Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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When the value of a is less than –1, the function  has what relationship to the base function  ? A | f(x) is compressed vertically | B | f(x) is
reflected and compressed vertically | C | f(x) is stretched
vertically | D | f(x) is reflected and stretched
vertically |
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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 equation of the transformed function is  ? 
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3.
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Which point on the graph  does not exist on the graph of  ?
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4.
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Which graph shows the solution to the radical equation  ?
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5.
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What is the solution to the radical equation  ?
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6.
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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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7.
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Determine the equation of a circle with centre at the origin and radius
8.
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8.
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Which is a possible value of q, to the nearest
hundredth of a radian, when cos q =
–0.58?
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9.
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Which graph represents the function y =  sin (  q), where q is in radians?
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10.
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Which function is represented by the graph shown below, where x is in
degrees? A | y = sin( x) | C | y = cos( x) | B | y =
cos(x) | D | y
= sin(x) |
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11.
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Which graph represents the sinusoidal function  ?
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12.
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Solve  to three decimal places on the interval  . A | x = 0.340, x = 5.943 | C | x = 1.911, x =
1.231 | B | x = 1.231, x = 5.052 | D | x = 1.911, x =
4.373 |
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13.
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Which expression is equivalent to  ?
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14.
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Determine the exact value of  .
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15.
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Which expression is equivalent to  ?
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16.
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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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17.
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A bacteria colony initially has 1500 cells and doubles every week. Which
function can be used to model the population, p, of the colony after t days?
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18.
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Mohamed purchased a car for $16 000. It depreciates by 20% of its current value
every year. How much will the car be worth 8 years after it is purchased?
A | $80 000 | C | $2684.35 | B | $2000 | D | $68 797.07 |
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19.
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Another way of writing  is
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20.
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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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21.
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Which graph represents the function  ?
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22.
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Which graph represents the function  ?
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23.
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Which graph represents the function  ?
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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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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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26.
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Which function has a graph in the shape of a parabola?
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27.
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Solve the equation  . A | x =  | C | x =
–6 | B | x = –8 | D | x =  |
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28.
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Solve the equation  . A | x =  | C | x =  | B | x = 3 | D | x = 4 |
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29.
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Given the functions  and  , what is the domain of the combined
function  ?
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30.
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If  and  , what is the simplified combined
function  ?
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31.
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Solve for the variable:  A |  | C | 60 | B |  | D | 7 |
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32.
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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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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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The leadership committee at a high school has 4 grade 10 students, 2 grade 11
students, and 6 grade 12 students. This year, 12 grade 10, 8 grade 11, and 10 grade 12 students
applied for the committee. How many ways are there to select the committee?
A | 2 910 600 | C | 733 | B | 100 590 336 000 | D | 163 136 |
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Short Answer
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1.
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Solve by factoring.
a) x3 –
2x2 – 5x + 6 = 0
b) x3 –
3x2 – 4x + 12 = 0
c) x3 =
4x2
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2.
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Solve for x: 
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3.
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Graph the function  . Identify the domain, the range, and the equation of the
vertical asymptote.
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4.
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Given the functions  and  , determine a simplified equation for
 .
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5.
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Use the binomial theorem to expand  .
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Problem
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1.
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For the base function  , a reflection in the y-axis is
followed by a reflection in the x-axis. a) Discuss the effect of each reflection on
the base function. b) Is there a point that you expect to be invariant during these
reflections? If so, state its coordinates. c) Graph the function after each
reflection. d) Use your graph in part c) to verify your answer for part b). e)
Make a general statement regarding invariant points after reflections in the x-axis and the
y-axis.
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2.
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Sketch the graph of  for  .
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3.
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Ranier has been researching the share price, V, of a stock for t
weeks. The data are shown below. Week | Price
($) | 0 | 8.00 | 1 | 8.40 | 2 | 8.82 | 3 | 9.26 | 4 | 9.77 | 5 | 10.21 | | |
a) Make a scatter plot for the
data. b) Describe the shape of the curve. c) Determine an equation to model the
data. d) Use the equation to determine the value of the stock in 9 weeks. e)
Approximately how long will it take for the share price of the stock to exceed $20?
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4.
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Ingrid is docking a motorboat. She turns off the power and lets the boat coast
toward the dock. The distance, d, in metres, between the boat and the dock as a function of
time, t, in seconds, is given by  . a) What is the average velocity of the boat
during the time interval from when Ingrid turns the boat off to when it meets the dock? b)
Determine the velocity of the boat when Ingrid turns off the power, to one decimal place. c)
Determine the velocity of the boat when it meets the dock, to one decimal place. d)
Sketch the graph of the function. On the same set of axes, sketch the graph of the speed of
the boat in relation to the time.
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5.
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Write an equation for the graph of the rational function shown. Explain your
reasoning. 
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