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 | 230 | C |  | B |  | D | 580 |
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7.
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An equilateral triangle has an area of 3.90 cm 2. What is the side
length of the triangle, to the nearest tenth of a centimetre?  A | 1.6 cm | C | 3.0 cm | B | 2.6 cm | D | 1.3 cm |
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8.
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An equilateral triangle has an area of 10.8 cm 2. What is the height
of the triangle, to the nearest tenth of a centimetre?  A |  cm | C |  cm | B | 5.0
cm | D | 2.2
cm |
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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 expression  is (are) A | x ¹  | C |  | B | x ¹  and x ¹
8 | D | there are no
restrictions |
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12.
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When fully simplified, ignoring non-permissible values,  is equal to
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13.
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Simplify the rational expression  . Express your answer with positive
exponents only.
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14.
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Express the quotient  in simplest form.
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15.
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When fully simplified,  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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When fully simplified, ignoring restrictions on the variable,  is equal
to
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18.
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Simplify  . State any non-permissible values.
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19.
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Solve the rational equation  . A | x = 17 and –3 | C | x =
–17 | B | x = 9 and –3 | D | x = –17 and 3 |
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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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Identify each number as a mixed radical or an entire radical, and then change it
to its other form.
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2.
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Write and simplify expressions for the perimeter
and area of the square.
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Determine if the function f(x) is the simplified form of g(x). If it is,
state the non-permissible values. If it is not, determine the
corrected simplified form, including the 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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The formula  represents the swing of a pendulum, where s is the
time, in seconds, to swing back and forth, and l is the length of the pendulum, in
feet. a) Solve the formula for l.b) What is the length of a pendulum that
makes one swing in 1.5 s?
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2.
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The speed, S, in metres per second, of sound near Earth’s surface
can be calculated using the formula  , where T is the surface temperature in degrees
Celsius. Suppose a racing team has designed a car that can travel 340 m/s, in hopes of breaking the
sound barrier. At what temperature will the speed of sound be 340 m/s?
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3.
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Resistors are components found on most circuit boards and in most electronic
devices. Since resistors do not come in every size, they have to be arranged in various ways to get
the needed resistance. When three resistors are in parallel, then the total resistance,  ,
can be calculated using the equation  , where each of the resistances is in ohms  . a)
Determine an expression for the total resistance,  . b) Determine an expression for
the total resistance if  . c) Determine an expression for the total
resistance if  .
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4.
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The area of a tennis court can be represented approximately by the function  ,
and its length can be represented by  , where x is a distance, in metres. a)
Write and simplify a function, w( x), to represent the width of a tennis
court. b) If x represent 5 m, what is the approximate width of the court?
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