Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Express  in simplified form.
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2.
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Determine the value of the expression  when  and  .
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3.
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Simplify  .
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4.
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The volume, V, in cubic units, of a cylinder is given by  , where
r is the radius and h is the height, both in the same units. Find the exact radius of a
cylinder with a height of 64 cm and a volume of 576 p cm 3.
Express your answer in simplest form.
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5.
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Express  in simplest form.
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6.
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A |  | C | 95 | B |  | D | 31 |
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7.
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An equilateral triangle has an area of 43.3 cm 2. What is the height
of the triangle, to the nearest tenth of a centimetre?  A |  cm | C | 10.0 cm | B | 3.5
cm | D | 
cm |
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8.
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Solve  . A | x = –6 | C | x = 6 | B | x = 24 | D | x = 12 |
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9.
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Solve  .
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10.
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Solve  .
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11.
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The non-permissible value(s) for the rational expressions  is
(are) A | x ¹  , x ¹ - | C | x ¹
 | B | x ¹  | D | x ¹ 4 |
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12.
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The non-permissible value(s) for the expression  is (are) A | x ¹  | C | x ¹  and x ¹
–7 | B |  | D | there are no restrictions |
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13.
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What is  in simplest form? State any non-permissible values.
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14.
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When fully simplified, ignoring non-permissible values,  is equal to
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15.
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When fully simplified, ignoring non-permissible values,  is equal to
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16.
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Simplify the rational expression  .
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17.
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Express the product  in simplest form.
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18.
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When fully simplified, ignoring restrictions on the variable,  is equal to
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19.
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Simplify  . State any non-permissible values.
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20.
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What is the exact solution to the equation  
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Short Answer
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1.
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Without using a calculator, arrange the following in order from least to
greatest. a)  b) 
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2.
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Rationalize the denominator in each expression. Express each answer in simplest
form.
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Simplify each expression and state any non-permissible values.
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3.
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Simplify each expression and state any non-permissible values.
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4.
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Problem
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1.
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A company manufactures fence sections for residential use. The number, s,
of sections that can be produced per day is related to the number of hours, h, of labour
required by the function  . a) State the
domain and range for the function.
b) How many sections can be produced using 200 h of
labour in a day?
c) How many more sections would be
produced if the number of hours of labour increased to 400 h?
d) How many hours of labour
are needed per day if the company wants to maintain a production rate of at least 35 sections per
day?
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2.
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The time, t, in minutes, it takes a satellite h kilometres above
Earth to complete one orbit can be determined by the equation  . How high should a
satellite be placed above the equator so that it always appears to be above the same point on the
ground? Round your answer to the nearest hundred kilometres.
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3.
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Consider a cylinder of height h and radius r.  a)
Determine the ratio of the volume of the cylinder to its surface area. b) What restrictions
are there on r and h?
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4.
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A patrol boat took 2.5 h for a round trip 12 km upriver and 12 km back. The
speed of the current was 2 km/h. What was the speed of the boat in still water?
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