Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What is the area of a square with sides of length 9.8 cm?
a. | 9.8 cm2 | c. | 39.2 cm2 | b. | 19.6 cm2 | d. | 96.04
cm2 |
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2.
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Which description about the number 225 is correct?
a. | perfect cube | b. | perfect square | c. | both a perfect cube
and a perfect square | d. | neither a perfect cube nor a perfect
square |
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3.
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Which description about the number 3375 is correct?
a. | a perfect cube | b. | a perfect square | c. | both a perfect cube
and a perfect square | d. | neither a perfect cube nor a perfect
square |
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4.
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What is  ?
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5.
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What is the next number in the sequence 23, 22,
21, 20, …?
a. | –1 | c. |  | b. | 2–2 | d. | 1 |
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6.
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Which expression represents a negative number?
a. | 2–3 | c. | –30 | b. | (–3)2 | d. | (–3)–1 |
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7.
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Determine the value of (–6)0 – 80.
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8.
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Evaluate 21 + 2–4.
a. |  | c. | –6 | b. |  | d. | 10 |
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9.
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Evaluate  .
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10.
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What is the value of  ?
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11.
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Jean invests $200 in a fund. The investment doubles in value each year. The
formula A = 200(2)n models the total value of the investment, A, in
dollars, after n years. What is the value of her investment after 4 years?
a. | $3200 | c. | $800 | b. | $1600 | d. | $200 |
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12.
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For what value of x do 4 x, 2 x, and
 have the same value? a. | x = 0 | c. | x = 2 | b. | x =  | d. | x = 4 |
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13.
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Express  as an equivalent mixed radical.
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14.
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Evaluate  . a. | 3 | c. |  | b. |  | d. | 9 |
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15.
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Which expression has the smallest value?
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16.
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What is the value of x in the equation  ? a. | 2 | c. |  | b. | 1 | d. |  |
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17.
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Express  as a power with a rational exponent.
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18.
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Which of the following is equivalent to  ?
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19.
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Order these irrational numbers from least to greatest:  ,  ,
 ,  . a. |  ,  ,  ,  | c. |  ,  ,
 ,  | b. |  ,  ,  ,  | d. |  ,  ,
 ,  |
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20.
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Express  as an equivalent radical.
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Short Answer
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1.
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State whether each number is a perfect square or a perfect cube. Show your
work.
a) 1521
b) 4096
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2.
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Write and evaluate an expression using exponents for the total volume of each
pair of cubes.
a) Cube A has edges 9.1 m long and cube B has edges 1.5 m long.
b)
Cube C has edges 1.9 m long and cube D has edges 3.7 m long.
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3.
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Order the following numbers from greatest to least. Describe the method you
used.  ,  ,  , 
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4.
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What is  expressed as a radical with positive exponents?
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5.
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Is the statement  always, sometimes, or never true? Explain your
reasoning.
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Problem
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1.
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An open-topped cubical box has a volume of 729 cm 3. Determine the
total surface area of the five faces of the box. 
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2.
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Develop three questions that have a solution of p6. For each
question, choose a different exponent law and apply it.
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3.
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The first five numbers in a pattern are 1, 2, 9, 64, and 625.
a)
Describe the pattern. Show how the first five terms were calculated.
b) Using a calculator,
determine the next three terms.
c) Determine the tenth term.
d) Write an
expression for the nth term in the pattern.
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4.
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The first three terms of a pattern are 0, 2, and 15. These terms were determined
using the following expressions:
11 – 00(1) = 0
22
– 11(2) = 2
33 – 22(3) = 15
a) Continue
the pattern and determine the next three terms.
b) Write an expression for the nth
term in the pattern.
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5.
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The height and the base of a triangle each measure  units. What is the area of
the triangle?
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