1

B. x = -1

C. y = 1

D. 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. x = 0

B. y = 1

C. y = 3

D. cannot be determined

SD-CP-M-3

What are the x-intercepts of the

graph of y = x2 – x – 20?

A. (5, 0) and (-4, 0)

B. (4, 0) and (-5, 0)

C. (-4, 0) and (-5, 0)

D. (4, 0) and (5, 0)

SD-CP-M-4

Which of the following is the equation

of a parabola?

A. x2 – 7x + y2 = 20

B. xy = -5

C. y2 = 2y + x + 4

D. x2 – y2 = 1

SD-CP-M-5

What are the coordinates of the vertex of

the graph of y = - (x + 4)2 – 2?

A. (-4, -2)

B. (4, -2)

C. (-4, 2)

D. (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 _________.

C. -16

SD-CP-M-7

SD-CP-M-8

The coordinates of the foci of the ellipse with the

equation 3x2 + 7y2 = 63 are _____.

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. (11, -4) & (-1, -4)

B. (5, -10) & (5, 2)

C. (2, -4) & (8, -4)

D. (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. (2, 2)

B. (2, -2)

C. (-2, -2)

D. (-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. parabola

B. ellipse

C. hyperbola

D. 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 _______.

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. 256

D. -14

SD-CP-M-24

SD-CP-M-25

Write log4 x = 2 in exponential form.

A. 4x = 2

B. 2x = 4

C. 42 = x

D. x4 = 2

SD-CP-M 26

SD-CP-M-27

Find the value of [log (5 log 100)]2

SD-CP-M-28

SD-CP-M-29

SD-CP-M-30

Which is the smallest number?

A. 1.2 x 10-6

B. 2.4 x 10-2

C. 3.1 x 10-5

D. 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 equals __.

A. 8 B.

SD-CP-M-37

If (x + x-1)2 = 16, then the value of x2 +

x-2 is _______.

SD-CP-M-38

Find the sum of the solutions of the equation

(4x - 8)(4x - 2) = 0.

B. log410

SD-CP-M-39

If = 2 then the difference of the

solutions for x is ______.

C. 2 D.

SD-CP-M-40

The sum of the solutions for

is ________.

SD-CP-M-41

The sum of the solutions for

A. -34

SD-CP-M-42

If which of the following

could NOT be a value of n?

SD-CP-M-43

If x is a real number and

SD-CP-M-44

The set of x values satisfying the inequality

A. x < -1 or x > 3

B. -4 < x < -1 or 3 < x < 6

C. 3 < x < 6 or -6 < x < -3

D. -6 < x < -4 or -1 < x < 3

SD-CP-M-45

The sum of the real values of x satisfying the

equality is _______.

SD-CP-M-46

If for all x such that

then the smallest possible

value of N is ______.

A. 0.0301

B. 0.0399

C. 0.0401

D. 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

SD-CP-M-49

If f (x) = cos (x – 6), then f ′(x) = ____.

A. cos (sin(x – 6))

B. -sin (x – 6)

C. - 6 cos x

D. 6 sin (x – 6)

SD-CP-M-50

If f (x) = , then

A. -14

SD-CP-M-51

If y = 16x2 + 8x + 10, then y′ = ____.

A. 32x + 18

B. 8x + 8

C. 16x + 4

D. 32x + 8

SD-CP-M-52

If y =

C. 1 D. 2

SD-CP-M-53

SD-CP-M-54

A. 2 – x-2

C. 2x2

D. x2 + x

SD-CP-M-55

A. -49x-8

B. -56x-8

C. -49x-6

D. -42x-6

SD-CP-M 56

If y = (2x – 3)(x + 1)2, then y′ = ___.

A. 6x2 – 2

B. 2(2x – 3)(x + 1)

C. 12x2 – 4x – 2

D. 2(x + 1)(3x – 2)

SD-CP-M-57

If y =

? = _______.

A. 4x3 + 4x

SD-CP-M-58

If y =

? = _______.

B. 2x2 + 2

C. 4x3 + 2x

D. 4x2 + 2x

SD-CP-M-59

If y = (x2 – 1)(x + 2), then y′ = _____.

B. -x2 – 4x + 1

C. 3x2 + 4x – 1

D. 2x2 - 2

SD-CP-M-60

If f (x) = sec x tan x,

then f′(x) = sec3 x + ____.

A. tan2 x sec x

B. tan x sec2 x

C. tan x sec x

D. tan3 x

SD-CP-M-61

If f (x) = 5x csc x, then f ′(x) = _______.

A. 5x cot x

B. -5 csc2 x + 5 cot x

C. -5 csc x cot x + 5

D. 5 csc x (1 – x cot x)

SD-CPM-62

A. sec2 u

B. -csc2 u

C. sec u tan u

D. -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?

SD-CP-M-64

Let f (x) = 4x5 – 5x4 – 40x3. Which of the

following statements is TRUE?

A. There is a relative max at x = -2

B. There is a relative max at x = 3

C. There is a relative min at x = 0

D. 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. y = 12x + 6

B. y = 12x + 3

C. y = 12x – 16

D. 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. 6x – y = 7

B. 6x – y = 0

C. 12x – y = 13

D. 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. The rate of change of V at t = 0 is 432

B. The volume decreases until t = 12

C. The rate of change of V at t = 3 is -54

D. 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. ¼ sec

B. ½ sec

C. ¾ sec

D. 1 sec

SD-CP-M-70

One-fourth of a short ton is how many

ounces?

A. 8000

B. 7250

C. 6000

D. 4000

SD-CP-M-71

Which of the following is NOT equal to

the other three?

A. 1 acre

B. 160 sq rods

C. 43,000 sq ft

D. 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

SD-CP-M-73

Which of the following is NOT

equal to one chain?

A. 0.1 furlong

B. 4 rods

C. 792 inches

D. 64 feet

SD-CP-M-74

Which of the following units of length

is in order from smallest to longest?

A. inch, hand, chain, rod

B. hand, rod, chain, furlong

C. hand, yard, furlong, rod

D. rod, chain, mile, furlong

SD-CP-M-75

Which is longest?

A. 1 rod

B. 1 foot

C. 1 hand

D. 1 yard

SD-CP-M-76

About how heavy (in pounds) is a

5-gallon bucket of water, if full?

SD-CP-M-77

Which is the smallest?

A. 174 tablespoons

B. 75 ounces

C. 15 cups

D. 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:

Indiana Academic Super Bowl Math Round Team/2015...A Program of the Indiana Association of School...

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