Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Compared to the graph of the base function  , the graph of the
function  is translated A | 9 units to the left | C | 9 units down | B | 9 units to the right | D | 9 units up |
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2.
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Compared to the graph of the base function  , the graph of the
function  is translated A | 5 units to the right | C | 5 units down | B | 5 units up | D | 5 units to the
left |
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3.
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When b > 0, the function  has what relationship to the base
function  ? A | f(x) is stretched vertically by a factor of |b| and reflected in the
x-axis | B | f(x) is stretched vertically by a factor of |b| | C | f(x) is
stretched horizontally by a factor of 1/|b| and reflected in the y-axis | D | f(x) is
stretched horizontally by a factor of 1/|b| |
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4.
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Which of the graphs shown below represents the base function  and the
stretched function g( x) = (  x) 2?
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5.
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Compared to the graph of the base function  , the graph of the
function  is translated A | 8 units to the left | C | 8 units to the right | B | 8 units up | D | 8 units down |
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6.
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When the graph of  is vertically stretched by a factor of 3, the point (9,
–10) will be translated to the point A | (–10, 9) | B | (3, –30) | C | (–30,
9) | D | (9, –30) |
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7.
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Which radical equation can be solved using the graph shown below? 
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8.
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If  is divided by  , then the restriction on x
is
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9.
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Determine the value of k so that  is a factor of  . A | k = –1 | C | k = 14 | B | k = –14 | D | k = 1 |
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10.
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One root of the equation  is
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11.
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If the angle q is 1600° in standard position, in
which quadrant does it terminate?
A | quadrant III | C | quadrant II | B | quadrant IV | D | quadrant I |
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12.
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The range (in radians) of the graph of  is
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13.
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Which graph represents the sinusoidal function  ?
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14.
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Give an equation for a transformed sine function with an amplitude of  , a
period of  , a phase shift of  rad to the right, and a vertical translation of 9 units
down.
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15.
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Which expression is equivalent to  ?
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16.
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 is equivalent to
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17.
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A colony of ants has an initial population of 750 and triples every day. Which
function can be used to model the ant population, p, after t days?
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18.
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An investment of $150 is placed into an account that earns interest, compounded
annually, at a rate of 5% for 12 years. The amount, A, in the account can be modelled by the
function  , where t is the time, in years. What is the domain of this function?
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19.
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A rumour is being spread in a community that the mayor is going to retire before
the next election. Initially, 6 people were told the rumour and each of these people told 6 others
the following day. Each of the 6 people told by the initial people told 6 others the day after they
were told. If this process keeps up, how many people will be told the rumour on the eighth
day?
A | 1 679 616 people | C | 10 077 696 people | B | 279 936 people | D | 48 people |
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20.
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To the nearest year, how long would an investment need to be left in the bank at
5%, compounded annually, for the investment to triple?
A | 15 years | C | 28 years | B | 26 years | D | 23 years |
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21.
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Compared to the graph of the base function  , the graph of the
function  is translated A | 4 units to the left | C | 4 units up | B | 4 units down | D | 4 units to the
right |
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22.
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Compared to the graph of the base function  , the graph of the function
 is translated A | 6 units to the right and 7 units up | C | 7 units to the right and 6 units
up | B | 7 units to the left and 6 units down | D | 6 units to the left and 7 units
down |
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23.
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Solve  . Round your answer to two decimal places.
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24.
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What is the equation for the vertical asymptote of the graph of the function
shown? 
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25.
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What are the x-intercepts of the graph of  ?
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26.
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Given the functions  and  , determine the equation for the combined
function  .
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27.
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Given the functions  and  , what is the domain of the combined
function  ?
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28.
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Given the functions  and  , determine the domain of the combined
function  .
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29.
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Solve for the variable:  = 252 A | 15 | C | 6 | B |  | D |  |
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30.
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An orchestra has 2 violinists, 3 cellists, and 4 harpists. Assume that the
players of each instrument have to sit together, but they can sit in any position in their own group.
In how many ways can the conductor seat the members of the orchestra in a line?
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31.
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Evaluate the expression  . A | 2184 | C | 794 976 | B | 87 178 291 200 | D | 239 500 800 |
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32.
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Rachael has a digital music player that holds 800 songs. She has 1500 songs in
her music library. She decides that her 50 favourite songs must be on the player. Which expression
can be used to calculate the number of ways can she load songs on to the MP3 player so that it is
full?
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33.
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For a mock United Nations, 6 boys and 7 girls are to be chosen. If there are 12
boys and 9 girls to choose from, how many groups are possible?
A | 846 720 | C | 960 | B | 33 264 | D | 120 708 403 200 |
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34.
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Determine the coefficient, a, for the term  of the binomial expansion
of  .
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35.
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A scout troop is arranged in a circle for an opening ceremony. If there are 9
scouts, in how many unique ways can they stand around the circle?
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Short Answer
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1.
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A student designs a special container as part of an egg drop experiment. She
believes that the container can withstand a fall as long as the speed of the container does not
exceed 80 ft/s. She uses the equation  to model the velocity, v, in feet per second, as a
function of constant acceleration, a, in feet per second squared and the drop distance,
d, in feet. Assuming the student’s specifications are correct, will the egg break if the
student drops the egg from shoulder height (5 ft) off a building 80 ft high? What is the maximum
height the egg can be dropped from? (Note: The acceleration due to gravity is 32
ft/s 2.)
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2.
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A child swings on a playground swing set. If the length of the swing’s
chain is 3 m and the child swings through an angle of  , what is the exact arc length through
which the child travels?
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3.
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For the function  , a) describe the transformations of the function
when compared to the function  b) sketch the graph of the given function and
 on the same set of axes c) state the domain, the range, and the equation of the
asymptote
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4.
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Write the equation for the function that results from each transformation or set
of transformations applied to the base function  . a) reflect in the
y-axis b) shift 3 units to the right c) shift 1 unit down and 4 units to
the left d) reflect in the x-axis and shift 2 units down
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5.
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Given the functions  and  , determine a simplified equation for  .
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Problem
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1.
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Two billiard balls collide and then separate from one another at the same,
constant speed. Assume the billiard table is frictionless. The angle between the balls is 1.25
radians. After 2 s, the distance between the balls is 1 m. How fast are the balls moving, to the
nearest hundredth of a metre per second?
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2.
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Solve the equation  .
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3.
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Write an equation for the graph of the rational function shown. Explain your
reasoning. 
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4.
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A ski club charters a bus for a ski trip at a cost of $480. In an attempt to
lower the bus fare per skier, the club invites non-members to go along. After five non-members join
the trip, the fare per skier decreases by $4.80. How many club members are going on the trip?
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5.
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Expand and simplify:  .
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