G r a d e 1 2 e s s e n t i a l M a t h e M a t i c s (4 0 s )

Midterm Practice Exam

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G r a d e 1 2 e s s e n t i a l M a t h e M a t i c s

Midterm Practice Exam

Name: ___________________________________

Student Number: ___________________________

Attending q Non-Attending q

Phone Number: ____________________________

Address: _________________________________

__________________________________________

__________________________________________

InstructionsThe midterm examination is based on Modules 1 to 4 of the Grade 12 Essential Mathematics course. It is worth 12.5% of your final mark in this course.

TimeYou will have a maximum of 3.0 hours to complete the midterm examination.

FormatThe format of the examination will be as follows: Module 1: Home Finance 33 marks Module 2: Geometry and Trigonometry 27 marks Module 3: Business Finance 17 marks Module 4: Probability 23 marks Total 100 marks

(see over)

For Marker’s Use Only

Date: _______________________________

Final Mark: ________ /100 = ________ %

Comments:

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Instructions (continued)Resources Provided

The following tables are provided at the end of this examinationn Amortization Tablen Manitoba Homeowner’s Insurance Rates ($500 deductible)n Interest Rate Factor Tablen Local Improvement Costs for Property Tax Credits

Resources Required (Not Provided)

To complete this examination, you will need:n pens/pencils (2 or 3 or each)n blank papern scientific or graphing calculatorn Midterm Exam Resource Sheet (The Midterm Exam Resource Sheet must

be handed in with the exam. You will receive your Midterm Exam Resource Sheet back from your tutor/marker with the next module that is submitted for marking.)

Notesn show all calculations and formulasn include units where appropriaten use decimal places in your calculations and round the final answers to the

correct number of decimal placesn clearly state your final answern diagrams may not be drawn to scale

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Name:

Answer all questions to the best of your ability. Show all your work.

Module 1: Home Finance (33 marks)

1. Alec wants to purchase a home where the monthly mortgage payment would be $739. He has a gross monthly income of $4100. He also knows that the monthly property taxes would be $163 and the monthly heating costs would be around $119. (3 marks)a) Calculate the Gross Debt Service Ratio. (Module 1, Lesson 1)

b) Would the financial institution grant a mortgage in this case? (Module 1, Lesson 1)

2. Haylee would like to purchase a condominium. Haylee has a gross annual income of $59,900. She has saved $19,000 for a down payment. Her financial institution has offered her a 3.5% interest rate on a mortgage amortized over 25 years. Haylee estimates her monthly property taxes will be $119 and her monthly heating costs will be $96. Condo fees are $450 per month. a) Use the chart to calculate the maximum price Haylee can pay for her condominium.

(4 marks) (Module 1, Lesson 1)

Maximum Affordable Home PriceGross monthly household incomeMultiply: (GDSR)Total affordable household expenses Subtract: Monthly property taxes Monthly heating costs One-half of condo/strata fees (if applicable)Monthly affordable mortgage paymentDivide: Interest factor (from Chart 1.1)Amount of affordable mortgageAdd: Cash down paymentMaximum affordable home price

$ $ $

$

$

$

$

$

$

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b) The condominium manager tells Haylee that he will cover emergency repairs, but that she needs to maintain her condo with daily and preventative maintenance. Describe which tasks the manager will complete and which tasks Haylee must do. (2 marks) (Module 1, Lesson 4)

3. The Russell family owns a home with a Boeckh replacement value of $195,000. The home is located in Metro Winnipeg. The family chooses Standard homeowner’s insurance with a deductible of $200. (Module 1, Lesson 3)a) What is the replacement value of a home based on? (1 mark)

b) Calculate the Russell family’s annual insurance premium. (2 marks)

c) Explain the difference between Comprehensive homeowner’s insurance and Standard homeowner’s insurance. (2 marks)

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Name:

4. Chance has just purchased a new home for $360,000. The possession date is October 15th. Annual property taxes are $1989 and they are due on June 30th. Chance’s home insurance is renewed December 1 of each year. He has to increase his home insurance from $300 to $460 per year and pay the difference for the extra months. (Module 1, Lesson 1)a) Calculate Chance’s home insurance adjustment. (3 marks)

b) Calculate Chance’s property tax adjustment. (2 marks)

c) Calculate the land transfer tax. (4 marks)

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5. Kade has purchased a home for $187,900. He makes a down payment of $21,000 and takes out a fixed-rate 25-year mortgage at 2.5% for the balance of the purchase price. (Module 1, Lesson 2)a) Determine the monthly mortgage payments. (2 marks)

b) Calculate the total amount of interest that Kade will pay on his mortgage over 25 years. (2 marks)

c) Calculate the interest on the unpaid balance for the first month. (1 mark)

d) Complete a schedule of mortgage payments for Kade for the first month. (3 marks)

Payment # Payment Interest Principal Unpaid Balance Owner’s Equity

$166,900.00 $21,000.00

1

6. List one benefit of renting an apartment and one benefit of buying a house or condo. (2 marks) (Module 1, Lesson 5)

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Name:

Module 2: Geometry and Trigonometry (27 marks)

1. Find the missing measures indicated. a) Find side a. (3 marks) (Module 2, Lesson 5)

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b) Find side a, and angle B. (3 marks) (Module 2, Lesson 6)

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Name:

2. Two ropes are being used to raise a heavy object from the bottom of a lake. The heavy object (point C) is between points A and B. How far is the heavy object below the surface of the water if the distance between A and B is 6 metres? Round your answer to one decimal place. (5 marks) (Module 2, Lesson 5)

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3. Find the measures in the following parallelogram ABCD. (4 marks) (Module 2, Lesson 3)

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Given: ÐDAB = 35°

segment DE = 4 cm

segment CE = 1.5 times segment BE

Find:a) ÐADC

b) ÐDCB

c) Diagonal length DB

d) Diagonal length AC

4. Describe when the Sine Law may be useful in a construction, industrial, commercial, or artistic application. (2 marks) (Module 2, Lesson 6)

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Name:

5. a) ABCD is a rhombus. Find x and y. (2 marks) (Module 2, Lesson 2)

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b) QRST and RSUV are parallelograms. State why QT is the same length as VU. (2 marks) (Module 2, Lesson 2)

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6. a) State the definition of an equilateral triangle. (1 mark) (Module 2, Lesson 4)

b) Are all equilateral triangles regular polygons? (1 mark)

7. Consider an octagon. (Module 2, Lesson 4)a) A polygon can be divided into a series of triangular regions by drawing diagonals

from one of the vertices. How many triangular regions can be drawn inside an octagon? (1 mark)

b) What is the sum of the interior angles of an octagon? (1 mark)

c) What is the sum of the interior angles of a nonagon? A nonagon has nine sides. (1 mark)

d) Is it possible for the sum of the interior angles of a polygon to be 1980º? How do you know? (1 mark)

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Name:

Module 3: Business Finance (17 marks)

1. State two possible advantages of working in a larger business rather than in a small business. (2 marks) (Module 3, Lesson 1)

2. Leah is trying to determine which small business idea is most feasible in her community as a way to earn money in the summer. Her community is a small town in northern Manitoba with 100 people. Leah is considering the two businesses below and she has asked your advice. Is each of the following two businesses feasible in the community? Explain your answer for both businesses. (2 marks) (Module 3, Lesson 1)a) Lawn Careb) Sports Equipment Rental

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3. Identify three expenses that you may have when operating a small business. You may identify business expenses or capital expenses. (3 marks) (Module 3, Lesson 1)

4. A business plans to produce 600 calendars and sell them for $13 each. The unit cost is $7 per calendar. How many calendars must be sold for the company to reach the break-even point? (1 mark) (Module 3, Lesson 2)

5. Hillary plans to make and sell 200 pairs of earrings. The cost for the metal required to make the earrings is $2050. (Module 3, Lesson 2)a) Will Hillary make a profit if she charges $15.00 per pair of earrings? Justify your

answer. (1 mark)

b) Will Hillary make a profit if she charges $9.00 per pair of earrings? Justify your answer. (1 mark)

c) How much must Hillary charge to break even? (1 mark)

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Name:

6. For a summer job, Curtis runs an exterior window cleaning business. His business expenses each week are for soap at $13.44, cloths at $11.20, and gas at $170. He also has a weekly expense of $70.20 for a loan he needed to buy ladders. He works 5 days each week and cleans the windows of 4 houses each day. Curtis charges $45 per house. (Module 3, Lesson 2)a) Calculate Curtis’s weekly profit. (2 marks)

b) Describe one thing Curtis might consider doing to increase the profit. (1 mark)

7. List the four sections of the T1 General income tax return. (2 marks) (Module 3, Lesson 3)

8. Which of the following expenses can be claimed only under business expenses and not under personal expenses? Circle the best answer. (1 mark) (Module 3, Lesson 3)a) telephone and utilitiesb) child care costsc) medical costsd) tuition fees

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Module 4: Probability (23 marks)

1. In a class of 32 students where they each take one option, 18 students take an Art option, 10 other students take a Drama option, and the rest of the students take a Choir option. One student is selected at random. Find the following: (4 marks) (Module 4, Lesson 2)a) the odds in favour of the selected student taking Drama

b) the odds against the selected student taking Choir

c) the odds in favour of the selected student either taking Art or Choir

d) the probability of the selected student either taking Art or Choir

2. The odds against a spring flood in Winnipeg are 6 : 7. (2 marks) (Module 4, Lesson 2)a) What are the odds in favour of a spring flood in Winnipeg?

b) What is the probability of a spring flood in Winnipeg?

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Name:

3. Keira studied how often Friday the 13th occurs. The following chart indicates her data showing how often the 13th day of the month falls on each of the seven days of the week. (6 marks)

Days of the Week S M T W T F Sa

How Often the 13th Day Occurs 687 685 685 687 684 688 684

a) Find the probability that the 13th day of the month occurs on a Friday. Express this probability as a percent, decimal (rounded to two decimal places), and a fraction. (2 marks) (Module 4, Lesson 1)

b) Find the probability that the 13th day of the month does not occur on a Friday. Express this probability as a percent. (2 marks) (Module 4, Lesson 1)

c) Is this an example of theoretical probability or experimental probability? Explain. (2 marks) (Module 4, Lesson 4)

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4. State an example of a situation where you would use the following type of probability to predict an outcome or make a decision: (3 marks) (Module 4, Lesson 4)a) Theoretical probability

b) Experimental probability

c) Subjective probability

5. An expert is to make a decision about the safety of the design of a vehicle. What kind of probability will be used as a basis for the decision? Explain. (2 marks) (Module 4, Lesson 4)

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Name:

6. Consider the following game. It costs $5 each time you draw a card from a shuffled standard deck. If you draw an ace, you win $50. If you draw a king, you win $25. If you draw any other card, you receive nothing. An expected value chart is included in this question. Use it only if you find it helpful. (Module 4, Lesson 3)a) Determine your expected value of the game. (4 marks)

Event Probability AmountWon

Cost ofPlaying

Payoff Probability xPayoff

Ace

King

Other Card

b) If you play this game 15 times, how much money can you expect to gain or lose? (1 mark)

c) Is this a fair game? Explain why or why not. (1 mark)

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Amortization Table

Amortization Period of Mortgage Loan(Blended payment of principal and interest per $1,000 of loan)

Interest Rate 5 years 10 years 15 years 20 years 25 years

1.50%1.75%2.00%2.25%2.50%2.75%3.00%3.25%3.50%3.75%4.00%4.25%4.50%4.75%5.00%5.25%5.50%5.75%6.00%6.25%6.50%6.75%7.00%7.25%7.50%7.75%8.00%8.25%8.50%8.75%9.00%9.25%9.50%9.75%

10.00%10.25%10.50%10.75%11.00%

$17.3117.4217.5217.6317.7417.8517.9618.0718.1818.2918.4018.5118.6218.7418.8518.9619.0719.1919.3019.4119.5319.6419.7519.8719.9820.1020.2120.3320.4520.5620.6820.8020.9121.0321.1521.2721.3821.5021.62

$8.989.099.209.319.429.539.659.769.889.99

10.1110.2310.3410.4610.5810.7010.8210.9411.0711.1911.3111.4311.5611.6811.8111.9412.0612.1912.3212.4512.5812.7112.8412.9713.1013.2413.3713.5013.64

$6.216.326.436.556.666.786.907.027.147.267.387.507.637.757.888.018.148.278.408.538.668.808.939.079.219.349.489.629.769.90

10.0510.1910.3310.4810.6210.7710.9211.0611.21

$4.824.945.055.175.295.415.545.665.795.916.046.176.306.446.576.716.846.987.127.267.417.557.707.847.998.138.288.438.598.748.899.059.209.369.529.689.849.99

10.16

$4.004.114.234.364.484.614.734.864.995.135.265.405.535.675.825.966.106.256.406.556.706.857.007.167.327.477.637.797.958.128.288.448.618.788.949.119.289.459.63

*Interest compounded semi-annually. Actual payment amount may differ slightly.

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Chart 1.1Interest Rate Factor Table

Based on 25-Year Amortization

Interest Rate Payment FactorFor Each Dollar of Loan

2.5% 0.004483.0% 0.004733.5% 0.004994.0% 0.005264.5% 0.005535.0% 0.005825.5% 0.006106.0% 0.006406.5% 0.006707.0% 0.007007.5% 0.007328.0% 0.00763

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Local Improvement Costs for Property Tax Credits Property Improvement Cost per Frontage Foot per Year

Asphalt surfacing roadwaysBoulevard constructionConcrete sidewalkConcrete street pavingGranular surface laneLand drainage systemLane lightingLane oilingLane pavingOrnamental lighting (lane)Ornamental lighting (street)Road oilingWastewater sewersWater mains

$ 26.22$ 10.81$ 7.86$ 39.32$ 9.01$ 8.62$ 1.80$ 9.00$ 11.80$ 10.82$ 14.42$ 8.00$ 9.98$ 11.54

Source: http://winnipeg.ca/publicworks/Services/LocalImprovements.asp