Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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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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2.
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Compared to the graph of the base function  , the graph of the function
 is translated A | 4 units to the right and 8 units up | C | 8 units to the left and 4 units
down | B | 4 units to the left and 8 units down | D | 8 units to the right and 4 units
up |
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3.
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Given the graph of f( x) shown below, what are the coordinates of
point A ¢ if the equation of the transformed function is  ? 
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4.
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Which graph represents an even-degree polynomial function with a
y-intercept of 9?
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5.
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When  is divided by  , the remainder is
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6.
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The fully factored form of  is
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7.
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The coordinates of the point that lies at the intersection of the terminal arm
and the unit circle at an angle of 110° are
A | (0.94, –0.34) | C | (–0.34, 0.94) | B | (–0.34, –2.75) | D | (–2.75,
0.94) |
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8.
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If the angle q is –5000° in standard
position, it can be described as having made
A |  rotations | C | 
rotations | B |  rotations | D |  rotations |
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9.
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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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10.
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Determine the point in quadrant II where the line represented by  intersects the
unit circle. A | (0.95, –0.32) | C | (–0.35, 0.94) | B | (–0.32, 0.95) | D | (–0.32,
0.94) |
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11.
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Giai got an answer of 3.86 when she was calculating the value of a trigonometric
function. Assuming Giai did her calculation correctly, which of the following was she
calculating?
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12.
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Which graph represents the function y =  sin (  q), where q is in radians?
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13.
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Which graph represents the function y =  cos(  x),
where x is in degrees?
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14.
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Given the trigonometric function  , find the value of the
y-coordinate of the point with x-coordinate –1200°.
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15.
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What are the solutions for   = 0 in the interval  ? A |     | C | x = 90° and 270°  | B | x = 30° and 210°  | D | x = 60°
and 240° and 45°
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16.
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What are the solutions for   = 0 in the interval  ? A | x = 90° and 270°  | C | x = 60° and 240° and 45° | B |     | D | x =
30° and 210°  |
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17.
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What is the general solution, in degress, to the equation  ?
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18.
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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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19.
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Solve for x. 
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20.
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Another way of writing  is
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21.
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Another way of writing  is
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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 | 4 units to the left | C | 4 units up | B | 4 units down | D | 4 units to the
right |
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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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A graduate student determines that the relationship between the length,
s, in metres, of the skull and the body mass, m, in kilograms, of a particular species
can be expressed using the equation  . Determine the body mass of an animal with a skull size of
0.56 m. Round your answer to the nearest kilogram. A | 547 kg | C | 343 kg | B | 376 kg | D | 313 kg |
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25.
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What is the equation for the vertical asymptote of the graph of the function
shown? 
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26.
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Which rational function has the following characteristics? • a vertical
asymptote with equation  • a horizontal asymptote with equation  • a point of discontinuity at 
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27.
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Solve the equation  . A | x =  | C | x =  | B | x = 3 | D | x = 4 |
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28.
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What are the x-intercepts of the graph of  ?
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For the following question(s), assume that x is in radians, if
applicable.
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29.
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Given the functions  and  , what is the value of  ?
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30.
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Given the functions  and  , what is the simplified form of  ?
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31.
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If  and  , what are the restrictions on the domain
for the combined function  ?
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32.
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If  and  , what is the simplified combined function
 ?
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33.
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Evaluate the expression  . A | 726 485 760 | C | 2002 | B | 240 240 | D | 126 |
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34.
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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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35.
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Which of the following has 30 terms in its binomial expansion?
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Short Answer
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1.
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For each of the following, describe the combination of transformations that must
be applied to the graph of  (shown in blue) to obtain the graph of g( x)
(shown in red). a)  b)  c) 
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2.
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Factor fully.
a) x3 + 6x2 +
11x + 6
b) 4x3 – 11x2 –
3x
c) x4 – 81
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3.
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Angles A and B are located in the first quadrant. If  and  , determine the exact value of sec A + sec B.
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4.
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If  and  , determine the values of m and
n.
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5.
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Consider the function  . a) Determine the key features
of the function: i) domain and
range ii) intercepts
iii) equations of any asymptotes b) Sketch the graph of the function. 
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Problem
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1.
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Two groups of students are conducting a lab to determine the relationship
between the period, p, in seconds, of a pendulum and the length, l, in metres, of the
string. The curves of best fit from the experiment are shown on the graph.  a)
When asked the type of function that could be used to model their findings, both groups argue that a
radical function can be used. Do you agree with each group? b) How do these graphs differ
from the graph of  ? c) Write a function to approximate the graph for
each group. d) What may have caused the differences in the data between the two groups?
Justify your answer in terms of transformations.
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2.
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Sketch the graph of  for  .
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3.
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Prove the identity  .
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4.
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The time, t, in hours, that it takes Alistair to jog 5 km is inversely
proportional to his average speed, v, in kilometres per hour.
a) Write a function
to represent the time as a function of the speed.
b) Sketch the graph of this function.
c) If Alistair jogs at 4.5 km/h, how long does it take him to complete a 5-km run, to the
nearest minute?
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5.
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The population, P, of a small town is modelled by the function  ,
where t is time, in years, since the start of 1990. a) Is the population increasing
or decreasing? Justify your answer. b) The town will need its own transit system if the
population exceeds 50 000. Will the town’s population ever exceed 50 000? Explain.
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