Round 2!
Double Jeopardy
Simplifying
Expressions
Solving
Equations
Graphs &
Graphing
Expand &
Condense
Logs
Word
Problems
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
DJ
Simplifying Expressions for
100
Rationalize the denominator:
3
2
Check Your Answer
Simplifying Expressions for
100
Answer:
3 2
2
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Simplifying Expressions for
200
Simplify:
 81bz 


 45a 
0
Check Your Answer
Simplifying Expressions for
200
Answer:
1
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Simplifying Expressions for
300
Simplify: Answer must have only
positive exponents.
2 2
3 4
2ab  3b 
Check Your Answer
Simplifying Expressions for
300
Answer:
8
81b
2
4a
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Simplifying Expressions for
400
Simplify:
  24 xy
 3 2
8
x
z

3



2
Check Your Answer
Simplifying Expressions for
400
Answer:
4
z
8 6
9x y
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Simplifying Expressions for
500
Simplify and rationalize the denominator:
a
3
2
6 2
ay
Check Your Answer
Simplifying Expressions for
500
Answer:
3
y
y
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Solving Equations for 100
Solve for x:
x 2
3
Check Your Answer
Solving Equations for 100
Answer:
x 2
3
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Solving Equations for 200
Solve for x:
( x  2)  200  43
5
Check Your Answer
Solving Equations for 200
Answer:
1
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Solving Equations for 300
Solve for x and simplify your answer:
4( x  3)  81  113
2
Check Your Answer
Solving Equations for 300
Answer:
x  2 2 3
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Solving Equations for 400
Solve for x:
2
3
( x  1)  7
Check Your Answer
Solving Equations for 400
Answer:
x  7 7 1
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Solving Equations for 500
Solve for x:
5
2
3  2(2 x  3)  4
Check Your Answer
Solving Equations for 500
Answer:
5
4 3
2
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Graphs & Graphing for 100
For the equation y  a  b ,
what does the a
represent?
x
Check Your Answer
Graphs & Graphing for 100
Answer: The y-intercept or
the initial amount
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Graphs & Graphing for 200
Question: What is the horizontal
asymptote for the equation
below?
y  3 4
x 2
5
Check Your Answer
Graphs & Graphing for 200
Answer:
y = -5
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Graphs & Graphing for 300
Question: Is the following graph a
growth or decay graph?
x
y  23
Check Your Answer
Graphs & Graphing for 300
Answer: Decay
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Graphs & Graphing for 400
Question: What are the intervals
of increasing and decreasing
in the following function?
x
4 2
y    
3 3
Check Your Answer
Graphs & Graphing for 400
Answer:
Increasing:(-∞,∞)
Decreasing: never
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Graphs & Graphing for 500
Question: What is the x – intercept for the
following function? Please round to the
nearest 3 decimal places.
y  3e
x 1
2
Check Your Answer
Graphs & Graphing for 500
Answer:
(0.595, 0)
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Expand & Condense Logs for
100
Expand:
log 3 (3x)
Check Your Answer
Expand & Condense Logs for
100
Answer:
log 3 3  log 3 x
or
1 log 3 x
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Expand & Condense Logs for
200
Condense to one logarithm:
log 5 6  2 log 5 x
Check Your Answer
Expand & Condense Logs for
200
Answer:
6
log 5 2
x
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Expand & Condense Logs for
300
Expand:
3
2y
log 2 2
x
Check Your Answer
Expand & Condense Logs for
300
Answer:
log 2 2  3 log 2 y  2 log 2 x
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Expand & Condense Logs for
400
Condense:
log( 5  x)  3 log x  2 log( x  1)
Check Your Answer
Expand & Condense Logs for
400
Answer:
(5  x) x
log
2
( x  1)
3
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Expand & Condense Logs for
500
Expand:
( x  3)
ln
2
3y
2
Check Your Answer
Expand & Condense Logs for
500
Answer:
2 ln( x  3)  ln 3  2 ln y
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Word Problems for 100
Question: Find the radius of a sphere
with a volume of 994 cubic
centimeters. Round to 3 decimals.
4
3
V    r
3
Check Your Answer
Word Problems for 100
Answer:
6.191cm3
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Word Problems for 200
Question: The velocity of a free falling object is given by
V  2 gh where V is velocity (in meters per second), g is
acceleration due to gravity (in meters per second), and
h is the distance (in meters) the object has fallen. The
value of g depends on which body/planet is attracting
the object. If an object hits the surface with a velocity
of 30 meters per second, from what height was it
2
dropped if you were on Mars where g  3.72 m / s .
Check Your Answer
Word Problems for 200
Answer:
120.968 meters
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Word Problems for 300
Question: The velocity of a free falling object is
given by V  19.62h , where V is velocity (in
meters per second) and h is the distance (in
meters) the object has fallen. If an object hit the
ground with a velocity of 55 meters per second,
from what height was it dropped? Round to 3
decimal places.
Check Your Answer
Word Problems for 300
Answer:
154.179 meters
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Word Problems for 400
Question: The lateral surface area S of a cone is
given by S    r r 2  h2 where r is the radius
and h is the height of the cone. The surface
2
B



r
area of the base B of the cone is given by
where r is the radius of the cone. The total
surface area of a cone with a radius of 9 inches
is 216 square inches. What is the height of the
cone?
Check Your Answer
Word Problems for 400
Answer:
12 inches
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Word Problems for 500
Question: The half-life of radium-226 is
about 1600 years. The amount A (in
grams) of radioactive radium-226 that
remains in a sample after t years is
given by A  N (.5) . If you start with 253
grams of radium-226, how long will it
take for the radium-226 to decay by
70%. Round to three decimals.
t
1600
Check Your Answer
Word Problems for 500
Answer:
2779.145 years
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