Multiple Choice Identify the
choice that best completes the statement or answers the question.
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1.
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What is the volume of a cube with edges of length 9 m?
a. | 2187 m3 | c. | 81 m3 | b. | 486 m3 | d. | 729
m3 |
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2.
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Which description about the number 3375 is correct?
a. | a perfect cube | b. | a perfect square | c. | both a perfect cube
and a perfect square | d. | neither a perfect cube nor a perfect
square |
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3.
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Which expression represents the volume of a cube of edge length
5x?
a. | (5x)(5x)(5x) | c. | 6(5x)2 | b. | 5x + 5x +
5x | d. | 125x2 |
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4.
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Which power is equivalent to ?
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5.
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Melanie’s bedroom floor has a width equal to 3x + 6 and a length
equal to 4x – 7. What equation represents the area of the floor?
a. | A = 12x2 + 45x – 42 | c. | A =
12x2 – 45x – 42 | b. | A = 12x2 + 3x
– 42 | d. | A =
12x2 – 3x – 42 |
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6.
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Multiply and simplify (5x + 2)2.
a. | 25x2 + 20x + 10 | c. | 25x2 + 10x
+ 4 | b. | 25x2 + 20x + 4 | d. | 25x2 +
4 |
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7.
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The greatest common factor (GCF) for the set of terms 30x, 45x,
60x2, and 30x2 is
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8.
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The area of a classroom door is represented by the equation A =
36z2 + 3600z. When the expression is factored fully, the factors are the
dimensions of the door. What are the actual height and width of the door if z = 5 cm?
a. | 180 cm by 105 cm | c. | 160 cm by 120 cm | b. | 170 cm by 100 cm | d. | 150 cm by 110
cm |
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9.
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The area, in metres, of a rectangle is x2 – 10x
– 75. When the expression is factored fully, the factors are the dimensions of the rectangle.
Determine the actual dimensions, in metres, of the rectangle when x = 25.
a. | 10 m by 30 m | c. | 25 m by 35 m | b. | 20 m by 40 m | d. | 30 m by 45 m |
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10.
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What is the factored form of 72 + 27x + x2?
a. | (x + 12)(x + 6) | c. | (x + 3)(x +
24) | b. | (x + 9)(x + 8) | d. | (x + 2)(x +
3) |
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11.
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Which expression is an example of a difference of squares?
a. | x2 – 21 | c. | 9x –
64 | b. | 4x + 16 | d. | 25x2 – 81 |
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12.
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Which value of k makes the trinomial x2 + 12x +
k a perfect square?
a. | | c. | 36 | b. | 144 | d. | 18 |
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13.
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A swimming pool is being drained. The table shows the volume of water, in
kilolitres, remaining after an elapsed time, in minutes. Which graph represents this
data? Time (min) | 0 | 40 | 120 | 180 | Volume of Water (kL) | 50 | 40 | 20 | 5 | | | | | |
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14.
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Which of the following represents the domain of the function ?
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15.
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Identify the slope of a line with run –5 and rise –15.
a. | 3 | c. | | b. | | d. | –3 |
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16.
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Points A(5, 0) and B(–4, 2) are on a line. What is the rise from point A
to point B?
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17.
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Taylor invested $200 in an account that pays 5% simple interest per year. The
equation representing Taylor’s investment is A = P + Prt, where A
is the value of the investment, in dollars, P is the starting principal amount, in dollars,
r is the interest rate written as a decimal, and t is the number of years the money is
invested. What is the value of the investment after 10 years?
a. | $2000 | c. | $400 | b. | $1000 | d. | $300 |
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18.
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When a linear equation is written in the form Ax + By + C =
0, A and B cannot both be
a. | fractions | c. | one | b. | integers | d. | zero |
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19.
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For the line 4x – 3y – 12 = 0, which statement is
true?
a. | The x-intercept is 3 and the y-intercept is
–4. | b. | The x-intercept is 3 and the y-intercept is 4. | c. | The
x-intercept is 4 and the y-intercept is –3. | d. | The
x-intercept is 4 and the y-intercept is 3. |
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20.
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Identify the equation of the line in general form when the slope is 0.6 and the
y-intercept is 0.4.
a. | 3x + 5y + 2 = 0 | c. | 3x – 5y + 2 =
0 | b. | 3x + 5y – 2 = 0 | d. | 3x – 5y – 2 =
0 |
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21.
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Identify the ordered pair that is the solution to the linear system 2x
– y = 2 and 2x + y = 6.
a. | (1, 1) | c. | (3, 3) | b. | (2, 2) | d. | (4, 4) |
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22.
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Translate the following into an algebraic equation: “Three times a number
subtracted from ten is five more than seven times the number.”
a. | 3x – 10 = 7x + 5 | c. | 10 – 3x = 7x +
5 | b. | 3x – 10 = 7x – 5 | d. | 10 – 3x = 5 –
7x |
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Answer the the following question(s) using the information from the scenario
below.
KC Fitness Club charges a flat fee of $25 per month plus $5 per visit. Workout Zone
charges a flat fee of $35 per month plus $3 per visit. Let x represent the number of visits
per month and let y represent the total cost per month, in dollars.
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23.
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Identify the graph that represents this situation.
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24.
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Determine which of the following linear systems shows coincident lines.
a. | 6x – y = 2 2x + y = 6 | c. | 3y = 18
– 6x 2x + y = 6 | b. | 4x + y = 5 6x –
y = 2 | d. | 3y = 18
– 6x 4x + y = 5 |
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25.
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Use the substitution method to determine the solution to the linear system
y = 4x + 34 and y = –2x – 26.
a. | (–10, –6) | c. | (–10, 6) | b. | (–6, –10) | d. | (10, –6) |
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26.
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Raoul and Kourosh run a buffet-style restaurant. It costs them $4200.00 for rent
and utilities each month, plus an average of $8.00 per person for food. If they charge their
customers $20.00 each, what are the costs at the point where the costs equal the revenue?
a. | $7000.00 | c. | $4200.00 | b. | $4228.00 | d. | $4550.00 |
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27.
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Marie had $40 000.00 to invest. She invested part of it in bonds paying 1.2% per
annum and the remainder in a second mortgage paying 2.8% per annum. If the total interest after 1
year was $960.00, how much did Marie invest at each rate?
a. | $39 040.00 at 1.2% and $960.00 at 2.8% | b. | $30 000.00 at 1.2% and $10 000.00 at
2.8% | c. | $10 000.00 at 1.2% and $30 000.00 at 2.8% | d. | $960.00 at 1.2% and
$39 040.00 at 2.8% |
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28.
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Let and , and then solve the following system of
equations for x and y.
a. | (6, 4) | c. | | b. | (4, 6) | d. | |
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29.
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If cos A = 0.9903, then the measure of A, to the nearest degree,
is
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30.
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Write the cosine ratio of .
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31.
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In , AB = 10 cm, , and . Determine the length of
AC to the nearest centimetre.
a. | 9 cm | c. | 11 cm | b. | 10 cm | d. | 12 cm |
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32.
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Which statement is incorrect?
a. | You can solve for the unknown side in any triangle, if you know the lengths of
the other two sides, by using the Pythagorean theorem. | b. | The hypotenuse is the longest side in a right
triangle. | c. | The hypotenuse is always opposite the 90° angle in a right
triangle. | d. | The Pythagorean theorem applies to all right
triangles. |
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33.
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What is the most appropriate SI measurement unit to use when estimating the
perimeter of this figure?
a. | centimetre | c. | metre | b. | kilometre | d. | millimetre |
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34.
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The flying distance from Dawson City to Whitehorse is 540 km. The distance shown
on the map is 4 cm. What is the scale of the map as a ratio in lowest terms?
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35.
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A florist requires 12 in. of ribbon for each bouquet of flowers he creates. How
many bouquets will he be able to create from 10 yd of ribbon?
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36.
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A low bridge has a posted height of 7 ft 6 in. If your truck is 2.3 m high, how
many centimetres over or under the bridge height will it be?
a. | 1.4 cm over | c. | 2.36 cm over | b. | 1.4 cm under | d. | 2.36 cm under |
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37.
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Calculate the surface area of the right pyramid, to the nearest tenth of a
square foot.
a. | 27.6 ft2 | c. | 53.4 ft2 | b. | 34.7 ft2 | d. | 54.7
ft2 |
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38.
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Calculate the surface area of the right cylinder, to the nearest square
foot.
a. | 93 ft2 | c. | 48 ft2 | b. | 68 ft2 | d. | 23
ft2 |
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39.
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What is the slant height of a right cone with surface area 275.7 m2
and radius 4.5 m?
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40.
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Determine the volume of a right cone with diameter 3.4 in. and height 10.8 in.
Express the answer to the nearest cubic inch.
a. | 33 in.3 | c. | 131 in.3 | b. | 98 in.3 | d. | 523
in.3 |
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Problem
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1.
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There are 6 bacteria in a dish at the beginning of an experiment. The number of
bacteria doubles every 2 h. How many bacteria are there after 9 days? Express your answer in both
exponential and simplified form.
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2.
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Greg works as a caretaker at a park. In the fall, he rakes all the leaves in the
rectangular park. The length of the park is (3x + 1) m. The width of the park is (2x +
4) m. a) Develop an expression that represents the area of the park. b)
Calculate the actual area that Greg has to rake if x = 5 m.
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3.
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Jill earns $8 per hour working at a fast-food restaurant. She takes the bus to
and from work for a total of $4 a day. Jill’s daily net earnings can be represented by the
function E(t) = 8t – 4. a) Make a table of
values of Jill’s net earnings for values of t from 0 to 4. b) Graph the
relation. c) How much does Jill earn if she works for 8 h?
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4.
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The equation F = C + 32 gives the temperature, in
degrees Fahrenheit for a given temperature, in degrees Celsius. a) Identify the slope and
the F-intercept and explain what they mean. b) What temperature in degrees
Fahrenheit corresponds to -40 °C?
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5.
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Lee has $200 and would like to buy ten books as gifts. A paperback book costs
$14 and a hardcover costs $24. Using a graph, determine the number of each kind of book that Lee
should buy to spend all of his $200.
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6.
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A spa is offering two deals. Clients can get five facials and three manicures
for $128, or two facials and three manicures for $62. What are the special prices of a facial and a
manicure?
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7.
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Max’s dog is lying on the ground 1.2 m away from him. The angle of
elevation from the dog to the top of Max’s head is 48°. How tall is Max, to the nearest
tenth of a metre?
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8.
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You are buying a sport bike that you would like to store in your garden shed.
The sport bike has a total length of 210 cm. Your garden shed is 6 ft by 8 ft. Will the sport bike
fit in the shed? Show how you know.
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Use the table of conversion factors to help answer the following
questions.
Imperial Unit | SI Unit | 1 in. | 2.54 cm | 1 ft | 0.3048
m |
1 yd | 0.9144 m |
1 mi | 1.609 km | | |
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9.
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Determine the volume of a right prism with dimensions 2 ft by 3 ft by 6 ft, to
the nearest hundredth of a cubic metre.
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