FD12

Year-End Practice Exam: Part I

:KIM

Name:

Block:

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. Determine the interest earned on a simple interest investment with a 15-year term at 5.7% on adeposit of $25 000.

A. $21 250B. $22 500C. $22 125D. $21 375

C 2. Determine the future value and the total interest earned for the investment.

Principal W) Interest Rateper Annum (%)

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35 000 3.7 quarterly 7 years

A. $45 239.99; 10 239.99B. $46 245.18; $11 245.18C. $45 293.23; $10 293.23D. $44 669.12; $9669.12

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3. Use the Rule of 72 to estimate the investment's doubling time.

PrincipailPICompound

Interest Rateper Annum (%) fMF

24 000 4.97 semi-annually 20 years

A. 3.6 yearsB. 14.5 yearsC. 15.0 yearsD. 114.9 years

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4. Yu needs a car. He can lease a car for 3 years for $300 per month and a down payment of $4100.He can purchase a new car for $28 000, which would be financed with a bank loan at an interestrate of 5.2%, compounded monthly, and a down payment of $3700. He would pay off this loanwith regular monthly payments. He can also rent a car at $75 per day. What is the total cost ofrenting the car for 3 years?

A. $27 375 - • v- ¦ ..

B. $86 225C. $54 750D. $81 900

5. What is the meaning of disjoint in set theory?

A. two or more sets having no elements in commonB. two or more sets that do not matchC. sets that are in different universal setsD. sets that contain no elements

6. Which statement is true?

A. The English language and the French language are disjoint sets.B. Hockey equipment and lacrosse equipment are disjoint sets.C. Band instruments and orchestral instruments are disjoint sets.D. Linear equations and quadratic equations are disjoint sets.

7. There are 28 students in Mr. Connelly's Grade 12 mathematics class.The number of students in the yearbook club and the number of students on student council areshown in the Venn diagram. Use the diagram to answer the following questions.

C {Mr. Connelly's class)

Y (yearbook club) S {student council)

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How many students are neither in the yearbook club nor on student council?

A. 2B. 5C. 1D. 20

8. Consider the following two sets:•J = {1,2, 3, 4,5,6, 7, 8, 9, 10, 11, 12}• B = {-9, -6, -3, 0, 3, 6, 9, 12}

Determine n(A u B).¦ *

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C 16 : :D. 20

9. Consider the following two sets:• C = {-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10}

• 5 = {-9,-6,-3, 0, 3, 6, 9, 12}

Determine C nB.K

A. {3,6,9,12}B. {-6,0,6}C. {0}D. {-6, 0, 6,12}

10. A restaurant offers Chinese, Thai, and Korean food. The following Venn diagram shows the typesof food the customers like.

A

Use the diagram to determine n((T n K) u C).

A. 71B. 47C. 55D. 93

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11. Which sentence is the converse to the conditional statement below?"If students are in school, then it is a weekday."

A. If it is a weekday, then students are in school.B. If it is not a weekday, then students are not in school.C. During the week, students are in school.D. Students go to school on weekdays.

12. What is the inverse?

A. a conditional statement in which the hypothesis and the conclusion are switchedB. a statement that is formed by negating both the hypothesis and the conclusion of a

conditional statementC. a statement that is formed by negating both the hypothesis and the conclusion of

the converse of a conditional statement

D. a statement that is formed by inverting both the hypothesis and the conclusion of aconditional statement

13. A combination lock opens with the correct four-letter code. Each wheel rotates through the lettersA to L. Suppose each letter can be used only once in a code. How many different codes arepossible when repetition is not allowed?

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A. 20 736 ' '0 * 122 _-2.. J_

B. 11 880 lC. 1320D. 8976

14. How many possible ways can you draw a single card from a standard deck and get an evennumber? , , ,

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A. 13 ^B. 20C. 21D. 26

15. Identify the expression that is equivalent to the following:

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A. n

B. -n

C. n2

D. n3

16. Suppose a word is any string of letters. How many two-letter words can you make from the lettersin LETHBRIDGE if you do not repeat any letters in the word?

A. 72B. 100C. 81D. 90

_ 17. How many ways can 7 friends stand in a row for a photograph if Sheng always stands beside hisgirlfriend? -

A. 1440 Sr-f..,' y '^r , i

B. 5040 - ^ ^ \

C. 360 yD. 720

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18. How many different arrangements can be made using all the letters in NUNAVUT?

A. 630 y : •B. 1260C. 2520 - ' -

D. 5040

19. The numbers 10 to 16 are written on identical slips of paper and put in a hat. How many ways can2 numbers be drawn simultaneously?" "" " "" "V""- y I *"% ¦" .

A. 21B. 15C. 30D. 42

y 20. How many ways can the 6 starting positions on a hockey team (1 goalie, 2 defense, 3 forwards) befilled from a team of 1 goalie, 4 defense, and 8 forwards?

A. 164 ? "3 v A " ...A

B. 254 ' ' """ ' .

C. 336 ' " ' ¦- -

D. 1716

Short Answer

21. Trahn wants to buy a new sound system but he has only $1000, half the amount he needs. Whencan Trahn buy the sound system if he invests his money at 3.7%, compounded quarterly, to thenearest year?

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22. Harro has invested $160 at the end of each month, at 5.59% compounded monthly, for 7 years.How much interest has he earned?

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23. Jody must now make a single payment of $30 000 to pay off her bank loan, which she borrowed 8years ago. The loan was compounded quarterly at an interest rate of 6.1%. How much did Jodyoriginally borrow?

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24. Vladimir is buying a house that costs $375 000. He has negotiated a mortgage with the bank thatrequires a down payment of 12% of the cost of the house. He will pay off the mortgage withregular monthly payments over 25 years at an interest rate of 2.8%, compounded semi-annually.How much interest will he pay?

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25. Yorgan is buying a scooter for $3700. He cannot afford it now, however his friend has offered toloan him the money. Yorgan must pay back his friend in 1 year with a $300 fee.What annual interest rate does this equate to if you assume the interest compounds quarterly?Round your final answer to the nearest tenth of a percent.

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26. The city surveyed 3000 people about how they travel to work.How many people did not cycle or use public transit? Write your answer using set notation.

• 1978 took public transit (P)• 1494 drove (D)•818 cycled (Q• 895 took public transit and drove• 462 took public transit and cycled•191 drove and cycled• 164 used all three modes of transportation

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27. A baseball coach is determining the batting order for the nine players she is fielding. The coachhas already decided who will bat first and second. How many different batting orders are possible?

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on bicycles find an empty bike rack with exactly eight spots for bikes. How manyeight bikes be parked so that Adya and Moira are parked next to each other?

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Problem

29. Solomon bought a $65 000 corporate bond. The bond earns 4.2%, compounded monthly. After 3years, the interest rate changed to 5.2%, compounded semi-annually. Determine the value ofSolomon's investment after 8 years. Show your work.

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30. Chang borrowed $2000 at 4.1 %, compounded monthly, to pay for school. He will pay off the debtby making regular monthly payments of $146.69.

a) How long will it take Chang to pay off his debt? Show your work.

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b) How much interest will Chang pay? Show your work.

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31. Evaluate the following. Show your work.

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32. Two friends are building stacks of 12 coins. Stack 1 has 5 identical pennies, 3 identical nickels,and 4 identical quarters. Stack 2 has 3 identical pennies, 3 identical nickels, and 6 identicalquarters.

Which set of coins can make more stacks of 12 coins? Show your work.

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33. Three vehicles are taking a choir of 25 students to a recital. A minibus can take 16 students, anSUV can take 6 students, and the remaining 3 students can ride with the choirmaster. How manyways can the 20 students be assigned to the 3 vehicles? Show your work.; ... , ¦¦¦ -

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Answer Section

MULTIPLE CHOICE

1. D

2. C

3. B

4. D

5. A

6. D

7. D

8. C

9. B10. A

11. A12. B13. B14. B15. C16. A17. A18. B19. A20. C

SHORT ANSWER

21. 19 years

22. $2962.74

23. $18483.5524. $128412.00

25. 7.9%

26. n(C u P)' = 666

27. 5040

28. 10 080

PROBLEM

29. FY = $95 282.36.

30. a) 14 monthsb)/= $53.66

31. 1260

32. 27720 arrangements of coins in stack 1

18480 arrangements of coins in stack 2

More arrangements can be made with stack 1.

33. 171 609 900 ways to assign rides to the 25 students