Mid Year Review 2019 Name: - MS. PETERSON · Mid Year Review – 2019 ... Identify the choice that...

Mid Year Review – 2019 Name:________________

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Determine the future value of a simple interest investment with a 6-year term on a principal of

$150 at 2.8%.

A. $180.50

B. $175.20

C. $402.00

D. $154.30

____ 2. Determine the interest earned on a simple interest investment where 2.3% interest is paid daily for

1 year on $500.

A. $230

B. $1150

C. $23

D. $11.50

____ 3. Aster invested $790 for 5 years. At the investment’s maturity, its value was $1090.20. What was

the annual simple interest rate?

A. 9.7%

B. 9.1%

C. 8.4%

D. 7.6%

____ 4. Devon invested $270 at 1.95% simple interest. At the investment’s maturity, its value was

$364.77. How long was the money invested?

A. 11 years

B. 14 years

C. 18 years

D. 17 years

____ 5. Jacob has $30 000 to invest for 5 years. Which investment option will earn him more interest?

How much more interest?

A. 6.2% simple interest, paid monthly

B. 4.2% compound interest, paid annually

A. Option B: $488.30

B. Option A: $2448.10

C. Option B: $230.10

D. Option A: $2303.23

____ 6. How many compounding periods are there for $1000 invested for 6 years at 4.2% compounded

semi-annually?

A. 6

B. 12

C. 42

D. 6000

____ 7. Which line of the table shows the correct values for i and n?

Compound

Interest Rate

per Annum (%)

Compounding

Frequency

Term

Interest Rate per

Compounding

Period, i (%)

Number of

Compounding

Periods, n

5.4 semi-annually 3 years 0.018 6

3.7 weekly 6 months 0.000 711... 104

0.9 monthly 4.5 years 0.0075 48

2.25 quarterly 7 years 0.005 625 28

A. Line 1

B. Line 2

C. Line 3

D. Line 4

____ 8. Use the Rule of 72 to estimate the investment’s doubling time and then determine the actual

doubling time.

Principal (P)

($)

Compound

Interest Rate

per Annum (%)

Compounding

Frequency

Term

24 000 5 semi-annually 20 years

A. 14.4 years; 13.95 years

B. 14.4 years; 14.04 years

C. 14.4 years; 13.86 years

D. 14.4 years; 14.21 years

____ 9. Determine the present value of a 3-year CSB with an interest rate of 3.9%, compounded

semi-annually, if the future value is $2000.

A. $1786.43

B. $1814.49

C. $1779.51

D. $1781.18

____ 10. Determine the interest earned on a 10-year investment with an interest rate of 5.4%, compounded

annually, if the future value is $80 000.

A. $32 719.30

B. $33 310.31

C. $33 605.82

D. $32 837.50

____ 11. Determine the future value of monthly payments of $200 into an account that pays 4.6% interest,

compounded monthly, for 15 years.

A. $56 879.79

B. $46 538.01

C. $64 636.13

D. $51 708.90

____ 12. Determine the future value of quarterly payments of $1000 into an account that pays 5.1% interest,

compounded quarterly, for 19 years.

A. $126 997.25

B. $133 347.11

C. $122 552.35

D. $123 822.32

____ 13. Regular semi-annual payments of $400 are deposited into an account paying 6.15% interest,

compounded semi-annually. If the final value of the account is $46 000, how long was the money

invested?

A. 26.84 years

B. 25.33 years

C. 24.96 years

D. 24.17 years

____ 14. This portfolio was started 10 years ago. What is the current value of the portfolio?

• Semi-annual deposits of $3000 into an account averaging 3.4%, compounded semi-annually

• A $25 000 bond earning 7.8%, compounded monthly

A. $120 534.88

B. $122 183.68

C. $124 430.38

D. $125 153.18

____ 15. This portfolio was started 25 years ago. What is the current value of the portfolio?

• Quarterly deposits of $650 into an account earning 3.25%, compounded quarterly

• A $15 000 investment averaging 4.5%, compounded annually

A. $138 653.40

B. $140 970.05

C. $142 368.70

D. $144 773.40

____ 16. This portfolio was started 12 years ago. What is the portfolio’s current rate of return?

• A 12-year $8000 GIC that earns 3.65%, compounded quarterly

• Monthly deposits of $325 into an account earning 2.75%, compounded monthly

A. 31.94%

B. 39.21%

C. 25.92%

D. 23.62%

____ 17. Oleg took out a $16 000 loan from the bank to pay for school. The bank offered him an interest

rate of 5.6%, compounded quarterly. The loan is to be repaid in 3 years. How much interest did

Oleg need to pay?

A. $2688.00

B. $2904.95

C. $2841.34

D. $2919.59

____ 18. A loan worth $10 000 is due in 5 years. Which compounding period will result in the highest

amount of interest?

A. annually

B. quarterly

C. monthly

D. daily

____ 19. Carlos was approved for a mortgage to finance his new house that he purchased for $325 000. He

made a down payment that was 20% of the purchase price. The mortgage is compounded

semi-annually at an interest rate of 4.2%. Carlos will repay the mortgage in 25 with regular

monthly payments. How much was the down payment?

A. $65 000

B. $260 000

C. $13 650

D. $32 500

____ 20. Dante wants to buy a truck that costs $35 000 and he has a two different options to finance the

purchase.

Option A: Finance the purchase through the dealership by making regular weekly payments for 4

years at an interest rate of 5.0%, compounded daily.

Option B: Finance the purchase with a bank loan by making regular monthly payments for 4 years

at an interest rate of 5.0%, compounded daily.

What is the total cost of the cheaper option?

A. $42 744.99

B. $38 634.90

C. $42 731.34

D. $38 696.89

____ 21. Garrick is purchasing equipment for his job as a builder. The equipment costs $1000 and he wants

to make monthly payments of $125. He has two different credit cards that he can use to finance the

purchase.

• Card A charges 9.9%, compounded daily, but it also charges a fee of $65 for all purchases over

$1000 that is immediately added to the balance.

• Card B charges 13.3%, compounded daily.


A. $1053.24

B. $1109.01

C. $1125.00

D. $1000.00

____ 22. Joanna needs to buy textbooks for school that cost $780. She cannot afford them now but she has

two different options to finance the cost.

Option A: Get a loan from her friend that must be paid back in 3 months with a $50 fee.

Option B: Use her credit card which charges 18.8%, compounded daily. She plans to make the

minimum monthly payment of $10 on the debt for 3 months, then pay off the remaining debt in

full.

What annual interest rate does the fee in Option A equate to if you assume the interest compounds

monthly?

A. 25.1%

B. 25.6%

C. 28.2%

D. 6.4%

____ 24. Soloman bought a used car for $12 000 during a sale. The sale was that as long as the debt was

paid off in three years, no interest would be charged. Otherwise, a penalty equal to an interest rate

of 10.5%, compounded monthly, would be charged, starting from when he first borrowed the

money. If he missed the deadline by 1 month, how much more would he have to pay than if he

made the deadline?

A. $16 420.60

B. $4564.28

C. $4420.60

D. $16 564.28

____ 25. 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 interest

rate of 5.2%, compounded monthly, and a down payment of $3700. He would pay off this loan

with regular monthly payments. He can also rent a car at $75 per day. What is the total cost of

leasing the car?

A. $10 800

B. $18 500

C. $14 900

D. $12 600

____ 26. 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 interest

rate of 5.2%, compounded monthly, and a down payment of $3700. He would pay off this loan

with regular monthly payments. He can also rent a car at $75 per day. What is the total cost of

renting the car for 3 years?

A. $27 375

B. $86 225

C. $54 750

D. $82 125

____ 27. Jace needs special equipment for his job as a landscaper. He has two options. He can buy the

equipment which costs $9600. Jace will finance this purchase through the vendor by making

regular monthly payments over 4 years at an interest rate of 6.2%, compounded monthly. At the

end of the 4 years, the equipment will be worthless. He can also lease the equipment at a cost of

$180 per month. Both options require a down payment of $750. What is the total cost of the

cheaper option?

A. $9390.00

B. $10 765.44

C. $10 015.44

D. $7890.00

____ 28. Jasmine needs a car. She has two different options. She can rent a car for $225 per month for three

years. She can also buy a new car for $21 000. She will finance the purchase through the

dealership by making regular monthly payments over 9 years at an interest rate of 4.9%,

compounded monthly. If she purchases the car, she will sell it after three years at market value.

The car depreciates at a rate of 25%. In both options, she must make a down payment of $1200.


A. $9300.00

B. $14 657.02

C. $9375.17

D. $8100.00

____ 29. Determine the degree of this polynomial function:

f(x) = x3 + 6x – 8

A. 0

B. 1

C. 2

D. 3

____ 30. Determine the number of turning points of this polynomial function:

f(x) = x2 – 5x – 1

A. 0

B. 1

C. 2

D. 3

____ 31. Determine the equation of this polynomial function:

A. f(x) = –x2 – 3x – 1

B. g(x) = x2 – 2x + 1

C. h(x) = –x3 – 2x2 + 1

D. j(x) = x3 + 2x

____ 32. Fill in the blanks to describe the end behaviour of this polynomial function:

The curve extends from quadrant ____ to quadrant ____.

A. II; I

B. II; IV

C. III; I

D. III; IV

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

____ 33. Fill in the blanks to describe the end behaviour of this polynomial function:

The curve extends from quadrant ____ to quadrant ____.

A. II; I

B. II; IV

C. III; I

D. III; IV

____ 34. The growth of a tree can be modelled by the function

h(t) = 2.3t + 0.45

where h represents the height in metres and t represents the time in years.

Approximately how tall will the tree be in 8 years?

A. 18.85 m

B. 17.15 m

C. 19.55 m

D. 16.75 m

____ 35. Use a ruler to help you estimate the y-intercept for a line that best approximates the data in the

scatter plot.

A. 12

B. 16

C. 20

D. 0

____ 36. Describe the characteristics of the trend in the data.

A. increasing

B. decreasing

C. constant

D. no trend

____ 37. Determine the equation of the cubic regression function for the data.

x 2 4 7 10 12 13 17 19

y 135 120 105 102 99 88 78 47

A. y = 0.05x3 – 1.5x2 – 16x + 162.5

B. y = –0.05x3 + 1.5x2 – 16x + 162.5

C. y = 0.05x3 + 1.5x2 + 16x – 162.5

D. y = –0.05x3 + 1.5x2 + 16x – 162.5

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

2 4 6 8 10 12 14 16 18 x

2

4

6

8

10

12

14

16

18

20y

2 4 6 8 10 x

100

200

300

400

500

600

700

800

900

1000y

____ 38. Determine the equation of the cubic regression function for the data.

x 0 2 3 3 6 8 11 12 12

y 18.5 26.7 31.3 32.8 41.5 45.0 48.3 47.6 49.1

A. y = 1.4x3 + 0.2x2 – 5.1x + 18.3

B. y = –1.4x3 + 0.2x2 + 5.1x + 18.3

C. y = 1.4x3 – 0.2x2 – 5.1x + 18.3

D. y = –1.4x3 – 0.2x2 + 5.1x + 18.3

____ 39. Use quadratic regression to interpolate the value of y when x = 5.

x 0 2 3 3 4 6 7 7

y 17.5 30.3 30.8 31.5 25.0 8.3 –7.6 –9.1

A. 17.1

B. 18.1

C. 19.1

D. 20.1

____ 40. Determine the y-intercept of the exponential function h(x) = ex.

A. 0

B. 1

C. 2

D. 4

____ 41. Which option best describes the behaviour of the exponential function h(x) = 0.1(0.1)x?

A. increasing because a > 1

B. decreasing because 0 < a < 1

C. increasing because b > 1

D. decreasing because 0 < b < 1

____ 42. The following data set involves exponential growth. Determine the missing value from the table.

x 0 1 2 3 4 5 6 7

y 3 6 12 24 48 192 384

A. 72

B. 96

C. 104

D. 144

____ 43. The equation of the exponential function that models a data set is

y = 78.20(0.87)x

Interpolate the value of y when x = 5.5.

A. 36.35

B. 46.49

C. 22.50

D. 38.98

____ 44. Which function will have the fastest increase in the y-values?

A. y = ln x

B. y = 9 ln x

C. y = ln x

D. y = 20 ln x

____ 45. Which function will have the fastest decrease in the y-values?

A. y = – ln x

B. y = –2 ln x

C. y = –ln x

D. y = –1.5 ln x

____ 46. Which exponential equation correctly represents the logarithmic equation y = ln 20?

A. 20y = e

B. ey = 20

C. y20 = e

D. ye = 20

____ 47. The equation of the logarithmic function that models a data set is y = 8.2 + 0.7 ln x.

Determine the domain of this function.

A. {x | x R}

B. {x | x > 0, x R}

C. {x | x > 0.7, x R}

D. {x | x > 8.2, x R}

____ 48. The following data set involves logarithmic growth. Determine the missing value.

x 1 2 3 4 6 8

y 0.0 2.0 3.2 5.2 6.0

A. 3.5

B. 4.0

C. 4.4

D. 5.0

____ 49. Match the following graph with its function.

A. y =

B. y =

C. y =

D. y =

____ 50. The equation of the logarithmic function that models a data set is y = 43.9 – 8.7 ln x.

Interpolate the value of y when x = 5.5.

A. y = 23

B. y = 25

C. y = 27

D. y = 29

____ 51. Determine the equation of the logarithmic regression function for the data.

x 1 2 3 4 5 6

y 32.0 19.5 12.2 7.0 3.0 –0.3

A. y = –18 – 32 ln x

B. y = –18 + 32 ln x

C. y = 32 + 18 ln x

D. y = 32 – 18 ln x

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Short Answer

1. Complete the table of values for the function f(x) = 2x.

x f(x)

–3

–2

–1

0

1

2

3

Problem

1.Otis bought a $7500 corporate bond. The bond earns 3%, compounded monthly. After 2 years, the

interest rate changed to 4.5%, compounded annually. Determine the value of Otis’ investment after

8 years. Show your work

2. Judith is investing $2000. She wants it to grow to $2500 in 4 years.

a) What annual rate of interest, compounded annually, does Judith need to meet her goal? Round

your answer to two decimal places. Show your work.

b) How would your answer change if the compounding frequency was daily? Show your work.

3. a) Ed plans to retire in 32 years, when he is 60, and hopes to have $500 000 saved. For each

investment option below, how much does he need to invest at the end of each period to reach his

goal? Show your work.

i) 3.8% compounded monthly ii) 4.05% compounded annually

b) Compare the rate of return for options i) and ii). Which option should he choose?

4. Both Jackson and Raven set up a 20-year investment and want to have $100 000 at the end of the

term. Jackson’s bank pays a rate of 4.25%, compounded monthly. Raven is investing through the

company she works for, at a rate of 4.8%, compounded monthly. Contributions are made at the end

of each month.

a) How much more does Jackson need to invest than Raven over the 20 years? Show your work.

b) Raven decides to make the same payments at the end of each month as Jackson. How much will

she have at the end of the 20 years? Show your work.

5. Susan opened this portfolio when she turned 45.

• Semi-annual deposits of $3000 into an account averaging 3.4%, compounded semi-annually

• A $25 000 bond earning 7.8%, compounded monthly

a) What will be the value of the portfolio when she turns 65? Show your work.

b) When she turns 65, she cashes in the entire portfolio. She keeps $80 000 to travel around the

world for a year and invests the remaining money in an account that pays 7.2%, compounded

quarterly. How much will the account be worth after 3 years? Show your work.

6. A hockey coach want to know the relationship between the number of shots his team takes during

a game and the number of goals they score. She collected the following data from the last few

games.

Shots 11 20 24 28 27 33 17 38

Goals 1 2 0 3 2 3 1 4

a) Create a scatter plot, and determine the line of best fit for the data.

b) Use your graph to estimate the number of shots required to score 3 goals.

7. Aisha screen prints T-shirts for sale at concerts. When buying blank T-shirts, the price Aisha must

pay is related to the size of the order. Four of her previous orders are listed in the table below.

Number of

Shirts

225

310

400

750

Cost per

Shirt ($)

14.90

14.56

14.20

12.80

Aisha has misplaced the information from her supplier about prices on bulk orders. Interpolate the

price per shirt if she orders 625 shirts. Show your work.

8. Ida hit a golf ball from the top of a hill. The height of the ball above the green can be modelled by

the regression equation

h(t) = –9.7t2 + 48.4t + 11.5

where h represent the height in metres and y represents the time in seconds.

a) Use your knowledge of polynomial functions to describe the curve of this function.

b) Determine the y-intercept. What does it represent in this context? Show your work.

c) The roots of this equation are near t = –0.2 and t = 5.2. What do these points represent, if

anything?

9. A research company summarized the average time spent everyday by teenagers on the phone.

Year 1999 2000 2002 2003 2005 2008 2009 2011

Time (min) 45 44 38 40 42 46 40 33

a) Create a scatter plot, and draw a curve of best fit for the data using cubic regression.

b) Use your graph to interpolate the average amount of time spent on the phone in 2006.

c) Do you think your curve of best fit is reasonable for extrapolating values? Explain.

10. Recall that the graph of y = 10x is a reflection of the graph of y = log x about the line y = x.

a) Draw the reflection of y = e–x about the line y = x. Is the reflection a logarithmic function?

Include a diagram and your reasoning.

b) What function might this be a graph of? Explain your reasoning.

Mid Year Review - 2019

Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: Grade 12 REF: Lesson 1.1

OBJ: 1.1 Explain the advantages and disadvantages of compound interest and simple interest.

TOP: Simple interest KEY: simple interest | principal | future value

2. ANS: D PTS: 1 DIF: Grade 12 REF: Lesson 1.1


TOP: Simple interest KEY: simple interest | principal




4. ANS: C PTS: 1 DIF: Grade 12 REF: Lesson 1.1





TOP: Exploring compound interest

KEY: simple interest | compound interest | principal | future value


OBJ: 1.1 Explain the advantages and disadvantages of compound interest and simple interest. |

1.2 Identify situations that involve compound interest. | 1.3 Graph and compare, in a given

situation, the total interest paid or earned for different compounding periods. | 1.8 Solve a

contextual problem that involves compound interest.

TOP: Compound interest: future value KEY: compound interest | compounding period






TOP: Compound interest: future value KEY: compound interest | compounding period






TOP: Compound interest: future value

KEY: compound interest | principal | future value | Rule of 72


OBJ: 1.2 Identify situations that involve compound interest. | 1.8 Solve a contextual problem that

involves compound interest. TOP: Compound interest: present value

KEY: compound interest | future value | present value

10. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 1.4





OBJ: 3.2 Determine, using technology, the total value of an investment when there are regular

contributions to the principal. | 3.5 Determine, using technology, possible investment strategies to

achieve a financial goal. | 3.8 Solve an investment problem.

TOP: Investments involving regular payments

KEY: compound interest | future value














OBJ: 3.1 Determine and compare the strengths and weaknesses of two or more portfolios. | 3.2

Determine, using technology, the total value of an investment when there are regular contributions

to the principal. | 3.3 Graph and compare the total value of an investment with and without regular

contributions. | 3.4 Apply the Rule of 72 to solve investment problems, and explain the limitations

of the rule. | 3.5 Determine, using technology, possible investment strategies to achieve a financial

goal. | 3.6 Explain the advantages and disadvantages of long-term and short-term investment

options. | 3.7 Explain, using examples, why smaller investments over a longer term may be better

than larger investments over a shorter term. | 3.8 Solve an investment problem.

TOP: Solving investment portfolio problems

KEY: compound interest | principal | future value | portfolio











KEY: compound interest | principal | future value | portfolio











KEY: compound interest | principal | future value | portfolio | rate of return




situation, the total interest paid or earned for different compounding periods. | 1.4 Determine,

given the principal, interest rate and number of compounding periods, the total interest of a loan. |

1.5 Graph and describe the effects of changing the value of one of the variables in a situation that

involves compound interest. | 1.6 Determine, using technology, the total cost of a loan under a

variety of conditions; e.g., different amortization periods, interest rates, compounding periods and

terms. | 1.8 Solve a contextual problem that involves compound interest.

TOP: Analyzing loans KEY: loans




















TOP: Analyzing loans KEY: mortgages












OBJ: 1.2 Identify situations that involve compound interest. | 1.7 Compare and explain, using

technology, different credit options that involve compound interest, including bank and store credit

cards and special promotions | 1.8 Solve a contextual problem that involves compound interest.

TOP: Exploring credit card use KEY: credit cards


OBJ: 1.2 Identify situations that involve compound interest. | 1.3 Graph and compare, in a

given situation, the total interest paid or earned for different compounding periods. | 1.4

Determine, given the principal, interest rate and number of compounding periods, the total interest

of a loan. | 1.5 Graph and describe the effects of changing the value of one of the variables in a

situation that involves compound interest. | 1.7 Compare and explain, using technology, different

credit options that involve compound interest, including bank and store credit cards and special

promotions. | 1.8 Solve a contextual problem that involves compound interest.

TOP: Solving problems involving credit KEY: credit cards | loans









TOP: Solving problems involving credit KEY: loans









TOP: Solving problems involving credit KEY: loans


OBJ: 2.1 Identify and describe examples of assets that appreciate or depreciate. | 2.2 Compare,

using examples, renting, leasing and buying. | 2.3 Justify, for a specific set of circumstances, if

renting, buying or leasing would be advantageous. | 2.4 Solve a problem involving renting, leasing

or buying that requires the manipulation of a formula. | 2.5 Solve, using technology, a contextual

problem that involves cost-and-benefit analysis. TOP: Buy, rent, or lease?

KEY: buy | lease | loans | rent







KEY: buy | lease | loans | rent







KEY: buy | lease | loans







KEY: buy | depreciation | loans | rent


OBJ: 1.2 Describe, orally and in written form, the characteristics of polynomial functions by

analyzing their equations. | 1.3 Match equations in a given set to their corresponding graphs.

TOP: Characteristics of the equations of polynomial functions KEY: polynomial functions




TOP: Characteristics of the equations of polynomial functions

KEY: polynomial functions | leading coefficient




TOP: Characteristics of the equations of polynomial functions KEY: polynomial functions





KEY: polynomial functions | end behaviour





KEY: polynomial functions | end behaviour


OBJ: 1.4 Graph data and determine the polynomial function that best approximates the data. | 1.5

Interpret the graph of a polynomial function that models a situation, and explain the reasoning. |

1.6 Solve, using technology, a contextual problem that involves data that is best represented by

graphs of polynomial functions, and explain the reasoning.

TOP: Modelling data with a line of of best fit

KEY: polynomial functions | line of best fit




















TOP: Modelling data with a curve of best fit

KEY: polynomial functions | regression function







KEY: polynomial functions | regression function







KEY: polynomial functions | regression function | interpolate


OBJ: 2.1 Describe, orally and in written form, the characteristics of exponential or logarithmic

functions by analyzing their graph. | 2.2 Describe, orally and in written form, the characteristics of

exponential or logarithmic functions by analyzing their equation. | 2.3 Match equations in a given

set to their corresponding graphs.

TOP: Relating the characteristics of an exponential function to its equation

KEY: exponential function









OBJ: 2.4 Graph data and determine the exponential or logarithmic function that best

approximates the data. | 2.5 Interpret the graph of an exponential or logarithmic function that

models a situation, and explain the reasoning. | 2.6 Solve, using technology, a contextual problem

that involves data that is best represented by graphs of exponential or logarithmic functions, and

explain the reasoning. TOP: Modelling data using exponential functions







explain the reasoning. TOP: Modelling data using exponential functions

KEY: exponential function | regression function | interpolate






TOP: Characteristics of logarithmic functions with base 10 and base e

KEY: logarithmic function







KEY: logarithmic function







KEY: logarithmic function | exponential function






explain the reasoning. TOP: Modelling data using logarithmic functions

KEY: logarithmic function | regression function





















KEY: logarithmic function | regression function | interpolate








SHORT ANSWER

1. ANS:

x f(x)

–3 2–3 = 0.125

–2 2–2 = 0.25

–1 2–1 = 0.5

0 20 = 1

1 21 = 2

2 22 = 4

3 23 = 8

PTS: 1 DIF: Grade 12 REF: Lesson 7.1


functions by analyzing their graph.

TOP: Exploring the characteristics of exponential functions KEY: exponential function

PROBLEM

1. ANS:

First two years: The principal is $7500.

The annual interest rate is 3%.

The compounding period is monthly, or 12 times per year.

The term (in years) is 2.

The future value is unknown.

The value of the investment after three years is $7963.18.

Last six years: The principal is $7963.18.

The annual interest rate is 4.5%.

The compounding period is annual, or 1 time per year.



The total value of the investment after eight years is $10 370.13.






TOP: Compound interest: future value KEY: compound interest | principal | future value

2. ANS:

a) The annual interest rate is unknown.

The compounding period is annual, or 1 time per year.


The present value is $2000.

The future value is $2500.

Judith needs an annual interest rate of 5.74% to meet her goal.

b) The annual interest rate is unknown.

The compounding period is daily, or 365 times per year.


The future value is $2500.

Judith needs an annual interest rate of 5.58% to meet her goal.

The interest rate decreased by 0.16%.





3. ANS:

a), b)

Option i) Option ii)

Future Value ($) 500 000 500 000

Interest Rate per Annum 0.038 0.0405

Periods per Year 12 1

Number of Years 32 32

Regular Payment Amount ($) 668.87 7902.65

Principal 256 846.08 252 884.80

Interest Earned 243 153.92 247 115.20

Rate of Return 94.67% 97.72%

Ed should chose option ii) because he earns more interest on less principal and has a slightly better

rate of return than option i).






KEY: compound interest | principal | future value | rate of return

4. ANS:

a)

Jackson Raven

Future Value ($) 100 000 100 000

Interest Rate per Annum 4.25 4.8

Periods per Year 12 12

Number of Years 20 20

Regular Payment Amount ($) 265.07 248.96

Principal 63 616.80 59 750.40

63 616.80 – 59 750.40 = 3866.40

Jackson needs to invest $3866.40 more over the 20 years.

b) The regular payment amount is $265.07.

The payment frequency is monthly, or 12 times per year.

The number of payments is 240.

The payments are made at the end of each payment period.


The compounding frequency is monthly, or 12 times per year.


Raven will have $106 472.00 at the end of 20 years.






KEY: compound interest | future value | principal

5. ANS:

a) Regular payment investment: The regular payment amount is $3000.

The payment frequency is semi-annual, or 2 times per year.

The number of payments is 40.

The payments are made at the end of each payment period.


The compounding frequency is semi-annual, or 2 times per year.


The investment is worth $169 875.63.

Lump sum investment: The principal is $25 000.


The compounding period is monthly, or 12 times per year.

The term (in years) is 20 years.


The investment is worth $118 371.47.

169 875.63 + 118 371.47 = 288 247.10

The portfolio is worth $288 247.10 when Susan turns 65.

b) 288 247.10 – 80 000 = 208 247.10

The principal is $208 247.10.


The compounding period is quarterly, or 4 times per year.

The term (in years) is 3 years.


The account is worth $257 959.96.











KEY: compound interest | future value | principal | portfolio

6. ANS:

a)

b)

Using the line of best fit, the team should take about 33 shots to score 3 goals.







KEY: polynomial functions | line of best fit | regression function

7. ANS:

I used a spreadsheet to determine the equation of the linear regression function:

C = 15.80 – 0.004t

where C represents the cost per T-shirt and t represents the number of T-shirts.

C = 15.80 – 0.004t

C = 15.80 – 0.004(625)

C = 13.30

The cost per T-shirt should be about $13.30 when she orders 625 shirts.







KEY: polynomial functions | regression function | interpolate

8. ANS:

a) This is a quadratic function with a negative leading coefficient, so it must be a parabola that

opens down (it extends from quadrant III to quadrant IV). It will have a turning point that is a

maximum value, one y-intercept, and up to two x-intercepts.

b) The y-intercept is the value when t = 0.

h(t) = –9.7t2 + 48.4t + 11.5

h(0) = –9.7(0)2 + 48.4(0) + 11.5

h(0) = 11.5

This is the initial height of the ball.

c) The negative root does not have any meaning here since t is time and can only be positive. The

positive root is the time when the ball reaches the green.







KEY: polynomial functions | regression function | curve of best fit

9. ANS:

a)

b)

Using the curve of best fit, the amount of time spent on the phone was about 43.5 min/day.

c) No. The values before and after the data are changing too quickly to be reasonable. The curve

suggests that in 2014 teenagers will stop using phones which is not possible.







KEY: polynomial functions | regression function | curve of best fit | interpolate

10. ANS:

a) I graph the exponential function y = e–x and its reflection.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

The graph of the reflection is decreasing.

It has no y-intercept and an x-intercept of 1.

It has the same domain and range as a logarithmic function.

The reflection is a logarithmic function.

b) The graph of the reflection passes through the point (e, –1). Since ln e = 1, the reflection might

be the graph of y = –ln x.







KEY: logarithmic function | exponential function

Mid Year Review 2019 Name: - MS. PETERSON · Mid Year Review – 2019 ... Identify the choice that...

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