Final Practice Exam Answer Key

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 )

Final Practice Exam Answer Key

F i n a l P r a c t i c e E x a m A n s w e r K e y 3 of 49

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

Final Practice Exam Answer Key

Name: ___________________________________

Student Number: ___________________________

Attending q Non-Attending q

Phone Number: ____________________________

Address: _________________________________

__________________________________________

__________________________________________

InstructionsThe final examination is based on Modules 5 to 8 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 final examination.

FormatThe format of the examination will be as follows: Module 5: Vehicle Finance 30 marks Module 6: Career Life 9 marks Module 7: Statistics 31 marks Module 8: Precision Measurement 30 marks Total 100 marks

(see over)

For Marker’s Use Only

Date: _______________________________

Final Mark: ________ /100 = ________ %

Comments:

Answer Key

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 s4 of 49

Instructions (continued)Resources Provided

The following tables are provided at the end of this examinationn Driver Safety Rating Chartn Amortization Tablen Manitoba Public Insurance Passenger Vehicles—2011 Rate Groups Tablen Manitoba Public Insurance 2011 Basic Rate Table

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 Final Exam Resource Sheet (The Final Exam Resource Sheet must be handed in

with the exam.)

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

Module 5: Vehicle Finance (30 marks)

1. Earna Wheeler is able to make a down payment of $4000 on a two-door sedan she purchases for $23,457, including tax. In order to finance the remaining portion, she takes out a three-year car loan at a fixed interest rate of 8.5%. (Module 5, Lesson 1)a) Calculate her monthly payment for the two-door sedan. (3 marks) Answer: Amount of the loan = $23,457 – $4000 = $19,457. Monthly payment/$1000 loan at 8.5% amortized over three years is $31.57 (from

Table 5.1).

Monthly payment =

$ ,

. $ .19 4571000

31 57 614 26× =

b) Calculate her deferred payment for the two-door sedan. (2 marks) Answer: The total of monthly payments = 36 ´ $614.26 = $22,113.36 The deferred payment = (36 ´ $614.26) + $4000 = $26,113.36

c) Calculate her finance charge for the automobile. (1 mark) Answer: The finance charge = $26,113.36 – $23,457 = $2656.36


2. A four-wheel-drive vehicle sells for $28,750, plus tax, and leases for $378 per month plus tax for a lease term of 24 months. A down payment of $5000 is required. The guaranteed residual value of the vehicle is 60% of the sales price. (Module 5, Lesson 2 and Lesson 4)a) Calculate the total monthly leasing payment. (1 mark) Answer: Total monthly leasing payment = $378 ´ 1.12 = $423.36

b) Calculate the total amount paid by the end of the lease. (2 marks) Answer: Total amount paid by the end of the lease = ($423.36 ´ 24) + $5000 = $15,160.64

c) Calculate the total residual value of the four-wheel-drive vehicle, including taxes. (2 marks)

Answer: Residual value = 60% ´ $28,750 = $17,250 Total residual value = $17,250 ´ 1.12 = $19,320

d) Calculate the total cost of the vehicle if it is purchased outright at the end of the lease. (1 mark)

Answer: Total cost of the vehicle if it is purchased outright at the end of the lease

= $15,160.64 + $19,320 = $34,480.64

e) Calculate how much the vehicle depreciates in two years. (2 marks) Answer: Depreciation in the first year = 20% ´ $28,750 = $5750 Value of the vehicle after the first year = $28,750 – $5750 = $23,000 Depreciation in the second year = 20% ´ $23,000 = $4600 Total depreciation after two years = $5750 + $4600 = $10,350


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3. Rosa wants to purchase a used car sold privately. The price the vendor is asking is $5500. A lien search costs $4, and a diagnostic test costs $35. The technician reports that the car needs the following repairs: suspension, $350; and tires, $680. A safety check costs $45. (Module 5, Lesson 3)

Calculate the total purchase price of this car if the book value is $5475. (5 marks) Answer: Asking price of the car $5500 PST on the book value of the car 7% ´ $5500 = $385.00 Lien search $4 Safety inspection 1.05 ´ $45 = $47.25 Diagnostic test 1.12 ´ $35 = $39.20 Repairs ($350 + $680) ´ 1.12 = $1153.60 Total $5500 + $385 + $39.20 + $4 + $47.25 + $1153.60

= $7129.05

4. Before purchasing a used vehicle privately, name two searches, tests, or checks that you should do. Explain why each should be done. (2 marks) (Module 5, Lesson 3)

Answer: Students must include two of the following, as well as the corresponding description.

n Lien search: to check whether the seller of a vehicle owns it outright and there is no money owing against it.

n Diagnostic test: to determine whether there are any mechanical problems with the vehicle.

n Check by qualified mechanic: to give you an opinion as to the vehicle’s condition and value.

n Safety check: Mandatory in Manitoba, this check is done to ensure the safety of the vehicle.

n Personal check: Check general condition of car, condition of interior, variations in colour of exterior (indication of accident).


5. A pick-up truck travels 72 km on 10 L of gasoline when driven on a smooth, paved road. The truck is only able to travel 48 km on the same amount of gasoline when driven on a gravel road. (Module 5, Lesson 4)a) Determine the fuel consumption rate of the truck on the paved road. (1 mark) Answer:

Fuel consumption rate

=

× =

1072

100 13 9 100. L/ km

b) Determine the fuel consumption rate of the truck on the gravel road. (1 mark) Answer:

Fuel consumption rate

=

× =

1048

100 20 8 100. L/ km

c) What is the percent increase in fuel consumption rates when driving on paved roads instead of gravel roads? (1 mark)

Answer: The increase in fuel consumption = 20.8 – 13.9 = 6.9 L/100 km

Rate of percent

=

× =

6 913 9

100 49 6..

. %

d) Calculate the cost of 3500 km of highway (smooth, paved road) if the cost of gasoline is $1.23/L. (1 mark)

Answer:

Cost

Lkm

km /km=

× ( )× =

13 9100

3500 1 23 598 40.

$ . $ .


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6. Brett is a motorist living in Territory 3. He owns a 2011 Toyota Camry Hybrid. He uses the vehicle for personal use only. He currently has 0 merit points (Module 5, Lesson 5)a) Calculate his 2011 Autopac rate. (2 marks) Answer: The rating for a 2011 Toyota Camry Hybrid is 24. The 2011 Autopac rate for a Pleasure Passenger Vehicle in Territory 3 with a merit

discount of 0% and a basic rate of 24 is $1333.

b) If he obtains one more merit from safe driving this year, what will be his Autopac rate next year? Assume the rates stay the same and still use the 2011 Basic Rate Table. (1 mark)

Answer: If he obtains one more merit, he will have one merit. One merit will give Brett a

discount of 5%. The 2011 Autopac rate for a Pleasure Passenger Vehicle in Territory 3 with a merit discount of 5% and a basic rate of 24 is $1266.

7. Mercedes is debating whether to buy a new or used vehicle. She has recently acquired a full time job as a receptionist. However, she lives in Steinbach and has to commute one hour to Winnipeg for her new job every day. Discuss at least two factors that might influence Mercedes’ decision on whether to buy a new or used vehicle. (2 marks) (Module 5, Lessons 1–5)

Answer: Answers may vary. Students get full marks for arguing their case using the pros and

cons of purchasing a new or used vehicle. The following is a sample answer: Mercedes might buy a new vehicle because:

n She needs a reliable vehicle that will get her to and from her job every day. As used vehicles are generally less reliable than new vehicles, Mercedes might consider purchasing a new vehicle.

n She has a full time job. Therefore, she should have enough money to pay for a new vehicle.

n Newer vehicles generally get better gas mileage. Therefore, Mercedes may save money on gasoline if she purchases a new vehicle instead of a used vehicle.

n New vehicles have a warranty, and used vehicles usually do not. She would not need to worry about major repair bills.


Module 6: Career Life (9 marks)

1. State the two careers you chose to research in the Career Life module. Specify which career was your career choice and which career was your alternate career choice. Answer all of the following questions in paragraph form.

For this question, you will be marked using a rubric. As you answer this question, refer to the rubric below to make sure you are answering this question correctly and completely.

3 marks 2 marks 1 mark 0 markInformation All of the

necessary information is included.

One or two pieces of information are not included.

Three or more pieces of information are not included.

Insufficient information included.

Explanation All information is justified or explanations are included for each point.

One or two pieces of information are not justified or do not include explanations.

Three or more pieces of information are not justified or do not include explanations.

No explanation included.

Writing Conventions(spelling, capitalization, grammar) and Organization

The paragraphs are organized and free of errors.

The paragraphs have a few errors or are not organized very well.

The paragraphs have many errors and/or are not organized well.

Not written in paragraph form.

Total 9 marks

Career Choice: Alternate Career Choice:

a) What aspect of your chosen career appeals to you the most? Explain.


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b) What aspect of your chosen career appeals to you the least? Explain.

c) After completing the Career Life module, do you still plan to pursue your career choice as your career? Are you planning to choose a different career? Explain.

d) What do you believe are the most important things you learned from the Career Life module?


Module 7: Statistics (31 marks)

1. Haley scores 47% on her law exam. A total of 382 students, including Haley, wrote the same exam. There were 36 other students received the same score that she did, but 244 received a lower score. (Module 7, Lesson 5)a) Find Haley’s percentile rank. (4 marks) Answer: B = 244 E = 36 + 1 = 37 (the number of people scoring 47% on the Law Exam) n = 382

Haley’s percentile rank

=

+ ×( )× = =

244 0 5 37382

100 68 7 69.

. th percentile

b) Explain the difference between Haley’s percentile rank and the percent mark she receives on the exam. (2 marks)

Answer: The percent mark is a comparison of the score a student receives to the total possible

score, expressed in percent form. The percentile rank is a comparison of the score a student receives to the scores of all

the other students who have written the test.

2. State one advantage and one disadvantage of using the trimmed mean as a measure of central tendency. (2 marks) (Module 7, Lesson 4)

Answer: Answers may vary. Advantages of using the trimmed mean:

n The trimmed mean is usually resistant to outliersn It is useful for data with extremely skewed valuesn The trimmed mean gives a reasonable estimate of the centre of the data

Disadvantages of using the trimmed mean:n If there are a significant number of outliers, such as more than 5% in a given

direction, the calculation of the trimmed mean may still include outliers


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3. Valerie scores 58% on a recent test. However, her percentile rank on the test was 92. (Module 7, Lesson 5)a) What can you conclude about the success rate of most of the other students who have

written the test? (1 mark) Answer: 92% of the students who wrote the test scored the same as or lower than Valerie.

b) Explain why the test results might be like this. (1 mark) Answer: One reason could be that the test was very difficult. A second reason could be that the students were not prepared for the test.


4. A stats person for a professional football team decides to track the number of touchdown passes thrown by the quarterback during a period of 20 games. She records the following numbers of touchdown passes during each game.

1 3 2 1 2 2 1 4 3 2

7 3 4 0 5 3 4 1 2 3

a) Calculate the mean of the number of touchdown passes per game. (1 mark) (Module 7, Lesson 1)

Answer:

Mean=+ + + + + + + + + + + + + + + + + + +

=

1 3 2 1 2 2 1 4 3 2 7 3 4 0 5 3 4 1 2 320

2 65.

b) Calculate the 10% trimmed mean of the number of touchdown passes per game. (1 mark) (Module 7, Lesson 2)

Answer: There are 20 values in this data set. 10% of 20 is 2. Therefore, you need to remove the

highest and lowest value to calculate the 10% trimmed mean.

10% Trimmed Mean=+ + + + + + + + + + + + + + + + +

=

1 3 2 1 2 2 1 4 3 2 3 4 5 3 4 1 2 318

2 5. 66

c) Identify the outlier(s) in this set of data. (1 mark) (Module 7, Lesson 2) Answer: Outliers: 0 and 7

d) Does the 10% trimmed mean get rid of the influence of outliers from this set of data? Explain. (2 marks) (Module 7, Lesson 2)

Answer: Yes, the outliers are 0 and 7. The trimmed mean removes the highest 5% of all data

values and the lowest 5% of all data values. In this situation, the values of 0 and 7 are removed when calculating the 10% trimmed mean.


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5. For the following set of numbers: 124, 210, 318, 124, 198, 342, 180

a) Find the mean, median, and mode. (3 marks) (Module 7, Lesson 1) Answer:

Mean=

+ + + + + +=

124 210 318 124 198 342 1807

213 7.

Ordered values: 124, 124, 180, 198, 210, 318, 342 Median: 198 Mode: 124

b) Add the number 10 to the set. Find the mean, median, and mode of this new set of numbers. (3 marks) (Module 7, Lesson 1)

Answer:

Mean=

+ + + + + + +=

124 210 318 124 198 342 180 108

188 25.

Ordered values: 10, 124, 124, 180, 198, 210, 318, 342

Median:

180 1982

189+( )

=

Mode: 124

c) How does adding a low outlier affect the mean, median, and mode of this data? (3 marks) (Module 7, Lesson 2)

Answer: The mean is lowered after adding a low outlier. The median is also lowered after adding a low outlier. The mode stays the same.

d) Which of the three measures of central tendency is most influenced by an extreme score? (1 mark) (Module 7, Lesson 2)

Answer: The mean.


6. Cassidy is trying to figure out what her mean monthly phone bill was for the previous year. For four months, her phone bill was $52 a month. For the other eight months in the year, her phone bill was $63 a month. Since the mean of $52 and $63 is $57.50, Cassidy states that her mean phone bill for the previous year was $57.50. Is her reasoning correct? Explain. (3 marks) (Module 7, Lesson 3)

Answer: No, her reasoning is incorrect. Cassidy did not realize that the values on her phone bills

have different weightings because she was not charged the same amount of money for equal amounts of time. The actual mean (weighted mean) value of her phone bill would

be:

52 4 63 88 4

59 33×( )+ ×( )

+=$ . .

7. Keegan is taking an Independent Study Grade 12 Physics course. He has received a mean mark of 86% on his assignments, 77% on his midterm exam, and 65% on his final exam. Assignments are worth 50% of his final mark, while the midterm exam is worth 20% and the final exam is worth 30%. Determine Keegan’s final mark in this course. (3 marks) (Module 7, Lesson 3)

Answer: Keegan’s final mark = Weighted mean

Weighted Mean=

×( )+ ×( )+ ×( )+ +

=86 0 50 77 0 20 65 0 30

0 50 0 20 0 307. . .

. . .77 91

77 9.

. %=


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Module 8: Precision Measurement (30 marks)

1. State whether each of the following target patterns displays a high degree of accuracy, a high degree of precision, both precision and accuracy, or neither. (4 marks) (Module 8, Lesson 1)

��

�

� � � �

��

��

�

��

��

Answer: A: Precision and Accuracy B: Neither—cannot have accuracy without precision C: Neither D: Precision but not accuracy

2. State two examples from everyday life that demonstrate the importance of not only precision, but also the importance of accuracy in measurement. (2 marks) (Module 8, Lesson 1)

Answer: Sample answers:

n Medicine: Pills must not only be similar, but must have the correct amount of medication.

n Mechanics: Engine parts must not only be measured with very precise measuring devices, but must also have the correct measurements so that they fit together properly.

n Commerce: When buying gas, the pump indicates the amount to

110

of a litre

(precision), but it is important that you receive the amount indicated (accuracy).n Sports: Timing devices must be precise to distinguish between very close finishes in

races, and must be accurate so that record books represent the correct times.


3. Measure the length of the following string, precise to the nearest indicated unit, using the given imperial ruler. (4 marks) (Module 8, Lesson 1)

a)

b) one inch

c)

18

12

___________________

___________________

___________________

___________________d)14

� � � �

��

Answer:

a) inches or inches

b) inches

c) inches

d) inches

178

134

2

2

134


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4. A farmer wants to build a fence around a rectangular field. He measures the field, and discovers that the dimensions are 200 m by 70 m. (Module 8, Lesson 1)a) How precise are each of the measurements? (1 mark) Answer: His measurements are precise to the nearest metre.

b) What is the perimeter of the field? (1 mark) Answer: Perimeter = 200 + 200 + 70 + 70 = 540 m

c) What is the area of the field? (1 mark) Answer: Area = 200 ´ 70 = 14 000 m2

5. Is it possible to have a measuring device that is precise but not accurate? Explain. Illustrate your explanation with an example. (2 marks) (Module 8, Lesson 2)

Answer: Yes, it is possible. A bowed ruler would always provide the same reading when measuring objects that

have the same length, but the measurements would all be wrong. An old bathroom scale may always show the same weight when you weigh yourself,

but if it is not calibrated to start at zero, the weight shown may always be too high or too low.


6. Thomas measures the diameter of a toonie (a $2 coin). The diameter of the coin is 2.815 cm. (3 marks) (Module 8, Lesson 2)a) State the precision of the measuring device used. Answer: This device is precise to the nearest 0.001 cm.

b) State the uncertainty of the measurement. Answer: The uncertainty of the measurement is ± 0.0005 cm.

c) State the measurement Thomas should report (including the uncertainty). Answer: Thomas should report the diameter of the coin as: 2.815 cm ± 0.0005 cm.

7. The accepted weight of a small gold bar is 35.58 grams. Sam weighed the gold and his reading was 35.62±0.05 grams. Is Sam’s reading accurate? Explain. (2 marks) (Module 8, Lesson 2)

Answer: Yes, his reading is accurate. The lower limit and upper limits for Sam’s readings are:

35.62 ± 0.05 = 35.57 – 35.67 grams, and the accepted weight of 35.58 grams is in this range.


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8. A metal cylinder has a radius of 11.3 ± 0.2 cm and a height of 14.6 ± 0.3 cm. The volume formula for a cylinder is V = pr2h. (Module 8, Lesson 4)

h = 14.6 ± 0.3 cm

r = 11.3 ± 0.2 cm

r

Calculate the following: (4 marks)a) nominal volumeb) maximum volumec) minimum volumed) tolerance in the volume measurement

Answers:a) Nominal Volume = pr2h = p(11.32)(14.6) = 5856.8 cm3

b) Maximum Volume = p(11.52)(14.9) = 6190.6 cm3 c) Minimum Volume = p(11.12)(14.3) = 5535.2 cm3 d) Volume Tolerance = 6190.6 – 5535.2 = 655.4 cm3


9. A thin rectangular metal plate has dimensions as shown on the diagram. (Module 8, Lesson 4)

w = 8.5 cm00.3

l = 15.5 ± 0.1 cm

For the top surface of the metal plate, calculate (2 marks)a) the maximum (upper limit) area Answer: A(max) = (15.6)(8.5) = 132.6 cm2

b) the minimum (lower limit) area Answer: A(min) = (15.4)(8.2) = 126.3 cm2


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A round hole is drilled through the plate. The radius of the hole is 2.2 ± 0.1 cm.

w = 8.5 cm00.3

l = 15.5 ± 0.1 cm

r

r = 2.2 ± 0.1 cm

For the circle, calculate (2 marks)c) the maximum (upper limit) area Answer: A(max) = pr2 = p(2.32) = 16.6 cm2

d) the minimum (lower limit) area Answer: A(min) = p(2.12) = 13.9 cm2

Calculate the area of the top surface of the metal plate remaining after the hole is drilled:

(2 marks)e) the maximum (upper limit) area Answer: A(max) = (a) – (d) = 132.6 – 13.9 = 118.7 cm2

f) the minimum (lower limit) area Answer: A(min) = (b) – (c)= 126.3 – 16.6 = 109.7 cm2



Driver Safety Rating Chart

Merits for Safe Driving Autopac Discount+15 33%+14 30%+13 29%+12 28%+11 27%+10 26%+9 25%+8 25%+7 25%+6 20%+5 15%+4 15%+3 10%+2 10%+1 5%

0 (base) 0%–1 0%–2 0%–3 0%–4 0%–5 0%–6 0%–7 0%–8 0%–9 0%–10 0%–11 0%–12 0%–13 0%–14 0%–15 0%–16 0%–17 0%–18 0%–19 0%–20 0%


Table 5.1Amortization TableAmortization Period

Monthly Payment Per $1000 Loan Proceeds

AnnualRate

1 YearMonthly

2 YearsMonthly

3 YearsMonthly

4 YearsMonthly

5 YearsMonthly

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%11.25%11.50%11.75%12.00%12.25%12.50%12.75%13.00%13.25%13.50%13.75%14.00%

$86.07$86.18$86.30$86.41$86.53$86.64$86.76$86.87$86.99$87.10$87.22$87.34$87.45$87.57$87.68$87.80$87.92$88.03$88.15$88.27$88.38$88.50$88.62$88.73$88.85$88.97$89.08$89.20$89.32$89.43$89.55$89.67$89.79

$44.33$44.44$44.56$44.67$44.78$44.89$45.01$45.12$45.24$45.34$45.46$45.57$45.68$45.80$45.91$46.03$46.14$46.26$46.38$46.49$46.61$46.72$46.84$46.96$47.07$47.19$47.31$47.42$47.54$47.66$47.78$47.89$48.01

$30.43$30.54$30.66$30.77$30.88$31.00$31.11$31.23$31.34$31.45$31.57$31.68$31.80$31.92$32.03$32.15$32.27$32.38$32.50$32.62$32.74$32.86$32.98$33.10$33.21$33.33$33.45$33.57$33.69$33.81$33.94$34.06$34.18

$23.49$23.61$23.72$23.84$23.95$24.07$24.19$24.30$24.42$24.53$24.65$24.71$24.89$25.00$25.12$25.24$25.36$25.48$25.60$25.72$25.85$25.97$26.09$26.21$26.33$26.46$26.58$26.70$26.83$26.95$27.08$27.20$27.33

$19.34$19.46$19.57$19.69$19.81$19.93$20.05$20.16$20.28$20.40$20.52$20.64$20.76$20.88$21.00$21.12$21.25$21.37$21.49$21.62$21.74$21.87$21.99$22.12$22.24$22.37$22.50$22.63$22.75$22.88$23.01$23.14$23.27
























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Final Practice Exam Answer Key