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Powers,
Roots, &
Radicals
Rationals
Conics,
Sequences,
& Series
Probability &
Statistics
Potpourri
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Powers,
Roots, &
Radicals
Rationals
Conics,
Sequences,
& Series
Probability &
Statistics
Potpourri
100
100
100
100
100
200
200
200
200
200
300
300
300
300
300
400
400
400
400
400
500
500
500
500
500
Powers, Roots, & Radicals - $100
For which of the following functions is
f (−3) < f (3)?
(A) f  x   4 x 2
(B) f  x   4
4
(C) f  x  
x
(D) f  x   4  x 3
(E) f  x   x 4  4
Powers, Roots, & Radicals - $100 Answer
 D f  x   4  x
3
Powers, Roots, & Radicals - $200
If 8  k  15, then k  ?
Powers, Roots, & Radicals - $200 Answer
49
Powers, Roots, & Radicals - $300
If a, b, and c are different
positive integers and
2  2  2  64, then
a
b
c
2 2 2 ?
a
b
c
Powers, Roots, & Radicals - $300 Answer
14
Powers, Roots, & Radicals - $400
If a and b are positive integers
1 6
3


and  a b  =432, what is the


value of ab ?
1
2
Powers, Roots, & Radicals - $400 Answer
12
Powers, Roots, & Radicals - $500
If m and k are positive and
2
10m k
1
1
 100m, what is
m in terms of k?
Powers, Roots, & Radicals - $500 Answer
1
10k
Rationals - $100
If 2r  5s and 5s  6t,
what does r equal in terms of t?
Rationals - $100 Answer
3t
Rationals - $200
If x is an integer greater than 1 and if
1
y  x  , which of the following must be true?
x
I. y  x
II. y is an integer
III. xy  x
2
Rationals - $200 Answer
I and III only
Rationals - $300
If a  2b is equal to 125 percent
a
of 4b, what is the value of ?
b
Rationals - $300 Answer
3
Rationals - $400
The total daily cost c, in dollars of producing
x units of a certain product is given by the function
600 x  200
c  x 
 k , where k is a constant and
x
x  100. If 20 units were produced yesterday for a
total cost of $640, what is the value of k ?
Rationals - $400 Answer
50
Rationals - $500
The force required to stretch a spring
beyond its natural length is proportional
to how far the spring is being stretched.
If a force of 15 pounds stretches a
spring 8 centimeters beyond its natural
length, what force, in pounds, is needed
to stretch this spring 20 centimeters
beyond its natural length?
Rationals - $500 Answer
37.5
Conics, Sequences, & Series - $100
In the xy-plane, the center of a circle has coordinates (3,−7).
If one endpoint of a diameter of the circle is (−2,−7), what
are the coordinates of the other endpoint of this diameter?
Conics, Sequences, & Series - $100 Answer
(8,−7)
Conics, Sequences, & Series - $200
What 2 numbers should be placed in the blanks
below so that the difference between consecutive
numbers is the same?
17, _____, _____, 41
Conics, Sequences, & Series - $200 Answer
25, 33
Conics, Sequences, & Series - $300
The depth of a pond is 180 cm and is being reduced by
1 cm per week. The depth of a second pond is 160 cm
and is being reduced by ½ cm per week. If the depths
of both ponds continue to be reduced at these constant
rates, in about how many weeks will the ponds have
The same depth?
Conics, Sequences, & Series - $300 Answer
40
Conics, Sequences, & Series - $400
A circle in the standard (x, y) coordinate plane is
tangent to the x-axis at 5 and tangent to the y-axis
at 5. What is an equation of the circle?
Conics, Sequences, & Series - $400 Answer
 x  5
2
  y  5  25
2
Conics, Sequences, & Series - $500
On his first day as a telemarketer, Marshall made
24 calls. His goal was to make 5 more calls on
each successive day than he had made the day
before. If Marshall met, but did not exceed, his
goal, how many calls had he made in all after
spending exactly 20 days making calls as a
telemarketer?
Conics, Sequences, & Series - $500 Answer
1,430
Probability & Statistics - $100
If a marble is randomly chosen from a bag that
contains exactly 8 red marbles, 6 blue marbles, and
6 white marbles, what is the probability that the
marble will NOT be white?
Probability & Statistics - $100 Answer
7
10
Probability & Statistics - $200
The median of a set of 9 consecutive integers
is 42. What is the greatest of these 9 integers?
Probability & Statistics - $200 Answer
46
Probability & Statistics - $300
In a poll, 35 people were in favor of building a
new library, 14 people were against it, and 1
person had no opinion. What fraction of those
polled were in favor of building a new library?
Probability & Statistics - $300 Answer
2
3
Probability & Statistics - $400
*Daily Double!*
A list of numbers consists of p positive and n
negative numbers. If a number is picked at random
from this list, the probability that the number is
3
n
positive is . What is the value of ?
5
p
Probability & Statistics - $400 Answer
2
3
Probability & Statistics - $500
If the average (arithmetic mean) of x and y is k,
Which of the following is the average of x, y, and z?
2k  z
3
2k  z
(B)
2
kz
(C)
3
2k  z
(D)
2
2 k  z
(E)
3
(A)
Probability & Statistics - $500 Answer
2k  z
(A)
3
Potpourri - $100
If f  x   x  1, then
2
f  x  h  ?
Potpourri - $100 Answer
x  2 xh  h  2
2
2
Potpourri - $200
What is the matrix product
a
 2a  1 0 1 ?

 
 3a 
Potpourri - $200 Answer
 a 0 a 
 2a 0 2a 


 3a 0 3a 
Potpourri - $300
In the complex numbers, where i  1,
1 1 i

?
1 i 1 i
2
Potpourri - $300 Answer
1 i
2
Potpourri - $400
What is a value of x that
satisifies log x 36  2?
Potpourri - $400 Answer
6
Potpourri - $500
If the volume of a cube is 8, what is the
shortest distance from the center of the
cube to the base of the cube?
Potpourri - $500 Answer
1
Final Jeopardy Category:
Logarithms
Final Jeopardy Question
If log a x  s and log a y  t ,
then log a  xy   ?
2
Final Jeopardy Answer
2s  t