Foundations of Mathematics 12
Resource Examination A
Multiple-Choice Booklet
Instructions
1. When using your calculator (scientific or approved graphing calculator):
• round only in the final step of the solution. Your final answer must be
accurate to at least two decimal places.
• use radian mode unless otherwise stated.
2. Diagrams are not necessarily drawn to scale.
RESOURCE EXAMINATION
The purpose of the Resource Examinations is to give teachers and students a wide range, but not
an exhaustive list, of questions that could be used to assess student understanding of the learning
outcomes presented in the Foundations of Math 12 course. However, this type of examination
does not allow for the assessment of all the mathematical processes described in The Common
Curriculum Framework for Grades 10–12 Mathematics, 2008 (CCF).
A number of comments that clarify the terminology or intent of a question are included on the
exams. They also provide some alternative solutions or state expectations, whenever appropriate.
The comments are given in the context of a specific question and may apply to other questions.
However, the comments will only appear once, therefore, teachers are encouraged to review both
resource examinations.
PART A: MULTIPLE-CHOICE QUESTIONS
Value: 44 marks
Suggested Time: 75 minutes
INSTRUCTIONS: For each question, select the best answer.
1. Which of the following items is most likely to appreciate in value over a ten-year term?
A.
B.
C.
D.
house
power boat
big-screen TV
dining-room set
Foundations of Mathematics 12 – Resource Exam A
Page 1
2. Jackie is considering investing $3000 into a high-risk account. Her financial planner shows
her a graph of how her money would grow.
Value of Investment over Time
y
Value of Investment ($)
7000
6000
5000
4000
3000
2000
1000
x
0
1
2
3
4
5
Years
To diversify her portfolio, Jackie is also considering investing a larger amount of money into a
low-risk account with a lower interest rate. The financial advisor adds a second curve to the graph
above showing this new situation. Compare the second curve to the curve shown above.
A. The second curve will initially start lower on the y-axis and will never intersect the
first curve.
B. The second curve will initially start lower on the y-axis and will eventually intersect the
first curve.
C. The second curve will initially start higher on the y-axis and will never intersect the
first curve.
D. The second curve will initially start higher on the y-axis and will eventually intersect the
first curve.
3. How can you determine the approximate amount of time it takes for an investment to double?
A.
B.
C.
D.
Page 2
Divide the annual interest rate by 72.
Divide 72 by the annual interest rate.
Multiply the annual interest rate by 72.
Double the annual interest rate and multiply by 72.
Foundations of Mathematics 12 – Resource Exam A
4. John decides to purchase a bicycle from Island Cycle for $2000 (including taxes).
He considers two options:
Option A
Option B
• pay $2000 cash
• pay an initial administration fee of $20 in cash
• no down payment
• monthly payments at 8% per annum, compounded
monthly over 1 year
How much more must he pay if he chooses Option B instead of Option A?
A.
$87.72
B. $107.72
C. $173.98
D. $2087.72
• The administration fee is paid prior to financing.
• When calculating the total amount paid for a loan, students should not round the
monthly payment.
5. Kathy receives the following two credit card offers. She wants to compare the effective annual
interest rate of each card.
• Card 1 – Interest is 0.05% per day, compounded monthly.
• Card 2 – Interest is 8% per year, compounded monthly for the first four months,
and 26% per year, compounded monthly for the next 8 months.
Calculate the effective annual interest rate of each card.
Card 1
A.
B.
C.
D.
18.25%
19.86%
19.86%
18.25%
Card 2
20%
21.90%
20%
17%
Foundations of Mathematics 12 – Resource Exam A
Page 3
Students are expected to know the vocabulary of effective annual interest rate. Some possible
strategies for solving this question are shown below:
Strategy 1
Strategy 2
0.05 × 365 = 18.25
Card 1
(
1 1+
0.1825
12
)
12
Strategy 3
eff (18.25 , 12 ) = 1.1985
N = 12
I% = 0.05 × 365
= 1.1985…
PV = −1
PMT = 0
FV = 1.1985…
P Y = 12
C Y = 12
PMT : END or BEGIN
Card 2
( ) = 1.02693452
0.26
= 1.2190…
1.02693452 (1 +
12 )
1 1+
0.08
12
N=4
4
I% = 8
8
PV = −1
PMT = 0
FV = 1.026…
P Y = 12
C Y = 12
PMT : END or BEGIN
N=8
I% = 26
PV = −1.026…
PMT = 0
FV = 1.2190…
P Y = 12
C Y = 12
PMT : END or BEGIN
Page 4
Foundations of Mathematics 12 – Resource Exam A
6. Consider the performance of the following two investment portfolios over the last year.
Amount
Rate of Return
(compounded annually)
GIC
$3000
3%
Mutual Fund
$8000
12%
Amount
Rate of Return
(compounded annually)
Naomi’s Investment
Jacob’s Investment
GIC
$5000
Mutual Fund
$9000
5.5%
10%
Which portfolio, Naomi’s or Jacob’s, has the greatest average annual rate of return over the last
year and by how much?
A.
B.
C.
D.
Jacob by 0.25%
Jacob by 0.5%
Naomi by 1.15%
Naomi by 2%
7. Hardeep just moved to California and needs a new car. She has $800 a month in her budget for
transportation. She knows that insurance for her new car will be $1444 per year. She estimates
she will spend $300 a month on gas.
Lease Offers
Finance Offers
Lease Term
Residual
Monthly Payment
Finance Term
Monthly Payment
24 months
$4019
$496
48 months
$342
48 months
$2623
$282
60 months
$279
With no down payment, which offer best allows Hardeep to purchase the car with the lowest price
and stay within her budget?
A.
B.
C.
D.
lease for 24 months
lease for 48 months
finance for 48 months
finance for 60 months
For questions involving leases, students will be expected to use the following formula:
Totalpaid on lease = Buyout + Down payment + Number of payments × Monthly payment
Calculations involving leases will be limited to this formula. Lease-end value may also be
referred to as residual value, buyout value, etc.
Foundations of Mathematics 12 – Resource Exam A
Page 5
8. Yolanda invests $1000 every year for 3 years. The interest rate is 10% per annum compounded
annually. She tries two strategies to calculate the value of her investment after 3 years:
Strategy 1
Strategy 2
N=3
I% = 10
PV = 0
PMT = −1000
FV = 3310
($1000 × 1.103 ) + ($1000 × 1.102 ) + ($1000 × 1.10 ) = $3641
P Y =1
C Y =1
PMT : END
Which of the following statements about Yolanda’s work is true?
A.
B.
C.
D.
Strategy 1 is incorrect because PMT should be BEGIN.
Strategy 1 is incorrect because it should be P/Y = 12 , C/Y = 12 , and N = 36 .
Strategy 2 is incorrect because 10% does not equal 1.10.
Yolanda has made mistakes in both calculations.
Investments at regular intervals are made at the beginning of each investment period.
This results in interest being earned as soon as the investment is made.
9. For an assignment, Sandra created several 3 by 3 magic squares. Which magic square below
is not correct?
A.
C.
Page 6
2
7
6
9
5
4
B.
8
1
6
1
3
5
7
3
8
4
9
2
6
1
8
4
9
2
7
5
3
1
6
8
2
9
4
7
3
5
D.
Foundations of Mathematics 12 – Resource Exam A
10. Which of the following items is the best continuation of the sequence below?
I.
II.
III.
IV.
A.
B.
C.
D.
Foundations of Mathematics 12 – Resource Exam A
V.
?
Page 7
11. Given the Venn diagram below, which statement correctly describes the shaded region?
X
Y
Z
A.
B.
C.
D.
Page 8
X ∩ Y ∩ Z′
X ∩ Y ∪ Z′
X∩Y∩Z
X∪Y∪Z
Foundations of Mathematics 12 – Resource Exam A
12. Christie is using a search engine on the Internet. She types the following:
bingle
Search Me
snowboard store + “British Columbia”
Which of the following Venn diagrams illustrates the information she will receive?
A.
Snowboard
B.
Snowboard
Store
Store
British Columbia
C.
British Columbia
Snowboard
D.
Snowboard
Store
British Columbia
Foundations of Mathematics 12 – Resource Exam A
Store
British Columbia
Page 9
The following examples demonstrate the convention that will be used for questions involving
an internet search.
Snowboard
snowboard store = snowboard OR store
Store
Snowboard
snowboard + store = snowboard AND store
Store
Snowboard
snowboard – store = snowboard and NOT store
Store
“British Columbia” will search Web pages where both words appear next to each other.
13. Camillo is asked to sort the elements of the set {10 , 15 , 20 , 25 , 30 , 35 , 40} into multiples of
two (set T) and multiples of five (set F).
T
F
Camillo uses the Venn diagram shown above to identify the empty set. How does he describe the
empty set?
A.
B.
C.
D.
Page 10
set T and set F
set T and not set F
set F and not set T
There is no empty set.
Foundations of Mathematics 12 – Resource Exam A
14. Gina claims that the converse of a true “if then” statement is false. As an example she chooses the
following statement: “If something is a banana, then it is a fruit.” Here is her explanation:
Statement
Converse
If something is a banana,
then it is a fruit.
Counterexample demonstrating
the converse is not true
If something is a fruit,
then it is a banana.
Fruit
Bananas
Bananas
nanas
Ba
Fruit
Fruit
Broccoli
Diagram I
Diagram II
Diagram III
Describe the flaw in her explanation, if any.
A.
B.
C.
D.
Her flaw is in diagram I because the diagram does not represent the given statement.
Her flaw is in diagram II because it does not represent the converse of the given statement.
Her flaw is in diagram III because the counterexample should be a fruit.
There is no flaw in her argument.
15. Andrew wrote the statements shown below:
Statement I:
If a student has 90% on his exam, then he passes
the course.
Statement II:
If a student does not get 90% on his exam, then
he does not pass the course.
How are statements I and II related?
A.
B.
C.
D.
Statement II is the inverse of Statement I.
Statement II is the converse of Statement I.
Statement II is the contrapositive of Statement I.
They are both biconditional statements.
Foundations of Mathematics 12 – Resource Exam A
Page 11
16. The probability of any occurrence of an event can be shown on the number line below.
0.5
0
1
Certain
Impossible
Correctly place the following probabilities of each event on the number line above.
You are writing a math exam right now.
Q. All students writing this test were born in October.
R. The chance that a student guesses a true–false question correctly.
S. The chance that a student guesses a multiple-choice question with four options incorrectly.
P.
Which of the following number lines has the correct placement of the probabilities of each event above?
Q
R
0
S
P
1
0.5
A.
Certain
Impossible
R
0
S
Q
P
1
0.5
B.
Certain
Impossible
Q
S
0
R
P
0.5
1
C.
Certain
Impossible
Q
0
S
P R
0.5
1
D.
Impossible
Page 12
Certain
Foundations of Mathematics 12 – Resource Exam A
17. Which of the following “odds for” and “probability” statements are equivalent?
A.
B.
C.
D.
Odds For
Probability
I.
1:2
1
2
II.
3:2
3
5
III.
4:6
2
5
I only
II only
I and II only
II and III only
If the number of outcomes favourable to an event is m and the number of outcomes
not favourable to an event is n , then:
• the odds in favour (odds for) is m : n
• the odds against is n : m
• The probability the event occurs is
Foundations of Mathematics 12 – Resource Exam A
m
m+n
Page 13
18. An insurance company performed research to determine the number of claims per thousand
people and the number of mortalities per thousand people. The information they collected is
on the following graph:
Life Expectancy – U.S. Single Life
200
180
160
0.028
0.024
Claims per Thousand
140
0.020
120
100
0.016
80
0.012
60
0.008
Mortalities per Thousand (at Age X)
Legend
Claims – bar graph
Mortalities – line graph
40
0.004
20
0
0.000
00 05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110
Years of Age (X)
What are the approximate odds for a person under the age of 50 making a claim?
A.
B.
C.
D.
Page 14
30 : 1000
30 : 970
20 : 980
23 : 1000
Foundations of Mathematics 12 – Resource Exam A
19. Marco represents an entire sample space (S) with the Venn diagram below. Each X represents a
possible outcome for events P and Q.
S
XX
P
XXX
XX
XXXXX
XXXXX
Q
Which statement below is true?
A. Q is the complement of P.
2
.
19
C. P and Q are not mutually exclusive.
B. The probability of P and Q is
D. Event Q is twice as likely to occur as event P.
20. In a biological study on genetically modified mice, 45% have blue eyes, 30% have a short tail
and 20% have both blue eyes and a short tail. What is the probability that a randomly selected
mouse from this study has neither blue eyes nor a short tail?
A. 5%
B. 25%
C. 45%
D. 75%
Foundations of Mathematics 12 – Resource Exam A
Page 15
21. A soccer team has practice jerseys in three different colours. The team bag contains 4 yellow, 6 white
and 5 orange jerseys. Beck randomly gives Jessica and Victoria each a jersey. Which expression
correctly represents the probability that both jerseys are the same colour?
A.
B.
C.
D.
( 42 ) ( 62 ) ( 25 )
( 42 ) + ( 62 ) + ( 25 )
(154 ) (143 ) + (156 ) (145 ) + (155 ) (144 )
(154 ) (154 ) + (156 ) (156 ) + (155 ) (155 )
22. A weatherman reports the probability of rain, P ( R ) , on any one day in Vancouver is 13%.
He then concludes the probability of rain on at least one day of the weekend is 26%.
A mathematician is irate and phones the TV station and tells them they are wrong. Assuming
independence, which expression did the mathematician use to calculate the probability correctly?
A.
(1 − P ( R )) (1 − P ( R ))
B.
P R P R
( ) ( )
C. 1 − P ( R ) P ( R )
( ) ( )
D. 1 − P R P R
23. Rogers Arena has 7 gates. In how many ways can you enter the arena and leave the arena
by a different gate?
A. 7 × 6
B.
7+7
C.
72
D. 7!
Page 16
Foundations of Mathematics 12 – Resource Exam A
24. The librarian asked Tanith to solve the following problem:
She just received 10 unique books and wishes to display all of them side by side in the library
window. How many arrangements could the librarian make with the 10 books?
Tanith wrote the following in her notebook.
Line I.
Line II.
Line III.
The librarian is arranging the books so order is
important.
After the librarian has displayed a book, the librarian
would have one less book to select from.
Therefore, the librarian would have 10! ways to
display the books.
In what line did Tanith make a mistake, if any?
A.
B.
C.
D.
Line 1
Line 2
Line 3
There is no mistake.
25. Karla is attempting to simplify
720!
because her calculator cannot do this calculation.
718! 6!
Steps
I.
720 × 719 × 718!
718! 6!
II.
720 × 719
6!
III.
120 720 × 719
6!
IV.
86 280
In which step is Karla’s first mistake, if any?
A.
B.
C.
D.
Step I
Step II
Step III
There is no mistake.
Foundations of Mathematics 12 – Resource Exam A
Page 17
26. Susan is playing a game of Scrabble. She picks the following 7 tiles from the bag.
In how many ways can she arrange all 7 tiles on her tray?
A.
24
B. 210
C. 420
D. 5040
Page 18
Foundations of Mathematics 12 – Resource Exam A
27. The rules for generating a BINGO card are:
• In the B column, the five squares can contain any number from 1 to 15.
• In the I column, the five squares can contain any number from 16 to 30.
• In the N column, there is a filled-in centre square containing no number. The other squares
in the N column can contain any number from 31 to 45.
• In the G column, the five squares can contain any number from 46 to 60.
• In the O column, the five squares can contain any number from 61 to 75.
• Numbers may not be repeated on any card.
BI N GO
12 17 32 47 72
9 24 34 54 63
4 27
FREE
58 75
8 16 42 53 62
15 29 39 46 66
Which of the following calculations will determine the total number of possible BINGO cards?
A. 15 × 15 × 14 × 15 × 15
B. 15 C5 + 15C5 + 15C4 +
15C5
+
15C5
C.
15 P5
+
15P5
+
15P4
+
15P5
+
15P5
D.
15 P5
×
15P5
×
15P4
×
15P5
×
15P5
Foundations of Mathematics 12 – Resource Exam A
Page 19
28. Oscar is trying to determine the value of 5 C3 by listing the combinations of EFGHI. He
chooses 3 letters at a time and creates the list shown below.
EFG
FEG
GHI
IEG
EFH
FEI
GEH
IGF
EFI
FGH
What is Oscar’s mistake, if any?
A.
B.
C.
D.
Oscar’s list represents permutations instead of combinations.
Oscar’s list is incomplete and he has repeated one of the combinations.
Oscar’s list is incomplete and he has repeated two of the combinations.
There is no mistake. Oscar’s list shows all the combinations for 5 C3 .
29. The game of Euchre uses the 9, 10, Jack, Queen, King and Ace from all four suits. Five cards
are dealt at random to each player. What is the probability that a person is dealt four kings in a
five-card hand?
A. 1.7 × 10 −1
B.
4.7 × 10 −4
C.
9.4 × 10 −5
D. 2.4 × 10 −5
Page 20
Foundations of Mathematics 12 – Resource Exam A
30. What are the characteristics of the following graph?
y
10
5
–10
–5
5
10
x
–5
–10
Sign of Leading
Coefficient
Degree
Number of
x-intercepts
A.
Positive
1
2
B.
Positive
3
3
C.
Negative
2
2
D.
Negative
3
3
Foundations of Mathematics 12 – Resource Exam A
Page 21
31. The table below shows the average price, in dollars, per 1000 cubic feet of natural gas for
residential use in British Columbia from 1985 through 1995.
Year since 1985
Price
0
1
2
3
4
5
6
7
8
9
10
3.68
4.29
5.17
6.06
6.12
6.12
5.83
5.54
5.47
5.64
5.77
Determine the polynomial function that best approximates the data.
A.
y = −4.34x 3 + 62.96x 2 − 296.24x + 454.40
B.
y = −0.06x 2 + 0.70x + 3.89
C.
y = 0.01x 3 − 0.24x 2 + 1.41x + 3.44
D.
y = 0.14x + 4.72
When going over the sample examinations in class, teachers may want to discuss with their
students the following process for selecting a regression model.
Theory
yes
no
Obvious point
match to graph
yes
no
R2
yes
no
Use your
judgement
Page 22
Foundations of Mathematics 12 – Resource Exam A
32. The table below shows the average price, in dollars, per 1000 cubic feet of natural gas for
residential use in British Columbia from 1985 through 1995.
Year since 1985
Price
0
1
2
3
4
5
6
7
8
9
10
3.68
4.29
5.17
6.06
6.12
6.12
5.83
5.54
5.47
5.64
5.77
According to the regression model, how many years after 1985 does the price first reach $8.00?
A.
B.
C.
D.
between 11 and 12 years
between 12 and 13 years
between 13 and 14 years
between 14 and 15 years
Foundations of Mathematics 12 – Resource Exam A
Page 23
33. The average gasoline price in Canada from 1992 to 2008 is shown in the table below.
Number of years
since 1992
Price per
litre (cents)
0
64
4
53
8
58
12
65
16
102
Using cubic regression, predict the price of gasoline in the year 2020.
A.
B.
C.
D.
Page 24
$3.75 to $3.85 per litre
$3.85 to $3.95 per litre
$3.95 to $4.05 per litre
$4.05 to $4.15 per litre
Foundations of Mathematics 12 – Resource Exam A
34. Which of the graphs below could be a graph of the equation y = Ax 2 + Bx + C , where A < 0 ?
y
y
x
A.
y
C.
x
B.
y
x
Foundations of Mathematics 12 – Resource Exam A
D.
x
Page 25
Time (minutes)
°C above
Room Temperature
2
70
3
62
4
53
6
38
8
26
°C Above Room
Temperature
35. The temperature of a cup of coffee is recorded as the coffee cools to room temperature.
The data is shown in the table and graph below.
Time (min)
Which type of function best models this situation and why?
A.
B.
C.
D.
Page 26
exponential because the coffee will not cool below room temperature
exponential or logarithmic because the curve fits the data well in both cases
linear because the coffee cools approximately the same amount every minute
logarithmic because the logarithmic curve fits the data better than the other possibilities
Foundations of Mathematics 12 – Resource Exam A
36. Match the equations with the graphs in the tables below.
()
1
2
Equation I
y=3
Equation III
y = ln x
x
y=
Equation IV
y = ln ( x ) + 6
Graph P
Graph Q
y
–10
y
10
10
5
5
–5
10
5
x
–10
–5
–5
–5
–10
–10
Graph R
Graph S
A.
B.
C.
D.
10
10
5
5
–5
5
10
5
10
x
y
y
–10
1 x
( 2)
3
Equation II
10
5
x
–10
–5
–5
–5
–10
–10
x
Equation I
Equation II
Equation III
Equation IV
Graph R
Graph P
Graph R
Graph P
Graph P
Graph R
Graph P
Graph R
Graph Q
Graph Q
Graph S
Graph S
Graph S
Graph S
Graph Q
Graph Q
Foundations of Mathematics 12 – Resource Exam A
Page 27
37. Amir sees the graph on the left in a newspaper. Amir is curious about the scale choice.
He decides to re-plot the graph with regular intervals, as shown on the right.
Newspaper’s Graph
Amir’s Graph
United States Public Debt
United States Public Debt
$12 000 000 000 000
$100 000 000 000 000
$1 000 000 000 000
$9 000 000 000 000
$10 000 000 000
$6 000 000 000 000
$100 000 000
$3 000 000 000 000
$1 000 000
$10 000
10/11/17
21/09/35
08/04/64
18/02/82
30/12/99
0
10/11/17
21/09/35
08/04/64
18/02/82
30/12/99
Date
Date
What conclusion can Amir draw from the graphs above?
A. The newspaper graph makes the recent increase in debt look less dramatic.
B. The newspaper graph makes the recent increase in debt look more dramatic.
C. After 1950, the newspaper graph shows the debt increases by approximately the same amount
every year.
D. There was no debt before 1964.
This question is an example of a real-world situation that uses the logarithmic scale.
The intent of this course is to try to use many real-world examples that a student may
encounter.
Logarithmic scale is used to make exponential graphs appear linear.
Page 28
Foundations of Mathematics 12 – Resource Exam A
38. Phenytoin is an anti-convulsant drug given to patients with epilepsy. A doctor prescribes this drug
to a patient and tracks the amount of phenytoin in the person’s body for one week.
Day
Amount of drug (mg)
1
3
5
7
300
327.47
340.24
348.65
The doctor knows that the daily maximum amount of a drug in the bloodstream over a short
period of time is approximately logarithmic. Determine the amount of Phenytoin in the
bloodstream on day 4.
A.
B.
C.
D.
329.09 mg
333.86 mg
334.66 mg
335.05 mg
Although theory suggests that the relationship should be exponential, the exponential
regression available to students is limited to y = ab x , where a > 0 and b > 0 . Because theory
suggests the data will level off (to a maintenance level), the logarithmic equation should not
be extrapolated much beyond the data.
39. Yumi invests $4000 with a bank. The value of her investment can be determined using the
formula y = 4000 (1.06 )t , where:
• y is the value of the investment at time t
• t is the time in years
Approximately how long will it take for Yumi’s investment to reach a value of $20 000?
A.
B.
C.
D.
15 to 20 years
20 to 25 years
25 to 30 years
more than 30 years
Students are not expected to use logarithmic operations to solve for unknown exponents.
Foundations of Mathematics 12 – Resource Exam A
Page 29
40. Matt’s blood pressure is recorded every 0.2 seconds.
Time (seconds)
Blood Pressure (mm of Hg)
0.0
108
0.2
122
0.4
86
0.6
107
0.8
123
1.0
86
1.2
106
After collecting the data, plotting points and finding the regression equation, Matt decides to
research blood pressure on the Internet. He learns that:
• Systolic refers to the highest point of blood pressure.
• Diastolic refers to the lowest point of blood pressure.
He also finds a chart that categorizes people by their blood pressure.
Rating
Systolic
Diastolic
Optimal
< 120
< 80
Normal
< 130
< 85
High Normal
130–139
85–89
Hypertension Stage 1
140–159
90–99
Hypertension Stage 2
160–179
100–109
Hypertension Stage 3
> 179
> 109
What category does Matt fit into?
A.
B.
C.
D.
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Optimal
Normal
High Normal
Hypertension (Stage 1)
Foundations of Mathematics 12 – Resource Exam A
41. The pressure, P, of a sound wave from a certain tuning fork can be modelled by
P = 0.0005 sin ( 2765t − 1000 ) + 100 , where:
• P is the pressure in kilopascals
• t is the time in seconds
The graph of the sound wave’s pressure over time is shown below.
Pressure (kPa)
100.001
99.999
0
0.001
0.005
Time (sec)
What is the sound wave’s frequency (number of cycles per second)?
A.
B.
C.
D.
between 100 and 300 cycles per second
between 300 and 500 cycles per second
between 500 and 700 cycles per second
more than 700 cycles per second
Foundations of Mathematics 12 – Resource Exam A
Page 31
42. Which of the following graphs best models the height of the point H on the bicycle tire as the bike
rolls forward?
H
Height
B.
Height
A.
Time
Time
D.
Height
Height
C.
Time
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Time
Foundations of Mathematics 12 – Resource Exam A
43. A typical wind turbine has blades that are 30 m long set on a tower which is 80 m high.
An equation which represents the height, h, of the top of one of the blades as a function
of time, t, in seconds, is given by h = 30 sin (1.5707t ) + 80 .
30 m
80 m
Determine the amplitude and maximum value of this sinusoidal function.
Amplitude
Maximum Value
A.
30 m
80 m
B.
30 m
110 m
C.
80 m
110 m
D.
110 m
80 m
Foundations of Mathematics 12 – Resource Exam A
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44. What are the characteristics of the function y = 3 sin
( 12 x ) ?
Amplitude
Mid-line
Period
A.
3
0
4π
B.
1
2
3
2π
C.
0
1
2
3
D.
3
0
1
2
This is the end of the multiple-choice section.
Answer the remaining questions directly in the Response Booklet.
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Foundations of Mathematics 12 – Resource Exam A