Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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The common difference in the arithmetic sequence  ,  ,  ,
 ,  , . . . is A |  | C | 9 | B | 3 | D |  |
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2.
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The sum of the series (–5) + (–7) + (–9) +  + (–19)
is
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3.
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For the arithmetic series (107) + (130) + (153) +  + (981), the values of
 , d, and n are A |  , d = 23, n = 39 | C |  =
–107, d = 23, n = 38 | B |  = 107, d = –23, n
= 39 | D |  =
–107, d = –23, n = 38 |
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4.
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In the formula for the general term of a geometric sequence  , the common
ratio is A |  | C | 4 | B | 5 | D |  |
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5.
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What is the value of S9 for the series 8 – 24 + 72
– 216 +  ? A | 39 366 | C | 52 491 | B | –13 122 | D | 39 368 |
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6.
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Determine the sum of the infinite geometric series 11 +  +  +
 +...
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7.
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What are the three other angles in standard position that have a reference angle
of 54°?
A | 99°, 144°, 234° | C | 144°, 234°, 324° | B | 108°, 162°, 216° | D | 126°, 234°, 306° |
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8.
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Solve to the nearest tenth of a unit for the unknown side in the ratio  .
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9.
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While flying, a helicopter pilot spots a water tower that is 7.4 km to the
north. At the same time, he sees a monument that is 8.5 km to the south. The tower and the
monument are separated by a distance of 11.4 km along the flat ground. What is the angle made by the
water tower, helicopter, and monument? 
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10.
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What are the x-intercepts of  ? A | 6 and 9 | C | –6 and 9 | B | –6 and –9 | D | 6 and –9 |
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11.
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What is the vertex of  ? A | (5, 4) | C | (–5, 4) | B | (–4, 5) | D | (7, –4) |
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12.
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What is  written in standard form?
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13.
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A rectangle has dimensions  and  , where x is in
centimetres. If the area of the rectangle is 72 cm 2, what is the value of x, to the
nearest tenth of a centimetre? 
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14.
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Solve  . A | 1 +  and 1 -  | C |  | B | –1 +  and –1 -  | D |  |
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15.
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A rectangle with an area of  is x centimetres wide and
( x + 8) centimetres long. To the nearest tenth of a centimetre, the width and length
are A | 50.0 cm and 50.0 cm | C | 46.2 cm and 54.2 cm | B | –46.2 cm and –54.2
cm | D | –14.0 cm and 114.0
cm |
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16.
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The table shows the coordinates of the curve of a parabolic arch at the entrance
to a park, where x is the horizontal distance from one side of the arch and h is the
height of the arch above ground, both in metres. x | h | 0.25 | 7.75 | 0.50 | 9.00 | 0.75 | 9.75 | 1.00 | 10.00 | 1.25 | 9.75 | 1.50 | 9.00 | 1.75 | 7.75 | | |
The quadratic equation that models the data
is
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17.
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18.
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An equilateral triangle has an area of 6.93 cm 2. What is the side
length of the triangle, to the nearest tenth of a centimetre?  A | 2.3 cm | C | 1.9 cm | B | 3.5 cm | D | 4.0 cm |
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19.
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Solve  .
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20.
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Simplify  .
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21.
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What is the simplified version of the rational expression  ?
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22.
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When fully simplified,  is equal to
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23.
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Solve the rational equation  . Identify all non-permissible
values.
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24.
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Solve the rational equation  . A | x = 10 | C | x = –10 | B | x = 4 and –1 | D | x = –10 and
1 |
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25.
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Solve  . A | x = –3 and x = –2 and x = 8 | C | x = 4 and
x = –8 and x = –8 | B | x = –4 and x =
8 | D | x =  |
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26.
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Determine the term of a $26 000 investment with an
interest rate of 2.95%, compounded monthly, if the future value is $100 000.
A | 44.44 years | B | 45.72 years | C | 43.20
years | D | 40.86 years |
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27.
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Determine the regular annual payment required to
have $5000 at the end of 12 years if the investment earns 3% interest, compounded
annually.
A | $320.08 | B | $333.82 | C | $348.61 | D | $352.31 |
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28.
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Regular semi-annual payments of $400 are deposited
into an account paying 6.15% interest, compounded semi-annually. If the final value of the account is
$46 000, how long was the money invested?
A | 26.84 years | B | 25.33 years | C | 24.96
years | D | 24.17 years |
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29.
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This portfolio was started 12 years ago. What is
the portfolio’s current rate of return?
• A 12-year $8000 GIC that earns 3.65%,
compounded quarterly
• Monthly deposits of $325 into an account earning 2.75%, compounded
monthly
A | 31.94% | B | 39.21% | C | 25.92% | D | 23.62% |
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30.
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The graph of  is
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A sports store makes a profit of $50 on every pair of cross-country skis sold
and $125 on every set of snowshoes sold. The manager’s goal is to have a profit of at least
$700 a day from the sales of these two items.
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31.
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Which graph represents the combinations of ski and snowshoe sales that will meet
or exceed this daily sales goal?
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32.
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Which number line represents the solution set to the inequality  ?
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33.
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Which graph represents the solution to the inequality  ?
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34.
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Which graph represents the solution to the inequality  ?
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A rock is thrown upward with an initial velocity of 14 m/s. The motion of the
rock can be modelled by the equation  .
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35.
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For how long is the rock’s altitude greater than 6 m? Answer to the
nearest hundredth of a second.
A | 2.86 s | C | 2.33 s | B | 1.81 s | D | 0.53 s |
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Short Answer
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1.
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A bouncy ball bounces to  its height when it is dropped on a hard
surface. Suppose the ball is dropped from 20 m. a) What height will the ball bounce back up
to after the sixth bounce? b) What is the total distance the ball travels if it bounces
indefinitely?
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2.
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A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the
base of the rectangle.
a) Write an exact expression for the base and the height of the
rectangle.
b) Use your expressions to find the exact area of the rectangle.
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3.
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State the vertex of the function  .
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4.
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Solve the quadratic function  by completing the square. Round roots
to the nearest hundredth, if necessary.
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5.
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Simplify each expression.
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Simplify each expression and state any non-permissible values.
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6.
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7.
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8.
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Arrange the investments in the order of least to
greatest return and give the return.
A. $15 000 invested for 8 years at a simple interest
rate of 4.7%
B. $20 000 invested for 6 years at a compound interest rate of 5%
C.
$10 000 invested for 15 years at a compound interest rate of 3%
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9.
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Which of the given ordered pairs belong to the solution to the inequality  ?
Use a graph of the inequality to show your reasoning in each case.   .
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10.
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Graph the quadratic inequality  . 
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