FOM12
Final Exam Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. For an investment with the same principal and term, which of these compounding periods would
yield the most interest?
A.
B.
C.
D.
____
2. Which of the following would be the most likely to appreciate over time?
A.
B.
C.
D.
____
Yearly
Weekly
Quarterly
Monthly
A big screen television
A new computer
An electric vehicle
An antique table
3. Gerry invested $1000 for 4 years at an interest rate of 6% compounded semi-annually. The
number he should enter into the TVM solver for N is:
A.
B.
C.
D.
2
4
6
8
Use the following information to answer the next two questions.
The equations represent the values of four investments over time.
Equation I:
Equation II:
Equation III:
Equation IV:
____
A  5000(1.13) x
A  8000(1.08) x
A  7000(0.97) x
A  500(2.17) x
4. Which of the equations represents an investment that is depreciating?
A.
B.
C.
D.
Equation I
Equation II
Equation III
Equation IV
____
5. The investment that had the highest value after 4 years is:
A.
B.
C.
D.
____
6. Claudia has an investment of $1000 that earns 6% simple interest annually. Five years later, her
investment will be worth:
A.
B.
C.
D.
____
5.5%
6.5%
15.3%
9.1%
8. Steve and Emily are looking to buy a house. They have saved up a down payment of $15,000, and
they calculate that they can afford a monthly mortgage payment of $1300. If they are approved for
a mortgage with a 25-year amortization and an interest rate of 5.1% compounded semi-annually,
that the most expensive house they can afford to buy costs approximately:
A.
B.
C.
D.
____
$300
$1060
$1300
$1338
7. Matt estimated that his investment would double in 11 years. If Matt was using the rule of 72, then
he must be earning:
A.
B.
C.
D.
____
Equation I
Equation II
Equation III
Equation IV
$206 000
$221 000
$236 000
$405 000
9. Wayne applied for a $9000 car loan. He has a $1200 down payment and plans to pay off the loan
in five years. Calculate Wayne’s monthly payment f the bank charges 9% compounded monthly.
A.
B.
C.
D.
$130.00
$150.00
$161.92
$186.83
____
10. An investment portfolio yields the following rates of return over three years:
Year 1: 8.9%
Year 2: -5%
Year 3: 7.2%
If the initial investment was $2000, the final balance would be:
A.
B.
C.
D.
____
11. Yolanda has a $185 000 mortgage. The mortgage is amortized over 25 years, but Yolanda is only
locked in for a four-year term. The annual interest rate is 4.8% compounded semi-annually, and
Yolanda makes monthly payments. How much does Yolanda still owe the bank after the four
years is finished?
A.
B.
C.
D.
____
$1 055.00
$134 360.00
$167 998.59
$223 651.28
12. Patrick is saving up to buy a $45 000 boat. He deposits $250 at the beginning of each month into a
savings account which earns 4.3% compounded monthly. Approximately how many years will it
be before Patrick can afford the boat?
A.
B.
C.
D.
____
$422.00
$2218.08
$2222.00
$2422.00
12 years
15 years
24 years
139 years
13. Given the following situation:
• A = {3, 6, 7, 8}
• B = {5, 7, 9, 10}
Which statement describes A  B ?
A.
B.
C.
D.
{7}
{3, 5, 6, 8, 9, 10}
{5, 7, 9, 10}
{3, 5, 6, 7, 8, 9, 10}
____
14. Given the following situation:
• P = {2, 4, 8, 16}
• Q = {factors of 6}
• R = {4, 8, 12, 16}
Which pair of sets is disjoint?
A.
B.
C.
D.
____
P and Q
P and R
Q and R
None of the above
15. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram shows
the types of activities the campers like.
Use the diagram to determine n((C  A)  R).
A.
B.
C.
D.
____
5
24
26
50
16. Some table games use a board, dice, or cards, or a combination these. The following Venn diagram
shows the number of games that use these tools.
Use the diagram to determine n((C  B)/ D).
A.
B.
C.
D.
____
14
26
51
95
17. Which of the four statements below is FALSE?
A.
B.
C.
D.
Salmon are a subset of fish.
Rectangles are a subset of squares.
Poodles are a subset of dogs.
Whole numbers are a subset of integers.
____
18. Identify the contrapositive of the following statement: If I give my brother money, he will buy ice
cream.
A.
B.
C.
D.
____
19. Consider the following statement: If a number is a multiple of 3, then it is a multiple of 6.
The statement that is true is
A.
B.
C.
D.
____
the conditional statement
the contrapositive statement
the converse statement
none of the above
20. The number of arrangements of the letters of the word HOCKEY is
A.
B.
C.
D.
____
If I do not give my brother money, he will not buy ice cream.
If my brother buys ice cream, I have given him money.
If my brother does not buy ice cream, I have not given him money.
If give my brother ice cream, he will not ask for money.
6
21
120
720
21. A committee consists of eleven elected members. From this committee, a President, a Treasurer
and a Secretary must be chosen. In how many distinct ways can this be done?
A. 11 P3
B. 11C3
C. 113
D. 11!  3!
____
22. Simplify:
(n  2)!
n(n  1)!
A. (n  2)(n  1)
B. (n  2)(n  1)
(n  1)
C. (n  2)(n  1)
n
D. (n  2)(n  1)
(n  1)!
____
23. A 5-card hand is dealt from a standard deck of 52 playing cards. The number of different hands
containing 4 diamonds and 1 spade is
A.
B.
C.
D.
____
24. Of all the different arrangements of the letters in the word FLAGPOLE, calculate how many of
them end with 3 vowels.
A.
B.
C.
D.
____
9 295
18 590
223 080
1 115 400
4320
720
360
120
25. Determine the number of pathways from A to B if you only move right and down following the
roads on this map.
A
B
A.
B.
C.
D.
____
18
36
55
84
26. A coffee chain is opening one new coffee shop in three towns: Mathville, Numberton, and
Combinatrix. There are 4 possible sites in Mathville, 3 in Numberton and 7 in Combinatrix. How
many different ways could the company select the new sites?
A.
B.
C.
D.
4 3 7
4  3 7
4!  3!  7!
4!  3!  7!
____
27. Nine boys and twelve girls have signed up for a trip. If a student is selected at random from this
group, the odds in favour of picking a girl are:
A.
B.
C.
D.
7:4
4:7
3:4
4:3
Use the following diagram to answer the next two questions.
This diagram shows the sample space of a number of equally likely outcomes.
A
•
B
•
•• • ••
•
•
____
28. Determine the probability of the complement of A.
A. 2
7
B. 2
9
C. 4
7
D. 4
9
____
29. Determine P(A|B).
A. 1
3
B. 1
7
C. 5
7
D. 5
9
____
30. If P(A) = 0.2, P(B) = 0.6, and P(A  B) = 0.68, what is true about A and B?
They are independent and mutually exclusive
They are dependent and mutually exclusive
They are independent and not mutually exclusive
They are dependent and not mutually exclusive
A.
B.
C.
D.
____
31. A committee of 6 students is to be selected randomly from 5 seniors and 6 juniors. The probability
that there are exactly 2 seniors on the committee is represented by.
A.
2
11
B. 5 C2
11 C 6
C. 5 C2  6 C4
11 C6
D.
5 C2
2 6 C4
____
32. In a recent survey of Grade 12 students, it was found that 76% took Math and 62% took Biology.
If 93% took either Math or Biology, then the percentage of students who took both courses is:
45%
31%
17%
14%
A.
B.
C.
D.
____
33. Determine the correct set of characteristics for this polynomial function:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
A.
B.
C.
D.
Cubic function, y-intercepts = 0 and 2, a is negative
Cubic function, y-intercept = 0, a is positive
Quadratic function, x-intercept = 0, a is positive
Quadratic function, x-intercepts = 0 and 2, a is negative
____
34. Which of the following functions results in a graph with the following characteristics:
* one turning point
* range of y  3
* no x-intercepts
A.
B.
C.
D.
____
f(x) = 4x2 + 3
f(x) = -x2 + 3
f(x) = -3x2 + 18x – 24
f(x) = 3x2 – 18x + 24
35. This polynomial function has a y-intercept of -1 and passes through both (-4, -5) and (1, -5).
Use regression to find the equation of the function, and use your equation to find the coordinates of
the vertex.
y
5
4
A.
B.
C.
D.
(-1.5, 1.25)
(-1.5, 1.33)
(-1.66, 1.25)
(-1.66, 1.33)
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
____
36. The growth of a tree can be modeled by the function h(t )  2.3t  0.45 , where h represents the
height in meters and t the time in seconds. Determine the time it takes for a tree to reach a height
of 32m.
A.
B.
C.
D.
____
13 years
14 years
15 years
16 years
37. Rewrite the exponential equation 4 x  500 in logarithmic form.
A.
B.
C.
D.
log x 500  4
log x 4  500
log500 4  x
log 4 500  x
____
38. Fred’s car depreciates by 24% a year. If it is worth $8000 now, which of the following would
correctly calculate the value of the car 6 years from now?
A.
B.
C.
D.
____
39. A graph extends from quadrant IV to quadrant I. Which kind of function has this end behaviour?
A.
B.
C.
D.
____
8000(0.24)6
8000(1.24)6
8000(0.76)6
8000(0.86)6
logarithmic
quadratic
sinusoidal
exponential
40. Match the graph below with the correct exponential function.
y
5
4
A.
5
y  (2) x
2
B.
3
2
x
51
y  
2 2
C.
2
y  (2) x
5
x
D.
21
y  
52
____
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
41. Use the exponential regression function for the data to extrapolate the value of y when x is 24 .
x
0
1
2
3
4
5
y
412
437
471
526
588
644
A.
B.
C.
D.
3727
3692
2477
1538
____
42. The following data set involves exponential decay. Determine the missing value from the table.
x
0
1
2
3
4
5
y
810
540
360
160
106.66
A.
B.
C.
D.
____
43. Choose the best estimate for 0.3 radians in degrees.
A.
B.
C.
D.
____
9°
17°
23°
26°
44. Choose the best estimate for the central angle in radians.
A.
B.
C.
D.
____
120
190
240
260
1.5
2.4
5.5
7.6
45. Determine the value of the following function when x = 62.
A.
B.
C.
D.
1
2
3
5
____
46. A sinusoidal graph has a maximum at the point (4, 10). The next minimum is at the point (12, 4).
Determine the amplitude of the graph.
A.
B.
C.
D.
____
47. Determine the period of the following function.
y = 3 sin 0.5(x + 120°) + 2
A.
B.
C.
D.
____
3
4
6
8
180°
360°
720°
1080°
48. Determine the midline of the following function.
y = 3 sin 0.5(x + 120°) + 2
A.
B.
C.
D.
y=2
y=3
y = 0.5
y = –1/3
Problem
1. Christine needs to borrow $6500 for her small business. She has two options:
• Borrow the money from the bank at an interest rate of 5.7%, compounded monthly, with monthly
payments of $500.
• Borrow the money from her parents at an interest rate of 4.5%, compounded monthly, with
monthly payments of $250.
a) How long would it take Christine to pay off each loan? Show your work.
b) What is the total amount Christine would pay on each loan? Show your work.
c) Which option would you recommend Christine do? Explain.
2. Solve:
7
Pn  210 . Show or explain your solution.
3. In a game, Bag A contains 10 white marbles and 6 black marbles.
a) draw a tree diagram to represent the possible outcomes of drawing two marbles from the bag
without replacing the first marble after you draw it. Show the probability for each branch.
b) use your tree diagram to determine the probability of drawing one white and one black.
c) what is the probability that you drew a black for the first marble, given that your second draw
was white?
4. Three vehicles are taking a choir of 20 students to a recital. A minibus can take 12 students, an
SUV can take 5 students, and the remaining 3 students can ride with the choirmaster. How many
ways can the 20 students be assigned to the 3 vehicles? Show your work.
5. Each of the following Venn diagrams shows set A on the left and set B on the right.
Match each diagram to the correct set notation.
I.
A  B _______
II.
III.
IV.
A  B _______
( B / A) _______
( A / B)  ( B / A) _______
6. Sketch a graph (in radians, from 0 to 2π) and write an equation for a sinusoidal function that has a
range of 2  y  8 and a period length of π.
7. Data from 12 employees is given in the table and a scatterplot of the data is shown.
One student looked at the data
and thought it looked linear.
Another student thought it
looked like a cubic function.
Calculate both a linear and a
cubic regression, and suggest
which one you think is the
best choice.
Satisfaction Productivity
3
44
8
81
7
75
5
66
9
90
6
70
6
71
10
98
8
75
2
25
5
68
7
77
8. A social-networking site tracked the growth of its membership during its first eighteen months.
Number of
3
6
9
12
15
18
Months
Number of Users
2.0
5.4
7.0
8.5
9.6
10.3
(thousands)
a) Create a scatter plot, and draw a curve of best fit for the data using logarithmic regression.
b) Use your graph to estimate the number of users after 3 years, to the nearest hundredth.
ANSWER KEY
Question
1
2
3
4
5
6
7
8
9
10
11
12
B
D
A
C
D
C
B
C
C
B
C
A
Question
13
14
15
16
17
18
19
20
21
22
23
24
D
A
B
A
B
C
C
D
A
A
A
B
Question
25
26
27
28
29
30
31
32
33
34
35
36
C
B
D
D
A
C
C
A
B
A
A
B
Question
37
38
39
40
41
42
43
44
45
46
47
48
D
C
A
A
B
C
B
D
A
B
C
A
1. a) Bank: 13.45 months
(Use TVM Solver: I%=5.7, PV=6500, PMT = -500, FV=0, PY=12, CY=12, END, solve for N)
Parents: 27.41 months
(Use TVM Solver: I%=5.7, PV=6500, PMT = -500, FV=0, PY=12, CY=12, END, solve for N)
b) Bank: 13.45 months x $500 = $6725
Parents: 27.41 months x $250 = $6852.50
c) Answers will vary
2.
3. a)
7! 7  6  5...

7
6!
6  5...
7! 7  6  5...

 7  6  42
7 P2 
5!
5  4...
7! 7  6  5  4...

 7  6  5  210
7 P3 
4!
4  3...
Therefore, n must equal 3
P
7 1
10 6
60
1
 
or
16 15 240
4
6 10 60
1
 
or
P(Black first, then white) =
16 15 240
4
b) P(White first, then black) =
Therefore the P(one W, one B) =
1 1 1
 
4 4 2
c) Make A = drawing a white second
Make B = drawing a black one first
P(Both B and A) we already know is ¼ or 0.25
P ( B  A)
10 9
90
P( B | A) 
P(A) = either black-white or white-white ( 16  15  240
P ( A)
= 0.25 + 0.375
0.25
= 0.625

0.625
 0.4 or 40%
4.
or
3
or 0.375
8
)
Do one vehicle at a time. Order doesn’t matter.
Minibus: 20 C12  125970
SUV (now 8 kids left): 8 C5  56
Remaning kids go with choirmaster.
Total # of possibilities = 125970  56 1  7 054320
5.
From left to right: III, I, IV, II
6.
Since the range is from 2 to 8, we know the midline is 5 and the amplitude is 3. The period is π,
which means that there will be two full cycles on our graph, and also that b in the equation (since
we are using radians) will be 2π/π or just 2. We aren’t told anything about the horizontal shift, so
we can use whatever we like. We can also use either a sin function or a cos function.
Equations must either be y  3sin 2( x  *)  5 or y  3cos 2( x  *)  5 where * can be anything.
Graphs will vary depending on what you chose for c and whether you chose sin or cos.
7.
You might be tempted to say the cubic is better because the r2 value is higher, but you will always
get a higher r2 value is you use a higher degree of polynomial regression. It basically comes down
to which you think makes more sense – whether if you measured thousands of people you would
see a constant rise in productivity as satisfaction goes up (linear) or whether productivity really
does “flatten out” in the mid-range of satisfaction. Answers will vary, but saying that cubic is
better because of r2 value is wrong.
8. a) Scatterplot:
Regression Equation:
b) There will be approx. 13 578 users after 3 years: