Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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One side of a square is 15g in length. What is the area of the
square?
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2.
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Which value of x satisfies the equation x–2 =
 ?
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3.
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Which power is equivalent to  ?
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4.
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Express  as an equivalent mixed radical.
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5.
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The expression –65x2 – 10x + 10 written in
factored form is
a. | –5(–13x2 + 2x – 2) | c. | –5(–13x2 – 2x + 2) | b. | –5(13x2 + 2x – 2) | d. | –5(13x2 –
2x + 2) |
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6.
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What is the expression –66x2 + 24x + 18 in
factored form?
a. | –6(11x2 – 4x – 3) | c. | –6(11x2 + 4x + 3) | b. | –6(–11x2 + 4x + 3) | d. | –6(–11x2 –
4x – 3) |
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7.
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Identify the factored form of x2 – 10x +
16.
a. | (x – 5)(x – 5) | c. | (x – 2)(x
– 8) | b. | (x – 4)(x + 4) | d. | (x + 2)(x +
5) |
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8.
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What is the factored form of x2 – 3x –
10?
a. | (x – 10)(x – 1) | c. | (x + 5)(x –
2) | b. | (x – 5)(x + 2) | d. | (x + 10)(x –
1) |
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9.
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What is the product (x + 9)(x – 5)?
a. | x2 + 9x – 45 | c. | x2 –
45x + 4 | b. | x2 – 45x – 45 | d. | x2 + 4x –
45 |
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10.
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The greatest common factor (GCF) for a polynomial can be
a. | a constant | b. | a constant, a variable, or a constant with a
variable | c. | a constant with a variable | d. | a variable |
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11.
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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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12.
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Which expression is not an example of a difference of squares?
a. | 225 – 100x2 | c. | 36x2 –
49 | b. | 64 – 16x2 | d. | 9x2 –
181 |
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13.
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Which scenario describes the distance-time graph shown below?  a. | A car speeds up at a constant rate, then continues at a constant speed. It slows down
for a period of time. It slows down at a slower rate, then slows down at a faster rate until it
returns to the original starting point. | b. | A car speeds up at an increasing rate, then
continues at a constant speed. It slows down for a period of time. It slows down at a slower rate,
then slows down at a faster rate until it returns to the original starting point. | c. | A car speeds up at a
constant rate, then stops for a period of time. It starts to move again, slower than before. It slows
down at a slower rate, then slows down at a faster rate until it returns to the original starting
point. | d. | A car speeds up at an increasing rate, then continues at a constant speed. It slows
down for a period of time. It slows down at a faster rate, then slows down at a slower rate until it
returns to the original starting point. |
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14.
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Which graph represents the relation y = 2x2
– 3?
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15.
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Given the equation f(x) = –6x – 2, determine
f(4).
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16.
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Which statement is not true?
a. | All relations are functions. | b. | All functions are relations.
| c. | A relation is a function if each value in the domain corresponds to exactly one value
in the range. | d. | Each function has its own rule that is often given using function
notation. |
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17.
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What is the equation y = 0.25x – 0.75 in general
form?
a. | –x + 4y – 3 = 0 | c. | x – 4y –
3 = 0 | b. | –x + 4y + 3 = 0 | d. | x – 4y + 3 =
0 |
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18.
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Marie invested $800 in an account that pays 10% simple interest per year. The
equation representing Marie’s investment is A = P + Prt, where A is
the value of the investment, in dollars, P is the starting principle amount, in dollars,
r is the interest rate written as a decimal, and t is the number of years the money is
invested. How many years will pass before the investment is worth $1200?
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19.
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The table of values represents a line. What is the equation of the
line?  a. | y = 3x + 5 | c. | y = –3x +
5 | b. | y = 3x – 5 | d. | y = –3x –
5 |
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20.
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Which equation represents a line that is perpendicular to a line passing through
points G(–3, 8) and H(0, 5)?
a. | y = –2x + 5 | c. | y = x –
5 | b. | y = –x + 8 | d. | y = 2x –
8 |
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21.
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Determine the ordered pair that is a solution to the linear system x
– y = 2 and y + 2x = 9.
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22.
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The graphed lines of x + Py = 15 and x – Py =
9 intersect at (12, 1). What is the value of P?
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23.
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Express the following statement as an equation: “Twice a number less three
is one half of three times the number.”
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24.
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If two lines in a linear system are coincident, how many solutions does the
linear system have?
a. | 0 | c. | indeterminate | b. | 1 | d. | an infinite
number |
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25.
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Determine the solution to the linear system y = 3x – 13 and
y = 5x – 19.
a. | (3, 4) | c. | (–4, 3) | b. | (3, –4) | d. | (–3,
–4) |
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26.
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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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27.
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Use the elimination method. The solution to the linear system 15x +
5y = 185 and –4x + 5y = –5 is
a. | (10, –7) | c. | (–10, –7) | b. | (10,
7) | d. | (–10,
7) |
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28.
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A rocket is fired down a practice range. The height of the rocket, h, in
metres, depends on the time it has been in flight, t, in seconds, as shown by the equation
h = at2 + bt + c. After 10 s, the rocket reaches a height of
1500 m. The height is 2000 m after 20 s and 1500 m after 30 s. What are the values of a,
b, and c?
a. | a = 5, b = –200, and c = 0 | c. | a = –5, b =
–200, and c = 0 | b. | a = 5, b = 200, and c =
0 | d. | a = –5,
b = 200, and c = 0 |
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29.
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Determine the measure of  , to the nearest degree. 
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30.
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In a right triangle, sin B = 0.2924. Determine the measure of  B, to the
nearest degree.
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31.
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Determine the value of cos 0°.
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Use the diagram to answer the following question(s).
Kelly is
flying a kite in a field. He lets out 40 m of his kite string, which makes an angle of 72° with
the ground. 
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32.
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Determine the height of the kite above the ground, to the nearest metre.
a. | 12 m | c. | 42 m | b. | 38 m | d. | 129 m |
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33.
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Which of the four imperial length units listed below is the smallest?
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34.
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Imagine baking a pizza that measures 70 ft in diameter. What would be the
pizza’s area, to the nearest square foot?
a. | 110 ft2 | c. | 3848 ft2 | b. | 220 ft2 | d. | 15 394
ft2 |
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35.
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How long is 2 m in feet and inches? Express your answer to the nearest
inch.
a. | 0' 79" | c. | 6' 0" | b. | 7' 9" | d. | 6' 7" |
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36.
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Which of the following measurements is equal to 9 yd, to the nearest
hundredth?
a. | 5.59 m | c. | 9.84 m | b. | 8.23 m | d. | 9.00 m |
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37.
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A right pyramid has a volume of 156 m3. What is the volume of a right
prism that has the same base and height as the pyramid?
a. | 52 m3 | c. | 312 m3 | b. | 156 m3 | d. | 468
m3 |
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38.
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What is the volume of a right pyramid that has a base area of 23.4
yd2 and a height of 20.7 ft?
a. | 53.82 yd3 | c. | 484.38 yd3 | b. | 161.46
yd3 | d. | 1453.14
yd3 |
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39.
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Calculate the volume of a sphere with radius 2.8 ft, to the nearest cubic
foot.
a. | 23 ft3 | c. | 69 ft3 | b. | 33 ft3 | d. | 92
ft3 |
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40.
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A juice carton is shaped like a right triangular prism on top of a right
rectangular prism. It is filled to 80% of the total volume of the container. How much juice is in the
carton, to the nearest cubic centimetre?  a. | 1254 cm3 | c. | 1568 cm3 | b. | 1382 cm3 | d. | 1728
cm3 |
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Short Answer
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1.
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Is the statement  always, sometimes, or never true? Explain your
reasoning.
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2.
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Use the graph to answer parts a) to f).  a) State the
coordinates of points E and F. b) Determine the rise between points E and F. c)
Determine the run between points E and F. d) Determine the slope of the line containing
points E and F. e) State the y-intercept of the line containing points E and
F. f) State the equation of the line containing points E and F.
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3.
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Translate each phrase into an algebraic expression.
a) seven less than
twice a number
b) four more than half a number
c) a number decreased by six,
times another number
d) a value increased by the fraction two thirds
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4.
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In  ABC, the hypotenuse AB is 15 cm, and  B is 25°.
How long is BC, to the nearest centimetre? 
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5.
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Determine the volume of each object, to the nearest tenth of a cubic
unit.
a) a right cone with radius 2.2 cm and height 6.4 cm
b) a sphere with
radius 5.8 ft
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Problem
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1.
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A helicopter landing pad has a radius of r metres. The pad is to be
enlarged by increasing the radius by 5 m. Develop an algebraic expression for the increase in
area.
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2.
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A hockey arena sells game tickets for $150 each. The hockey team’s
salaries, arena workers’ salaries, and other expenses are fixed at $45 000 per game, no matter
how many tickets are sold.
a) Write an equation for the total amount of money, H,
earned after expenses if t tickets are sold for a game.
b) How many tickets have to
be sold for a game in order for the arena to earn $90 000 after expenses?
c) If the team
sells 200 tickets for a game, how much money does the arena earn or lose after expenses?
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3.
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Adam and Tanya are making snack bars to sell as part of a fundraiser for their
art club. The bars will have 3.5 times as many kilograms of raisins as of dried cranberries. Adam and
Tanya have already bought all of the other ingredients. What masses, in kilograms, of raisins and
dried cranberries do they need to buy if they want to spend all of their $264.25? Raisins cost
$5.50/kg and dried cranberries cost $18.50/kg.
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4.
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Mingmei is purchasing a new tractor that she would like to store in her new
shed. The shed is 4 ft wide. It has a floor made of 35 two-inch boards that are each 4 ft long. The
gaps between the boards add up to 2 in. Mingmei wants a tractor that is 180 cm long and 120 cm wide.
Will this tractor fit into her shed?
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