2013fom12_a_mc

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 1012 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.

Foundations of Mathematics 12 Resource Exam A Page 1

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. house B. power boat C. big-screen TV D. dining-room set

Foundations of Mathematics 12 Resource Exam A

2. Jackie is considering investing $3000 into a high-risk account. Her financial planner shows her a graph of how her money would grow.

1000

2000

3000

4000

5000

6000

7000

2 3 4 510

y

x

Years

Value of Investment over Time

Valu

e of

Inves

tmen

t ($)

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. Divide the annual interest rate by 72. B. Divide 72 by the annual interest rate. C. Multiply the annual interest rate by 72. D. Double the annual interest rate and multiply by 72.


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 Card 2 A. 18.25% 20% B. 19.86% 21.90% C. 19.86% 20% D. 18.25% 17%


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 Strategy 3

Card 1

0.05 365 = 18.25

1 1+ 0.182512( )12

= 1.1985

N = 12

I% = 0.05 365PV = 1PMT = 0

FV = 1.1985P Y = 12

C Y = 12

PMT : END or BEGIN

eff 18.25, 12( ) = 1.1985

Card 2

1 1+ 0.0812( )4= 1.02693452

1.02693452 1+ 0.2612( )8= 1.2190

N = 4

I% = 8

PV = 1PMT = 0

FV = 1.026

P Y = 12

C Y = 12

PMT : END or BEGIN

N = 8

I% = 26

PV = 1.026PMT = 0

FV = 1.2190

P Y = 12

C Y = 12

PMT : END or BEGIN


6. Consider the performance of the following two investment portfolios over the last year.

Naomis Investment

Amount Rate of Return

(compounded annually) GIC $3000 3% Mutual Fund $8000 12%

Jacobs Investment

Amount Rate of Return

(compounded annually) GIC $5000 5.5% Mutual Fund $9000 10%

Which portfolio, Naomis or Jacobs, has the greatest average annual rate of return over the last year and by how much?

A. Jacob by 0.25% B. Jacob by 0.5% C. Naomi by 1.15% D. 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. lease for 24 months B. lease for 48 months C. finance for 48 months D. 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 paymentsMonthly payment

Calculations involving leases will be limited to this formula. Lease-end value may also be referred to as residual value, buyout value, etc.


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 = 1000FV = 3310

P Y = 1

C Y = 1

PMT : END

$1000 1.103( ) + $1000 1.102( ) + $1000 1.10( ) = $3641

Which of the following statements about Yolandas work is true?

A. Strategy 1 is incorrect because PMT should be BEGIN. B. Strategy 1 is incorrect because it should be P/Y = 12 , C/Y = 12 , and N = 36 . C. Strategy 2 is incorrect because 10% does not equal 1.10. D. 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. 2 7 6

9 5 14 3 8

B. 8 1 6

3 5 74 9 2

C. 6 1 8

7 5 32 9 4

D. 4 9 2

1 6 8

7 3 5


10. Which of the following items is the best continuation of the sequence below?

I.

II.

III.

IV.

V. ?

A.

B.

C.

D.


11. Given the Venn diagram below, which statement correctly describes the shaded region?

X Y

Z

A. X Y Z B. XY Z C. XY Z D. XY Z


12. Christie is using a search engine on the Internet. She types the following:

bingleSearch Mesnowboard store + British Columbia

Which of the following Venn diagrams illustrates the information she will receive?

A.

Snowboard

Store

British Columbia

B.

Snowboard

Store

British Columbia

C.

Snowboard

Store

British Columbia

D.

Snowboard

Store

British Columbia


The following examples demonstrate the convention that will be used for questions involving an internet search. Snowboard

snowboard store = snowboard OR storeStore

Snowboard

snowboard store = snowboard and NOT storeStore

Snowboard

snowboard + store = snowboard AND storeStore

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. set T and set F B. set T and not set F C. set F and not set T D. There is no empty set.


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 Counterexample demonstrating

the converse is not true

If something is a banana, then it is a fruit.

Fruit

Bananas

Diagram I

If something is a fruit, then it is a banana.

Bananas

Fruit

Diagram II

Bananas

Fruit

Broccoli

Diagram III

Describe the flaw in her explanation, if any.

A. Her flaw is in diagram I because the diagram does not represent the given statement. B. Her flaw is in diagram II because it does not represent the converse of the given statement. C. Her flaw is in diagram III because the counterexample should be a fruit. D. 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. Statement II is the inverse of Statement I. B. Statement II is the converse of Statement I. C. Statement II is the contrapositive of Statement I. D. They are both biconditional statements.


16. The probability of any occurrence of an event can be shown on the number line below.

Impossible

0 1

Certain

0.5

Correctly place the following probabilities of each event on the number line above.

P. 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 truefalse question correctly. S. The chance that a student guesses a multiple-choice question with four options incorrectly.

Which of the following number lines has the correct placement of the probabilities of each event above?

A. Impossible

0 1

Certain

0.5Q PR S

B. Impossible

0 1

Certain

0.5Q PR S

C. Impossible

0 1

Certain

0.5PRSQ

D. Impossible

0 0.5 1

Certain

P RSQ


17. Which of the following odds for and probability statements are equivalent?

Odds For Probability

I. 1 : 2 12

II. 3 : 2 35

III. 4 : 6 25

A. I only B. II only C. I and II only D. 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

mm+n


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

Years of Age (X)

Clai

ms

per T

hous

and

Mortalities per Thousand (at Ag

e X)

0.028

20

00500 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110

40

60

80

100

120

140

160

180

200

0.024

0.020

0.016

0.012

0.008

0.004

0.000

LegendClaims bar graphMortalities line graph

What are the approximate odds for a person under the age of 50 making a claim?

A. 30 : 1000 B. 30 : 970 C. 20 : 980 D. 23 : 1000


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

X XX X

X X

X X

X

X X XX XX X X

P

Q

Which statement below is true?

A. Q is the complement of P. B. The probability of P and Q is 219 . C. P and Q are not mutually exclusive. 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%


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. 24( ) 26( ) 25( ) B. 24( ) + 26( ) + 25( ) C. 415( ) 314( ) + 615( ) 514( ) + 515( ) 414( ) D. 415( ) 415( ) + 615( ) 615( ) + 515( ) 515( )

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!


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. The librarian is arranging the books so order is important.

Line II. After the librarian has displayed a book, the librarian would have one less book to select from.

Line III. Therefore, the librarian would have 10! ways to display the books.

In what line did Tanith make a mistake, if any?

A. Line 1 B. Line 2 C. Line 3 D. There is no mistake.

25. Karla is attempting to simplify 720!718! 6! because her calculator cannot do this calculation.

Steps

I. 720 719 718!718! 6!

II. 720 7196!

III. 120 720 7196!

IV. 86 280

In which step is Karlas first mistake, if any?

A. Step I B. Step II C. Step III D. There is no mistake.


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


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.

B I N G O12 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. 15C5 + 15C5 + 15C4 + 15C5 + 15C5 C. 15P5 + 15P5 + 15P4 + 15P5 + 15P5 D. 15P5 15P5 15P4 15P5 15P5


28. Oscar is trying to determine the value of 5C3 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 Oscars mistake, if any?

A. Oscars list represents permutations instead of combinations. B. Oscars list is incomplete and he has repeated one of the combinations. C. Oscars list is incomplete and he has repeated two of the combinations. D. There is no mistake. Oscars list shows all the combinations for 5C3 .

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. 1.7 101 B. 4.7 104 C. 9.4 105 D. 2.4 105


30. What are the characteristics of the following graph?

y

x5

5

5

510

10

10

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


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 0 1 2 3 4 5 6 7 8 9 10 Price 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 = 4.34x3 + 62.96x2 296.24x + 454.40 B. y = 0.06x2 + 0.70x + 3.89 C. y = 0.01x3 0.24x2 +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

R2

Obvious point match to graph

Use your judgement

yes

yes

yes

no

no

no


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 0 1 2 3 4 5 6 7 8 9 10 Price 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. between 11 and 12 years B. between 12 and 13 years C. between 13 and 14 years D. between 14 and 15 years


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. $3.75 to $3.85 per litre B. $3.85 to $3.95 per litre C. $3.95 to $4.05 per litre D. $4.05 to $4.15 per litre


34. Which of the graphs below could be a graph of the equation y = Ax2 + Bx +C , where A < 0 ?

A.

y

x

B.

y

x

C.

y

x

D.

y

x


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 (minutes) C above Room Temperature 2 70 3 62 4 53 6 38 8 26

Which type of function best models this situation and why?

A. exponential because the coffee will not cool below room temperature B. exponential or logarithmic because the curve fits the data well in both cases C. linear because the coffee cools approximately the same amount every minute D. logarithmic because the logarithmic curve fits the data better than the other possibilities

Time (min)

C

A

bove

Roo

mTe

mpe

ratu

re


36. Match the equations with the graphs in the tables below.

Equation I y = 3 12( )x

Equation II y = 13 2( )x

Equation III y = ln x Equation IV y = ln x( ) + 6

Graph P Graph Q

y

x5

5

5

510

10

10

10

y

x5

5

5

510

10

10

10

Graph R Graph S

y

x5

5

5

510

10

10

10

y

x5

5

5

510

10

10

10

Equation I Equation II Equation III Equation IV A. Graph R Graph P Graph Q Graph S B. Graph P Graph R Graph Q Graph S C. Graph R Graph P Graph S Graph Q D. Graph P Graph R Graph S Graph Q


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.

Newspapers Graph Amirs Graph

$10 00021/09/35

United States Public Debt

10/11/17 30/12/9918/02/8208/04/64

$1 000 000

$100 000 000

$10 000 000 000

$1 000 000 000 000

$100 000 000 000 000

Date

0

United States Public Debt

Date

$3 000 000 000 000

$6 000 000 000 000

$9 000 000 000 000

$12 000 000 000 000

21/09/3510/11/17 30/12/9918/02/8208/04/64

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.


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 persons body for one week.

Day 1 3 5 7 Amount of drug (mg) 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. 329.09 mg B. 333.86 mg C. 334.66 mg D. 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 Yumis investment to reach a value of $20 000?

A. 15 to 20 years B. 20 to 25 years C. 25 to 30 years D. more than 30 years

Students are not expected to use logarithmic operations to solve for unknown exponents.


40. Matts 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 130139 8589 Hypertension Stage 1 140159 9099 Hypertension Stage 2 160179 100109 Hypertension Stage 3 > 179 > 109

What category does Matt fit into?

A. Optimal B. Normal C. High Normal D. Hypertension (Stage 1)


41. The pressure, P, of a sound wave from a certain tuning fork can be modelled by P = 0.0005sin 2765t 1000( ) +100 , where: P is the pressure in kilopascals t is the time in seconds

The graph of the sound waves pressure over time is shown below.

0

100.001

99.999

0.0050.001

Pres

sure

(kPa

)

Time (sec)

What is the sound waves frequency (number of cycles per second)?

A. between 100 and 300 cycles per second B. between 300 and 500 cycles per second C. between 500 and 700 cycles per second D. more than 700 cycles per second


42. Which of the following graphs best models the height of the point H on the bicycle tire as the bike rolls forward?

H

A.

Hei

ght

Time

B.

Hei

ght

Time

C.

Hei

ght

Time

D.

Hei

ght

Time


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 .

80 m

30 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


44. What are the characteristics of the function y = 3sin 12 x( ) ?

Amplitude Mid-line Period

A. 3 0 4

B. 12 3 2

C. 0 12 3

D. 3 0 12

This is the end of the multiple-choice section. Answer the remaining questions directly in the Response Booklet.

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2013fom12_a_mc