FOM11 Final Review 2
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Rosie made the following conjecture.
All polygons with five equal sides are regular pentagons.
Which figure, if either, is a counterexample to this conjecture?
a.
b.
c.
d.
____
2. Which of the following choices, if any, uses deductive reasoning to show that the sum of three even
integers is even?
a.
b.
c.
d.
____
x + y + z = 2(x + y + z)
2x + 2y + 2z = 2(x + y + z)
2 + 4 + 6 = 12 and 4 + 6 + 8 = 18
None of the above choices
3. Which of the following choices, if any, uses inductive reasoning to show
that the sum of two even numbers and one odd number is an odd number?
a.
b.
c.
d.
____
Figure B only
Figure A only
Neither Figure A nor Figure B
Figure A and Figure B
6 + 6 + 7 = 19 and 4 + 6 + 3 = 13
(2x + 1) + (2y + 1) + (2z + 1) = 2(x + y + z) + 3
2x + 2y + (2z + 1) = 2(x + y + z) + 1
None of the above choices
4. What type of error, if any, occurs in the following proof?
2
4(2)
4(2) + 3
8+3
11
a.
b.
c.
d.
=2
= 4(1 + 1)
= 4(1 + 1) + 3
=6+3
=9
a false assumption or generalization
an error in reasoning
an error in calculation
There is no error in the proof.
____
5. Determine the value of d.
a.
b.
c.
d.
____
6. Which statement about the angles in this diagram is false?
a.
b.
c.
d.
____
YXZ = 63°, XZY = 91°
YXZ = 53°, XZY = 91°
YXZ = 63°, XZY = 81°
YXZ = 53°, XZY = 81°
8. Determine the sum of the measures of the interior angles of this polygon.
a.
b.
c.
d.
____
b = 50°
c = 50°
e = 130°
f = 62°
7. Which are the correct measures for YXZ and XZY?
a.
b.
c.
d.
____
48°
36°
52°
42°
1080°
1440°
720°
540°
9. Each interior angle of a regular convex polygon measures 144°.
How many sides does the polygon have?
a.
b.
c.
d.
10
11
8
9
____ 10. Determine the measure of R to the nearest degree.
a.
b.
c.
d.
52°
54°
50°
56°
____ 11. Determine the indicated side length to the nearest tenth of a centimetre.
a.
b.
c.
d.
8.0 cm
8.5 cm
9.0 cm
cannot be determined
____ 12. Which test point is in the solution set for the linear inequality
{(x, y) | 7x + 5y 0, x I, y I}?
a. (2, 2)
b. (–1, –1)
c. (1, 1)
d. (2, –2)
____ 13. Identify the point of intersection for the following system of linear inequalities.
{10y – 5x 0, 4x + 2y > 10, x  I, y I}
a. (2, –1)
b. (–2, –1)
c. (2, 1)
d. (–2, 1)
____ 14. The following model represents an optimization problem. Determine the maximum solution.
Restrictions:
x W
y W
Constraints:
0 x 100
–50 y 50
x
25 – y
x–y
60
Objective function:
A = y – 2x + 10
a.
b.
c.
d.
(34, 4)
(0, 25)
(68, 8)
(–10, –50)
____ 15. Rewrite –8p2 – 4p = –23p2 + 4p – 1 in standard form. Then solve the equation in standard form by graphing.
a.
b.
c.
d.
p = –0.333, p = 0.2
p = 3, p = 5
p = 0.333, p = 0.2
p = 0.333, p = 5
____ 16. Solve x2 + 5x + 4 = 0 by factoring.
a.
b.
c.
d.
x = –5, x = –1
x = 5, x = 1
x = 4, x = 1
x = –4, x = –1
____ 17. Solve 3y2 – 12y = –2y2 + 5y + 12 by factoring.
a. y = –3, y = 4
b.
y=– ,y=4
c.
y=– ,y=4
d. y = –5, y = 4
____ 18. The graph shows how a cyclist travels over time.
Over which interval is the cyclist travelling the slowest?
a.
b.
c.
d.
BC
DE
EF
FG
____ 19. It takes 4 h 26 min to fill a 3600 L water tank. Which equation determines
the length of time, t, in minutes, it will take to fill a 1700 L water tank?
a.
b.
c.
d.
____ 20. A 1:6 scale model of canoe is 30 in. long, with a beam (width) of 5.3 in. and a depth of 2.2
in. What are the dimensions of the actual canoe?
a. 15 ft long, 31.8 in. beam, 13.2 in. deep
b. 18 ft long, 38 in. beam, 12 in. deep
c. 13 ft long, 32 in. beam, 15 in. deep
d. 12 ft long, 18.5 in. beam, 3.2 in. deep
____ 21. Describe the boundary lines for the following system of linear inequalities.
{2y – 6x < 12, 4x + 4y 8, x I, y I}
a. Dashed line along y = 3x + 6; dashed line along y = 2 – x
b. Dashed line along y = 3x + 6; solid line along y = 2 – x
c. Solid line along y = 3x + 12; dashed line along y = 2 – x
d. Solid line along y = 3x + 12; solid line along y = 2 – x
____ 22. How many zeros does f(x) = a(x – 5)2 have if a < 0?
a.
b.
c.
d.
0
It is impossible to determine.
2
1
____ 23. Which scale factor(s) will produce an image that is larger than the original?
I. 0.86
II. 116%
III.
a.
b.
c.
d.
I only
I and II only
II and III only
I, II, and III
Short Answer
24. Which law could you use to determine the unknown angle in this triangle?
25. 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.
26. Why would you use a dashed boundary line when graphing the solution set of the linear inequality
1.6x – 3y < 50?
27. A publisher makes romance and adventure novels. Romance novels sell for $9.95 and adventure novels for
$8.95. The publishers noticed that each month they sell between 500 and 800 romance novels and that the
number of adventure novels sold is never more than double the number of romance novels sold.
Let r represent the number of romance novels sold.
Let a represent the number of adventure novels 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 novels.
28. Rewrite x2 = – 3x + 4 in standard form. Then solve the equation in standard form by graphing.
29. Determine the roots of the corresponding quadratic equation for the graph.
y
1
30. Use the graph to determine
the equation of the parabola.
–3
–2
–1
1
x
–1
–2
–3
31. Solve 9x2 – 30x = –25 by factoring. Verify your solution.
32. Determine the value of x in the diagram to the right.
33. Determine two angles between 0° and 180° that have the sine ratio 0.8480.
34. Solve
. State solution as exact values.
35. The base and height of a trapezoid with an area of 35 cm2 will be enlarged by a scale factor of 4.
Determine the area of the enlarged trapezoid.
Problem
36. An airplane is flying directly toward two forest fires. From the airplane, the angle of depression to one fire is
43° and 20° to the other fire. The airplane is flying at an altitude of 2500 ft. What is the distance between the
two fires to the nearest foot? Show your work.
37. The stylists in a hair salon cut hair for women and men.
• The salon books at least 5 women’s appointments for every man’s appointment.
• Usually there are 90 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 45 min, and a man’s cut takes about 20 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?
38. a) Write a quadratic function with zeros at 0.50 and 0.75.
b) Determine two other possible functions with the same zeros.
39. 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?
40. Lamar jogs at 11 km/h. When Lamar jogs at this rate for 15 min, he burns 276 Cal. Angela
jogs at a slower rate, 9 km/h, burning 641 Cal in 60 min. If Angela jogs for 2.5 h, how long
will Lamar have to jog in order to burn the same amount of Calories as Angela?
41. This scale diagram, drawn on 0.5 cm grid paper, shows the plan of a
swimming pool, drawn using a scale factor of 1:250.
a) Determine the perimeter of the pool.
b) Determine the area of the bottom of the pool.
FOM11 Final Review 2
Answer Section
MULTIPLE CHOICE
1.
5.
9.
13.
17.
21.
A
B
A
C
C
B
2.
6.
10.
14.
18.
22.
111
B
A
A
B
B
D
3.
7.
11.
15.
19.
23.
A
C
C
C
A
C
4.
8.
12.
16.
20.
C
A
B
C
A
SHORT ANSWER
24.
the cosine law then the sine law
25. two triangles:
26. To indicate that the points on the boundary line are not part of the solution set.
27. Constraints:
r 0
a 0
500 r 800
2r a
Objective function:
P = 9.95r + 8.95a
28. x = 1, x = 4
29. x = 0, x = 4
30. y = –2(x + 1.5)(x + 0.5)
31. x =
32. x = 48°
33. 58°, 122°
34.
35. 560 cm2
PROBLEM
,
36. Draw a rough (not-to-scale) sketch of the situation, as shown. Determine the unknown angles using the property
that the measures of the angles in a triangle sum to 180°. Let A and B represent the positions of the fires.
By the sine ratio,
By the sine law,
The fires are 4188 ft apart.
37. 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 5y
x + y 90
Objective function to minimize:
E = 45x + 20y
Graph the lines and find the intersection points of the solution area.
The intersection points are (90, 0) and (75, 15).
The minimum occurs when x is minimized.
The minimum is at point (75, 15) and represents 75 women’s appointments and 15 men’s appointments.
E = 75(45) + 20(15)
E = 3675
The minimum amount of time is 3675 h.
38. a)
b) Other possible functions are multiples of the function where a  1.
Examples may vary:
f(x) = 2x2 – 2.50x + 0.650
f(x) = –2x2 + 2.50x – 0.650
39. a)
b) The slopes represent the snowboarder's speed in metres per second (m/s).
40. 15 min = 0.25 h
Angela burns 2.5(641 Cal) = 1602.5 Cal in 2.5 h of jogging.
Use equivalent ratios to determine the amount of time, t, Lamar must jog to burn 1602.5 Cal:
Lamar will have to jog for 1.45 h, or about 87 min, to burn the same amount of Calories.
41. a) Side lengths from top going counter clockwise are:
6.0 cm, 3.0 cm , 1.5 cm, 1.5 cm, 2.5 cm, 2.5 cm, 1.5 cm, 4.0 cm
Perimeter = sum of side lengths
Perimeter = 6.0 cm + 2(3.0 cm) + 3(1.5 cm) + 2.5 cm + 4.0 cm
Perimeter = 23 cm
The scale is 1 cm to 250 cm so the scale factor is 250.
Actual perimeter = 250(perimeter)
Actual perimeter = 250(23 cm)
Actual perimeter = 5750 cm or 57.5 m
The actual perimeter of the pool is 57.5 m.
b) The area of the scale diagram is 60 square units.
The side length of each square represents 250(0.5 cm) = 125 cm or 1.25 m.
So the area each square represents is (1.25 m)2 or 1.5625 m2.
60(1.5625 m2) = 93.75 m2
The area of the bottom of the pool is 93.75 m2.