Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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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
4 | D | x ¹  |
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2.
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The non-permissible value(s) for the expression  is (are) A | x ¹  and x ¹ –3 | C | x ¹  | B |  | D | there are no restrictions |
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3.
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What is  in simplest form? State any non-permissible values.
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4.
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What is the simplified version of the rational expression  ?
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5.
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When fully simplified, ignoring non-permissible values,  is equal to
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6.
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Express the product  in simplest form.
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7.
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Express the quotient  in simplest form.
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8.
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Simplify the rational expression  .
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9.
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When fully simplified, ignoring restrictions on the variable,  is equal
to
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10.
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Courtney and Kurtis are planning to travel 140 km in a car by travelling at
x kilometres per hour for the first half of the distance, and then increasing their speed by 5
km/h to finish the distance. Which is the correct simplified expression for the total time of the
trip?
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Short Answer
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1.
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Determine if the following functions are equivalent. a) 
and  b)  and 
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Simplify each expression and state any non-permissible values.
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2.
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Simplify each expression and state any non-permissible values.
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3.
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Problem
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1.
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A square sheet of cardboard 100 cm by 100 cm is to have corners of side length
x cut out. These cutouts will create flaps that can be folded up to form a box with no lid.
The length and width of the base of the box are given by the expression (100 – 2x), and
the height of the box is x, where x is in centimetres.
a) Express the volume
of the box as a function of x.
b) Express the surface area of the box as a function
of x.
c) What is a simplified expression for the ratio of the volume of the box to
its surface area? Identify any non-permissible values of x.
d) Find the value of the
ratio for the box for each value of x.
i) 10 cm
ii) 20 cm
iii)
30 cm
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2.
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In a triathlon, a contestant swims 5 km, cycles 30 km, and then runs 20 km. In
general, a contestant runs at an average speed of x, swims
at an average speed of  , and cycles at an average speed of 5 x, where
x is in kilometres per hour. a) Determine an expression for the total time taken to
complete the race. b) Cynthia can swim at 2 km/h. How long will it take her to complete the
race? c) If Shaitha can cycle at 40 km/h, how much longer will it take her to complete the
race, compared to Cynthia?
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