Exam Practice
Short Answer
1. What conjecture could you make about the product of two odd integers
and one even integer?
2. Tyler made the following conjecture:
A polygon with more than two right angles must be a rectangle.
Do you agree or disagree? Briefly justify your decision with a counterexample if possible.
3. Prove, using deductive reasoning, that the product of an even integer
and an even integer is always even.
4. Determine the measure of ABF.
5. Determine the measure of PQT.
6. Determine the sum of the measures of the interior angles of this seven-sided polygon.
Show your calculation.
7. Determine the length of c to the nearest tenth of a centimetre.
8. Determine the measure of  to the nearest degree.
9. Determine the length of w to the nearest tenth of a centimetre.
10. Determine the measure of  to the nearest degree.
11. A kayak leaves a dock on Lake Athabasca, and heads due north for 2.8 km. At the same time, a second kayak travels in a
direction N70°E from the dock for 3.0 km.
How you can determine the distance between the kayaks?
12. Which law could you use to determine the unknown angle in this triangle?
13. In ABC, A = 45°, a = 6.0 cm, and b = 7.5 cm. Determine the number of triangles (zero, one, or two) that are possible
for these measurements. Draw the triangle(s) to support your answer.
14. At the end of a bowling tournament, three friends analyzed their scores.
Lucia’s mean bowling score is 144 with a standard deviation of 12.
Zheng’s mean bowling score is 88 with a standard deviation of 6.
Kevin’s mean bowling score is 108 with a standard deviation of 5.
Who is the more consistent bowler?
15. Four groups of students recorded their pulse rates after a 2 km run.
126
168
158
192
146
166
104
Group 1
158
132
156
160
108
150
178
Group 2
136
174
156
176
150
166
142
Group 3
144
150
142
152
174
176
118
Group 4
164
136
156
152
116
172
130
178
138
140
182
164
172
126
180
128
136
154
166
158
152
130
148
158
128
160
172
166
Determine the standard deviation of Group 1, to one decimal place.
16. A teacher is analyzing the class results for a computer science test. The marks are normally distributed with a mean (µ) of
77.4 and a standard deviation () of 4.2.
Determine Kath’s mark if she scored µ – 2.
17. Is the data in this set normally distributed? Explain.
10–19
20–29
30–39
Interval
1
8
11
Frequency
40–49
13
50–59
9
60–69
3
18. Is the data in this set normally distributed? Explain.
82–85
86–89
90–93
Interval
5
3
8
Frequency
94–97
20
98–101
11
102–105
1
19. Determine the z-score for the given value.
µ = 9.3,  = 0.4, x = 8.8
20. The results of a survey have a confidence interval of 42.8% to 51.6%, 19 times out of 20.
Determine the margin of error.
21. A poll was conducted about an upcoming election. The result that 65% of people intend to vote for one of the candidates is
considered accurate within ±4.2 percent points, 9 times out of 10.
State the confidence interval.
22. How would you graph the solution set for the linear inequality 10y – 2x
23. Graph the solution set for the linear inequality 5y – 2x
–20?
15.
24. Graph the system of linear inequalities:
{(x, y) | x + y 2, x > –3, x  R, y R}
25. Graph the solution set for the following system of inequalities.
{(x, y) | x + y > 0, x + y < 4, x R, y R}
26. A cafeteria offers pepperoni and vegetarian pizza slices. Pepperoni slices sell for $3.75 and vegetarian slices sell for
$3.25. The manager noticed that every day they sell between 80 and 120 slices of vegetarian pizza. The total sales is
never more than 300 slices.
Let p represent the number of pepperoni slices sold.
Let v represent the number of vegetarian slices sold.
Write a system of linear inequalities to describe the constraints. Then, write an objective function that represents the
profit made from the sale of pizza slices.
27. Fill in the table for the relation y = –0.5x2 + 0.5x + 3.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
28. Fill in the table for the relation y = –x2 – 4x + 12.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
29. A quadratic function has an equation that can be written in the form f(x) = a(x – r)(x – s). The graph of the function has
x-intercepts at (3, 0) and (6, 0) and passes through the point (7, –4). Write the equation of the function.
30. Solve
. State the solution as exact values.
31. A 4.0 L can of Coloura paint will cover 45 m2.
A 2.5 L can of Brights paint will cover 30 m2.
Determine the area that one litre of each type of paint will cover.
Which brand of paint will cover a greater surface area?
32. Today, gold is worth $1200.60/oz (1 oz = 28.3495 g).
What is the value of 0.9 g of gold?
33. On a plan, an actual length of 8.5 m is represented by 3 cm.
Determine the scale and the scale factor of the plan.
34. The sides of a square with an area of 49 cm2 will be reduced by a scale factor of
.
Determine the area of the reduced square to the nearest square centimetre.
35. 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.
36. A 1:2.5 scale model of a clothes wringer is 18.9 in. tall, 6.1 in wide, and 1.3 in. deep. The wringer
handle is 4.7 in. long. Determine the actual dimensions of the clothes wringer.
37. An orange has a diameter of 8 cm. A honeydew melon has a diameter of 18 cm.
Estimate how many times greater the volume of a melon is, compared with the volume of an orange.
Problem
38. Alison discovered a number trick in a book she was reading:
Choose a number.
Add 3.
Multiply by 2.
Add 4.
Divide by 2.
Subtract 5.
Prove deductively that any number you choose will be the final result.
39. Determine, to the nearest centimetre, the perimeter of the triangle.
40. Determine the perimeter of this quadrilateral to the nearest tenth of a centimetre.
41. A canoeist leaves the dock and paddles toward a buoy 560 m away. After reaching the buoy, she changes directions and
paddles another 110 m. From the dock, the angle between the buoy and the canoeist’s current position measures 10°.
How far is the canoeist from the dock? Give two possible answers. Show your work.
42. The stylists in a hair salon cut hair for women and men.
• The salon books at least 3 women’s appointments for every man’s appointment.
• Usually there are 120 or more appointments, in total, during a week.
• The salon is trying to reduce the number of hours the stylists work.
• A woman’s cut takes about 60 min, and a man’s cut takes about 25 min.
What combination of women’s and men’s appointments would minimize the number of hours the stylists work? How
many hours would this be?
43. 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?
44. A parabola has the vertex (–7, –2).
a) Write an equation to describe all parabolas with this vertex.
b) A parabola with the given vertex passes through the point (–9, 10). Determine the equation for this parabola.
c) State the domain and range of the function.
45. a) Solve 3x2 + 5x – 2 = 0 using the quadratic formula.
b) Solve the equation by factoring.
46. This graph represents the path of a snowboarder sliding down a mountain.
a) Calculate the slopes of segments AB, BC, CD, and DE. Show your work.
b) What do these slopes represent?
47. Steve runs a kennel and purchases dog food from a U.S. supplier.
The supplier sells 25 lb bags for $28.95 U.S.
a) Each dog eats about 3.5 kg/week and Steve boards an average of 16 dogs per day.
How many bags of dog food will he need for three months?
b) The exchange rate is $1 U.S. for $1.06 Cdn on the day that Steve orders the food.
How much will the three month supply of dog food cost in Canadian dollars?
48. A movie theatre sells popcorn in a box shaped like a rectangular prism that is 18.0 cm high and has a square base sides
with 10.0 cm long. The movie theatre wants a similar container that can hold one-third more popcorn.
a) Determine the ratio that compares the capacity of the new container to the volume of the original container.
b) Determine the dimensions of the new container to the nearest tenth. Explain what you did.
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Answer Section
SHORT ANSWER
1. ANS:
For example, the product will be an even integer.
2. ANS:
For example, disagree: the following figure has more than two right angles, and it is not a rectangle.
3. ANS:
For example:
(2x)(2y) = 4xy
The final product is a multiple of 4, so it is even.
4. ANS:
ABF = 66°
5. ANS:
PQT = 36°
6. ANS:
180°(7 – 2) = 900°
7. ANS:
c = 42.7 cm
8. ANS:
 = 53°
9. ANS:
w = 27.3 cm
10. ANS:
 = 57°
11. ANS:
Since the measures of two sides and a contained angle are given, I would use the cosine law.
12. ANS:
the cosine law then the sine law
13. ANS:
two triangles:
14. ANS:
Kevin
15. ANS:
23.4
16. ANS:
69.0
17. ANS:
Yes. The graph of the data has a rough bell shape.
18. ANS:
No. The graph of the data does not have a bell shape.
19. ANS:
–1.25
20. ANS:
±4.4%
21. ANS:
60.8% to 69.2%
22. ANS:
Draw a solid boundary line y =
x – 2, then shade above the line.
23. ANS:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
1
2
3
4
5
x
1
2
3
4
5
x
–2
–3
–4
–5
24. ANS:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
25. ANS:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
26. ANS:
Constraints:
p 0
v 80
v 120
p + v 300
Objective function:
P = 3.75p + 3.25v
27. ANS:
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
(0, 3)
(–2, 0), (3, 0)
x = 0.5
(0.5, 3.125)
xR
y  3.125
28. ANS:
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
(0, 12)
(–6, 0), (2, 0)
x = –2
(–2, 16)
xR
y  16
29. ANS:
f(x) = –(x – 3)(x – 6)
30. ANS:
,
31. ANS:
Coloura: 11.25 m2/L
Brights: 12.0 m2/L
Brights paint will cover a greater surface area.
32. ANS:
$38.11
33. ANS:
scale: 3 cm:8.5 m or 3 cm:850 m
scale factor:
or about 0.0035
34. ANS:
19 cm2
35. ANS:
2.5
36. ANS:
47.3 in. tall
15.3 in. wide
3.3 in. deep
handle 11.8 in.
37. ANS:
e.g., about 11 times greater
PROBLEM
38. ANS:
For example:
n
n
+3
n+3
2n + 6
2
+4
2n + 10
n+5
2
–5
n
39. ANS:
Since RST is isosceles, R = S and r = s.
Determine the measure of T.
R + S + T = 180°
68° + 68° + T = 180°
T = 44°
Determine the length of r.
Perimeter = r + s + t
Perimeter = 12.012... + 12.012... + 9
Perimeter = 33.025...
The perimeter is 33 cm.
40. ANS:
AD2
AD2
AD2
AD2
AD
= AB2 + BD2 – 2AB·BD cos ABD
= 6.42 + 7.02 – 2(6.4)(7.0) cos 50°
= 40.96 + 49.00 – 89.60(0.6427…)
= 32.366…
= 5.689…

BDC = 180° – 48° – 73°
BDC = 59°
Perimeter = AB + BC + CD + DA
Perimeter = 6.4 + 6.3438… + 5.5 + 5.689…
Perimeter = 23.932…
The perimeter of ABCD is 23.9 cm.
41. ANS:
A rough (not-to-scale) sketch of the situation is shown, with known sides and angles labelled.
By the sine law, find both possibilities for angle B. Use this to find side a.
The canoeist is either 500 m or 603 m from the dock.
42. ANS:
Let x represent the number of women’s appointments.
Let y represent the number of men’s appointments.
Let T represent the total time.
Restrictions:
x  W, y  W
Constraints:
x 3y
x + y 120
Objective function to minimize:
E = 60x + 25y
Use technology to graph the lines and find the intersection points of the solution area.
50
y
45
40
35
30
25
20
15
10
5
20
40
60
80 100 120 140 160 180
x
The intersection points are (120, 0) and (90, 30).
The minimum occurs when x is minimized.
The minimum is at point (90, 30) and represents 90 women’s appointments and 30 men’s appointments.
E = 90(60) + 30(25)
E = 6150
The minimum amount of time is 6150 h.
43. ANS:
a)
b) 0  x  2, 0  y  2.3
c) 1.2 s
44. ANS:
a) y = a(x + 7)2 – 2, where a R.
b) Substitute (–9, 10). into the equation and solve for a.
y = a(x + 7)2 – 2
10 = a(–9 + 7)2 – 2
12 = a(4)
3 =a
The equation is y = 3(x + 7)2 – 2.
c) y  –7, x R
45. ANS:
a) 3x2 + 5x – 2 = 0
a = 3, b = 5, c = –2
or
b)
or
46. ANS:
a)
b) The slopes represent the snowboarder's speed in metres per second (m/s).
47. ANS:
a)
In one week, one dog eats 7.7 lb of food.
Sixteen dogs eat 16(7.7 lb/week) or 123.2 lb per week.
There are 52 weeks in a year, so three months is about 13 weeks.
In 13 weeks, the dogs will eat 13(123.2 lb) or 1601.6 lb of food.
= 64.064 bags
Steve will need about 64 bags for three months.
b) 64($28.95 U.S.) = $1852.80 U.S.
$1852.80 U.S.
= $1963.97 Cdn
The three month supply of dog food will cost $1963.97 Cdn.
48. ANS:
a) An increase of
the volume means that the new volume will be
The ratio of the old capacity to the new capacity is
b) Calculate the cube root of
times the original volume.
or 3:4.
to determine the scale factor for the side lengths.
Multiply each original dimension by this number to determine the new dimensions.
18.0 • 1.1 = 19.8
10.0 • 1.1 = 11.0
10.0 • 1.1 = 11.0
The new container will be 19.8 cm high, with a base that is 11.0 cm by 11.0 cm.
The new volume will be:
19.8 cm • 11.0 cm • 11.0 cm = 2395.8 cm3
The original volume is:
18.0 cm • 10.0 cm • 10.0 cm = 1800.0 cm3
Checking:
, which is about