Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What are the x- and y-intercepts for the function
f(x) = x2 + 7x + 10?
a. | x = –5, x = 5, no y-intercept | b. | x = 10,
y = –2 | c. | x = –5, x = –2,
y = 10 | d. | no x-intercepts, y = –2 |
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2.
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Which set of ordered pairs satisfy the function f(x) =
x2 + 9x + 3?
a. | (–6, –15), (0, 3), (1, –15) | b. | (–5,
–17), (–2, 10), (2, 25) | c. | (–8, –5), (–3,
–15), (3, 39) | d. | (–4, –17), (–1,
–4), (1, 13) |
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3.
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The points (–5, 26) and (3, 26) are located on the same parabola. What is
the equation for the axis of symmetry for this parabola?
a. | x = –2 | b. | x = 4 | c. | x =
–1 | d. | x = 0 |
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4.
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Which relation is the factored form of f(x) = x2
+ 2x – 3?
a. | f(x) = x(x + 2) + 3 | b. | f(x) =
(x – 2)2 | c. | f(x) = (x +
3)(x – 1) | d. | f(x) = (x –
3)(x + 1) |
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5.
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Which relation is the factored form of f(x) = x2
+ 2x – 8?
a. | f(x) = (x – 2)(x + 4) | b. | f(x) =
(x + 2)(x – 4) | c. | f(x) = (x –
1)(x + 8) | d. | f(x) = 2(x + 2)(x –
2) |
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6.
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Solve 100n2 = 121 by factoring.
a. | x = 10, x = –11 | b. | x =  , x = – | c. | x =  , x = – | d. | x = 11, x
= –11 |
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7.
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Solve 2y2 – 3y + 1 = 0 using the quadratic
formula.
a. | y = 1, y = – | b. | y = 1, y
= – | c. | y = –1, y =  | d. | y = 1, y =  |
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8.
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Solve 2x2 + 4x = –5 –
2x2 using the quadratic formula.
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9.
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A bridge is supported by three arches. The function that describes the arches is
h(x) = –0.25x2 + 2.375x, where h(x) is
the height, in metres, of the arch above the ground at any distance, x, in metres, from one
end of the bridge. How far apart are the bases of each arch?
a. | 8.6 m | b. | 10.3 m | c. | 9.5
m | d. | 9.2 m |
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10.
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A 454 g block of butter costs $4.37. What is the price per 100 g?
a. | $0.96/100 g | b. | $1.0$1.04/100 g | c. | $0.10/100
g | d. | $1.09/100 g |
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11.
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Which situations could be described using the rates $15.56/lb, 80 km/h, and
$1.58/L?
a. | price of nails, average human running speed, price of sunflower
oil | b. | price of coffee, cruising speed of an airplane, price of milk | c. | price of lobster,
highway speed limit, price of apple juice | d. | price of crude oil, average speed of a truck,
price of cola |
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12.
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Which situations could be described using the rates 15 L/min,
$2.89/ft2, and $3.60/100 g?
a. | water flow from a leaky faucet, price of fabric, price of cheese | b. | fuel consumption,
price of sod, price of gold | c. | water flow through a hydro electric plant,
price of ceramic tile, price of trail mix | d. | water flow through a garden hose, price of
carpet, price of salami |
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13.
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15 kg of Yukon gold potatoes costs $32.70. Which equation determines the price,
P,
in dollars, of 4 lb of potatoes?
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14.
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A computer can transfer 17 MB (megabytes) of data in 2.5 s.
Which equation
determines the length of time, t, in seconds,
the computer will take to transfer 2.3 GB
(gigabytes) of data?
(1 GB is equivalent to 1024 MB.)
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15.
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A screw has 64 turns over a distance of 40 mm of
thread.
Which equation does not determine the number of turns, t,
that a screw
with the same pattern has over 30 mm of thread?
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16.
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The distance between two towns on a map is 5.4
cm. The map was made using a scale of 1 cm to 300 km. What is the actual distance between the two
towns?
a. | 1600 km | b. | 1550 km | c. | 1620
km | d. | 1520 km |
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17.
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Data for triangle ABC is shown on the first line of the table.
Triangle ABC is enlarged so the area is 270 cm 2. Which triangle is the
enlargement of triangle ABC? Triangle Name | Length of Base (cm) | Height of Triangle (cm) | Scale Factor | Area (cm2) | | ABC | 5 | 3 | 1 |
7.5 | 1 | DEF | 30 | 18 | 6 | 270 | 36 | GHI | 30 | 18 | 36 | 270 | 6 | JKL | 36 | 16 | 6 | 270 | 36 | MNO | 18 | 30 | 6 | 270 | 6 | | | | | | |
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18.
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Data for rectangle ABCD is shown on the first line of the table.
Rectangle ABCD is enlarged so the width is 19.5 cm. Which rectangle is the enlargement
of rectangle ABCD? Rectangle Name | Length (cm) | Width (cm) | Scale Factor | Area (cm2) | | ABCD | 9.0 | 13.0 | 1.00 | 117.00 | 1 | EFGH | 13.5 | 19.5 | 1.35 | 265.25 | 2.25 | JKLM | 12.5 | 19.5 | 1.25 | 253.25 | 2.125 | NOPQ | 13.5 | 19.5 | 1.50 | 263.25 | 2.25 | RSTU | 15.5 | 19.5 | 1.50 | 302.25 | 2.5 | | | | | | |
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19.
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A 1:25 scale model of a garbage truck is 0.5 ft
tall, 0.32 ft wide, and 1.4 ft long. What are the dimensions of the actual garbage
truck?
a. | 25 ft by 12.5 ft by 50 ft | b. | 9 ft by 6.4 ft by 25 ft | c. | 15 ft by 7.4 ft by
33.5 ft | d. | 12.5 ft by 8 ft by 35 ft |
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20.
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A stage director needs a large chess pawn for a
scene. The pawn in her chess set is 35 mm tall and she estimates that the height of the enlarged
pawn must be 700 mm.
How many times greater will the volume of the larger pawn
be?
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Short Answer
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21.
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Determine the domain and range for the relation y =
–x2 – 3x.
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22.
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Dortea is grilling chicken for a school reunion.
Her barbecue sauce recipe is one fifth molasses, and she needs 200 mL of sauce per pound of chicken.
She is grilling 18 kg of chicken legs. How many millilitres of molasses does she need?
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23.
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Triangle A has an area of 19.00 cm2 and similar triangle B has an
area of 118.75 cm2. Determine what scale factor makes triangle B an enlargement of
triangle A.
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24.
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A 1:5 scale model of an iron bed frame is 39.4 cm long and 28.6 cm wide.
The
headboard is 26.2 cm tall and the footboard is 21.2 cm tall.
Determine the actual dimensions of
the bed frame.
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25.
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A carpenter creates two similar boxes with their dimensions related by a scale
factor of  . The smaller box has a surface area of 670 m 2. Determine the surface area of
the larger box.
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Problem
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26.
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The height of a soccer ball above the ground, y, in metres, is modelled
by the function
y = –4.9x2 + 5x + 1, where x
is the time in seconds after the ball is kicked.
a) Use technology to determine the maximum
height the ball will reach. Round your answer to the nearest tenth of a metre.
b) State any
restrictions on the domain and range of the function.
c) For how long is the ball in the
air?
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27.
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Rosa is building three enclosed gardens as shown. She bought 200 m of fencing
and wants to maximize the total area for the gardens. She wrote the function A( x)
= – x2 + 100 x to represent the total area of the gardens,
A( x) , in square metres, if each garden is x metres wide. 
a) Determine the maximum total area of the three gardens. b) State the
domain and range of the variables in her equation. c) What are the dimensions of one
garden?
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28.
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A theatre sells tickets to a musical. The profit function for the show is
p(t) = –30t2 + 550t – 400, where
p(t) is the profit and c is the price of each ticket,
both in
dollars.
a) What ticket price will result in the theatre breaking even on the
show?
b) What ticket price will raise the most money for the theatre?
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29.
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Triangle A is 42 cm wide and 20 cm high.
Triangle B is 7 cm wide and similar
to triangle A.
a) Determine the scale factor by which triangle A was reduced to form
triangle B.
Sketch the triangles if it will help you.
b) Determine the areas of triangle
A and triangle B.
c) How many triangles congruent to triangle B would fit inside triangle
A?
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30.
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A band poster that measures 90 cm by 40 cm is reduced by a scale factor of  so
it can fit on a postcard. a) What are the dimensions of the postcard image? b) By
what scale factor, to the nearest hundredth, was the area of the poster decreased in the reduction
process?
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