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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Given the graph of f( x) shown below, what are the coordinates of
point A if the transformed graph is represented by  ? 
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3.
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The function  represents a transformation that can best be described as
A | a reflection in the x-axis | C | a reflection in the
y-axis | B | a reflection in the x-axis and the y-axis | D | a reflection in the line y =
x |
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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 | 9 units to the left and 4 units down | C | 9 units to the right and 4 units
up | B | 4 units to the left and 9 units down | D | 4 units to the right and 9 units
up |
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6.
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Given the function  with a domain of  and a range of  ,
which of the following best describes the vertical and horizontal translations with respect to the
graph of  ? A | 5 units to the left and 8 units up | C | 8 units to the left and 5 units
up | B | 8 units to the left and 5 units down | D | 5 units to the left and 8 units
down |
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7.
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Which of the graphs shown below represents the base function  (in black)
and the stretched function g( x) =  (in red)?
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8.
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Which graph shows the solution to the radical equation  ?
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9.
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When solving the equation  , which values must be checked for
extraneous roots? A | –4 and 7 | C | 8 and 6 | B | 7 and –7 | D | –4 and
–7 |
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10.
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Which set of values for x should be tested to determine the possible
zeros of  ? A | ±5, ±7, and ±35 | C | 1, 5, 7, 12, and
35 | B | ±1, ±5, ±7, and ±35 | D | 1, 5, 7, and 35 |
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11.
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Which of the following angles, in degrees, is coterminal with, but not equal to,
  radians?
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12.
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Determine the measure of the angle in standard position shown on the graph
below. Round your answer to the nearest tenth of a degree. A | 161.6° | C | 71.6° | B | 341.6° | D | 251.6° |
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13.
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John cuts a slice from a circular ice cream cake with a diameter of 24 cm. His
slice is in the shape of a sector with an arc length of 7 cm. What is the measure of the central
angle of the slice, in radians? Round your answer to two decimal places, if necessary.
A | 1.71 rad | C | 0.29 rad | B | 3.43 rad | D | 0.58 rad |
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14.
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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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15.
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The point P(0.391, 0.921) is the point of intersection of a unit circle and the
terminal arm of an angle q in standard position. What is the equation of
the line passing through the centre of the circle and the point P? Round the slope to two decimal
places.
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16.
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Which function, where x is in radians, is represented by the graph shown
below? 
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17.
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The range (in radians) of the graph of  is
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18.
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What is the amplitude of the sinusoidal function  ? A |  | C | –5 | B | –8 | D | 7 |
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19.
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Which function represents the graph shown, where x is in radians? 
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20.
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 is equivalent to
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21.
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 can be rewritten as
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22.
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What is the solution to the equation  over the domain  ? A | 60° and 240° | C | no solution | B | 120°, 180°, and 240° | D | 120° |
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23.
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What is the general solution, in radians, to the equation  ? A |  where  | C |  where  | B | no solution | D |  where  |
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24.
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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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25.
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Another way of writing  is
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26.
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If  ,  , and  , an algebraic expression
in terms of s, v, and z for  is A | v - 2s + 2z | C | v - 2(s - z) | B | v - 2(s + z) | D | v - 2s
+ z |
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27.
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Solve  . A | x = 6 | C | x =  | B | x =  | D | x =
729 |
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28.
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Given the functions  and  , determine an equation for the combined
function  .
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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 range of the composite
function  ?
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30.
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The number of different ways that 9 bikes can be locked in a bike rack is
A | 3 628 800 | C | 40 320 | B | 20 160 | D | 362 880 |
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31.
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Jenni and Hari go to a local Chinese restaurant for dim sum. If there are 20
items on the menu, and Jenni orders 7 items and Hari orders 11 items, which expression represents the
total number of choices between them?
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32.
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Determine the coefficient, a, for the term  of the binomial expansion
of  .
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33.
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Determine the 5th term in the expansion of  .
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34.
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Prom’s friend gives him a row of Pascal’s triangle and asks which
row it comes from. Prom adds the numbers and obtains a sum of 65 536. Which row do the numbers come
from?
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35.
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How many terms are there in the expansion of  ?
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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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Solve the equation  algebraically.
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3.
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Solve by graphing using technology. Round the root(s) to one decimal place.
a) x4 + x3 + x2 + x =
1
b) 0.1x4 = x3 + x2
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4.
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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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5.
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Michael has invested some money with a financial institution. The scatter plot
shows how his money has grown over time.  a) Do the data show an
exponential trend? Explain your reasoning. b) Estimate values of a and b to
develop a model for the information of the form  , for t in years. c) Use
your model to predict the expected value of Michael’s investment in 30 years. d) How
does the result in part c) illustrate the power of exponential growth?
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Problem
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1.
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The volume of a drinking cup can be approximated by the formula  , where the
top and bottom of the cup are circular and h is the height. If the cup has a bottom diameter
of 6 cm, a height of 10 cm, and sides that slope outward at an angle of 0.09, determine the
cup’s volume.
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2.
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A windmill has blades that are 20 m in length, and the centre of their circular
motion is a point 23 m above the ground. The blades have a frequency of 4 revolutions per minute when
in operation.
a) Use a sinusoidal function to model the height above the ground of the tip
of one blade as a function of time.
b) Graph the function over three complete
cycles.
c) How far above the ground is the tip of the blade after 10 s?
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3.
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Express  in terms of cosines and sines of x, y,
and z.
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4.
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Solve  .
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5.
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Use the graph of the combined function  to determine an
approximate solution to the inequality  . 
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