Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which of these numbers is rational?  ,  ,  ,
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2.
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Determine which of these numbers is the least.  ,  ,  ,
 , 
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3.
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For which number will the fifth root be irrational?
625, 7776, 16 807,
–32
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4.
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Write  in simplest form.
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5.
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Order these numbers from greatest to least:  ,  ,  ,
 ,  a. |  ,  ,  ,  ,  | c. |  ,  ,  ,  ,  | b. |  ,  ,  ,  ,  | d. |  ,
 ,  ,  ,  |
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6.
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Evaluate  without using a calculator. a. | 8 | b. | 4 | c. | –4 | d. |  |
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7.
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Write  as a power.
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8.
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Evaluate  a. | 0.4804 | b. | 0.1012 | c. | 0.0256 | d. | 0.010
24 |
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9.
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Biologists use the formula  to estimate the brain mass, b
kilograms, of a mammal with body mass m kilograms. Estimate the brain mass of a mammal with
body mass 276 kg. a. | About 4.24 kg | c. | About 9.13 kg | b. | About 0.42 kg | d. | About 253.92 kg |
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10.
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Evaluate 
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11.
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Evaluate  without using a calculator.
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12.
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Paleontologists use measurements from fossilized dinosaur tracks and the
formula  to estimate the speed at which a dinosaur travelled. In the formula, v is
the speed in metres per second, s is the distance between successive footprints of the same
foot, and f is the foot length in metres. Estimate the speed of the dinosaur when the
distance between footprints, s, is 1 m and the foot length, f, is 0.65 m. a. | About 0.09 m/s | c. | About 0.43 m/s | b. | About 0.07 m/s | d. | About 0.26 m/s |
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13.
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Evaluate  without using a calculator.
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14.
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How many times as great as  is  ?
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15.
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Simplify  by writing as a single power.
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16.
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Evaluate 
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17.
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Simplify 
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18.
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Simplify 
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19.
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Simplify 
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20.
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Short Answer
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21.
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Which of these numbers are rational numbers, but not integers?  ,
–4,  ,  , 2.4,  , 0,  , 
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22.
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Write  in simplest form.
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23.
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Evaluate  .
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24.
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A sphere has volume 1417 cm  . What is the radius of the sphere to the
nearest tenth of a centimetre?
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25.
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A sphere has volume 2245 cm  . What is the surface area of the sphere
to the nearest tenth of a square centimetre?
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Problem
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26.
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Determine whether the perimeter of a square with area 28 m  is a rational
number or an irrational number.
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27.
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Another formula for the approximate surface area, SA square metres, of a
person’s body is  , where h is the person’s height in
centimetres, and m is the person’s mass in kilograms. a) Calculate the surface area of a newborn
with height  cm and mass 7.3 kg. Write the answer as a decimal to
the nearest hundredth of a square centimetre. b)
Calculate the surface area of a person with height 170 cm and mass 66
kg. Write the answer as a decimal to
the nearest hundredth of a square centimetre.
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28.
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Here is Tanisha’s solution for evaluating a power:    Identify the errors Tanisha made. Write a correct solution.
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29.
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For a spherical space station, this formula is used to estimate the number of
rotations per minute, N, required so that the force inside the station simulates the gravity
on Earth:  , where r is the radius of the space station, in
metres Suppose the radius of the space station is 12.7 m. Calculate the number of rotations
per minute required to simulate the gravity on Earth. Write the answer to the nearest
hundredth.
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30.
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A tree farmer used the formula  to estimate the volume, V cubic
metres, of a tree with height h metres and mean trunk diameter d metres. The height of
a tree is 20 times its mean trunk diameter, and its volume is 230 m  . What is the mean trunk
diameter of this tree to the nearest metre?
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