Workplace and Apprenticeship Math 30



November 2013

Revised October 2016

Grade 12 Prototype Examination

Workplace and Apprenticeship Mathematics 30

Course Code 8423

Barcode Number

Month Day

Date of Birth

Workplace and Apprenticeship Mathematics 30

TIME: Two and One-Half Hours

Calculating devices MUST meet the requirements of the Calculator Use Policy. Before an examination begins, devices must be removed from their cases and placed on the students’ desks for inspection by a mathematics or science teacher. Cases must be placed on the floor and left there for the duration of the examination. Students using a standard scientific or graphing calculator must clear all information stored in its memory before the examination begins.

Devices such as cell phones, tablets, and iPods may be used as a calculating device if they meet the requirements of the Calculator Use Policy. The school or writing center must be able to lock and control the device using a feature such as Guided Access, or a management software that limits its functionality to permissible graphing and financial applications (apps) with similar functionality to an approved graphing calculator. It is the student’s responsibility to ensure their device complies with the Calculator Use Policy in advance of the departmental examination session.

Do not spend too much time on any one question. Read each question carefully.

The examination consists of 38 multiple-choice questions followed by 7 numeric response questions of equal value which will be machine scored. Record your answers on the Student Examination Form which is provided. Each multiple-choice question has four suggested answers, one of which is better than the others. Select the best answer and record it on the Student Examination Form as shown in the example below:

Student Examination Form:

Multiple-Choice Questions

This examination is being written in the subject

A. Chemistry.

B. Workplace and Apprenticeship Mathematics.

C. Pre-calculus.

D. Foundations of Mathematics.

1. A B C D

Numeric Response Questions

Record your answer in the numeric response section on the answer sheet.

What is 10% of $2000? (Round to the nearest dollar.)

[pic]

What is 10% of $248.50? (Round to the nearest dollar.)

[pic]

What is 10% of 24 125? (Round to the nearest whole number.)

[pic]

Use an ordinary HB pencil to mark your answers on the Student Examination Form. If you change your mind about an answer, be sure to erase the first mark completely. There should be only one answer marked for each question. Be sure there are no stray pencil marks on your answer sheet. If you need space for rough work, use the space in the examination booklet beside each question.

Do not fold either the Student Examination Form or the examination booklet. Check that your personal information on the Student Examination Form is correct and complete. Make any necessary changes, and fill in any missing information. Be sure to complete the Month and Day of Your Birth section.

Workplace and Apprenticeship 30

Rate of Change (Slope) Formula

|[pic] | | |

Direct and Partial Variation Formulas

|[pic] |[pic] | |

Angles and Polygons

Sum of the Measures of the Interior Angles of a Polygon with n-sides: [pic]

Central Angle of a Regular Polygon with n-sides: [pic]

Sine Law and Cosine Law

|[pic] | | |

|[pic] |[pic] | |

Percentile Rank

|[pic] | | |

L = number of values less than the one being considered

F = frequency or number of values equal to the one being considered

n = number of values in the data set

GRADE 12 DEPARTMENTAL EXAMINATION

WORKPLACE AND APPRENTICESHIP 30 PROTOTYPE

NOVEMBER 2013, REVISED OCTOBER 2016

|VALUE |Answer the following 45 questions on the computer sheet entitled “Student Examination Form.” |

|(45 ( 2) | |

|MULTIPLE - CHOICE QUESTIONS |

1. Jennifer wants to earn more profit from her small business without increasing her prices. Which of the following could she do to improve her profit without increasing her prices or frustrating her customers?

A. provide lower quality goods

B. close the store on weekends

C. hire younger and less experienced staff for less salary

D. find a supplier who can provide the same materials at a lower price

2. Owen needs a reliable vehicle to deliver pizzas. He agrees to a deal for $82 biweekly at 3.99% interest for a 4-year term. The vehicle will go back to the dealership at the end of the term. Which option did Owen use to acquire this vehicle?

A. lease

B. lease to purchase

C. purchase with credit

D. purchase without credit

3. Armand was provided the following information comparing leasing a vehicle to buying a vehicle with a car loan:

| |Lease |Car Loan |

|Retail price |$30 000.00 |$30 000.00 |

|Final negotiated price |$28 695.00 |$28 140.00 |

|(including all add-on costs) | | |

|Down payment |$3000.00 |$3000.00 |

|Residual value |$15 300.00 |N/A |

|Annual interest rate |6.5% |3.5% |

|(compounded monthly) | | |

|Term |36 months |48 months |

|GST and PST rate |10% |10% |

| | | |

|Monthly payments |$439.76 |$624.94 |

|(including fees, interest, and tax) | | |

| | | |

|Sales tax |$1339.50 |$2814.00 |

|Total interest and fees paid |$4396.86 |$2043.12 |

|Total payments |$15 831.36 |$29 997.12 |

|Total cost |$18 831.36 |$32 997.12 |

Considering only the information in the table above, which of the following statements is true?

A. In both cases, he will own the vehicle at the end of the term.

B. Purchasing a car with a loan will result in lower monthly payments.

C. If he buys out the lease at the end of the term, it will be more expensive than purchasing the car with a loan.

D. If he returns the vehicle at the end of the lease, the amount of tax to pay will be higher than if he purchases the car.

4. Sara buys a used vehicle in Alberta for $3500. In order to register the vehicle in Saskatchewan, she has to pay 5% PST, get a safety inspection for $109.99, and pay $983.23 for car insurance. What is her total cost for purchasing and registering this car?

A. $4593.22

B. $4768.22

C. $4773.72

D. $4822.88

5. A hardware store buys bolts in bulk for 5 cents each. The bolts are then put into packages of 12 and sold for $0.99 a package. What is the minimum number of packages the store needs to sell in order to cover its daily overhead costs of $12 per day?

A. 12 packages

B. 20 packages

C. 24 packages

D. 31 packages

6. The average heights of boys between the ages of 12 and 18 was collected and displayed in a scatter plot. Which scatter plot below would most likely show the relationship between their age and their height?

A.

B.

C.

D.

7. Sheldon created a scatterplot to show his summer income from his

part-time job.

Which of the following equations best represents the relation between the income earned (E) and the time (t)?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

8. A gym machine was designed to give a linear relationship between the number of strides completed and the number of calories burned (see chart below):

Approximately how many calories would be burned after a person completed 2500 strides on this machine?

A. 150 calories

B. 165 calories

C. 180 calories

D. 195 calories

9. Which of the following is a linear relationship?

A.

|Time (h) |Speed (km/h) |

| 0.75 |120 |

| 1.0 |90 |

| 1.75 |60 |

| 3.0 |30 |

B.

|Age (y) |Height (in) |

|10 |54 |

|14 |62 |

|18 |71 |

|22 |82 |

C.

|Number of Bricks | |

| |Mass (kg) |

|5 |10 |

|8 |16 |

|11 |22 |

|14 |28 |

D.

|Time (s) |Height (m) |

|1 |31.6 |

|2 |30.9 |

|3 |30.4 |

|4 |29.9 |

10. On a particular day, a meteorologist finds that the temperature climbed at a linear rate between midnight and 2 p.m. At 10 a.m., the temperature was 12°C and at 2 p.m., it was 20°C. Which linear relation represents the temperature (T ) in °C if h is the number of hours after midnight?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

11. Which of the following is a regular polygon?

A.

B.

A.

D.

12. A saw is designed to cut copper pipe into 8 foot lengths. A random sample of pipes from this saw was measured. They were found to be 7′4″, 7′4″, 7′5″, and 7′4″ long. Which of the following would be true about this saw?

A. It is both precise and accurate.

B. It is accurate, but not precise.

C. It is precise, but not accurate.

D. It is neither accurate nor precise.

13. An oven timer is set using whole minute intervals. What is the precision of the timer?

A. 1 second

B. 30 seconds

C. 1 minute

D. 2 minutes

14. The new image on the right has been created by reflecting the original

2-D image on the left. What is the line of reflection?

A. [pic]

B. [pic]

C. x-axis

D. y-axis

15. Which of the following statements is TRUE?

A. A triangle can be right and scalene at the same time.

B. A triangle can be isosceles and scalene at the same time.

C. A triangle can have a right and an obtuse angle at the same time.

D. A triangle can have an obtuse angle and be equilateral at the same time.

16. Which property applies to every rhombus?

A. The diagonals are perpendicular.

B. The diagonals are equal in length.

C. The diagonals do not bisect each other.

D. The diagonals do not bisect opposite angles.

17. The length of any 8 foot two-by-four can be between [pic]and [pic] What is the tolerance?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

18. A lighthouse and 2 boats are located as shown below.

When the lighthouse keeper receives a distress call from boat A, he quickly determines the distances to the boat and to the Coast Guard. If the angle measure between the two known distances is 45°, approximately how far will the Coast Guard travel to get to the distressed boat?

A. 8 km

B. 15 km

C. 18 km

D. 22 km

19. The paths connecting 3 campfires form a triangle as shown below.

What is the distance between campfire A and campfire C?

A. 2.2 km

B. 2.4 km

C. 2.9 km

D. 3.1 km

20. The triangular image shown below was reflected across the line x = 2 and then shifted 2 units down. Which of the following represents the image resulting from these 2 transformations?

A.

B.

C.

D.

21. A factory operator is filling a truck on a scale with an accuracy of

[pic] kg. When the truck is filled, the scale reads 14 875 kg. Which of the following shows the range of values for the actual mass of the loaded truck?

A. 14 855 kg to 14 895 kg

B. 14 855 kg to 14 875 kg

C. 14 865 kg to 14 885 kg

D. 14 875 kg to 14 895 kg

22. Which of the following objects has the most planes of symmetry?

A.

B.

C.

D.

23. The sum of the angles in a triangle is 180°. Which of the following properties can be used with this fact to determine the size of [pic]

A. A scalene triangle has no angles of equal measure.

B. The base angles of an isosceles triangle are congruent.

C. An isosceles triangle has 2 legs that are equal in length.

D. A triangle is acute if all 3 angle measures are less than 90°.

24. A scalene triangle has three sides of lengths a, b, and c. What formula is the correct calculation to determine the measure of [pic]

A. [pic]

B. [pic]

C. [pic]

D. [pic]

25. A blue-print for a pentagon-shaped table is drawn to a scale of 1 : 2. On the drawing, the sides are 0.5 m long and the angles are 108°. What are the side lengths and the angle measures of the table?

A. Each side is 0.25 m and each angle is 54°.

B. Each side is 0.25 m and each angle is 108°.

C. Each side is 1.0 m and each angle is 108°.

D. Each side is 1.0 m and each angle is 216°.

26. An interior designer has cut out 2-D paper shapes to represent various pieces of furniture he is arranging in a large room. Once the customers agree on which option they prefer, the furniture will be purchased to match the appropriate paper cut-outs.

What transformation(s) have been applied to the cut-out representing the shaded sofa from Option 1 to Option 2?

A. a rotation of 180° about the centre of the room

B. a reflection across the room’s vertical midline and a translation down

C. a reflection across the room’s horizontal midline and a translation to the right

D. a rotation of 180° about the centre of the sofa, a translation to the right, and a translation down

27. In an archery competition, five archers earned scores of 26, 37, 33, 28, and 26. What is the median score?

A. 26

B. 28

C. 30

D. 33

28. Which statement below refers to the mode of a set of data?

A. The average weight of a baby is 3.5 kilograms.

B. The lowest mark on an accounting exam was 68%.

C. The most common score on the 7th hole of a golf course was 4.

D. A price comparison for a brand of cereal among three stores showed the middle price to be $4.58.

29. The following 8 measurements were taken in centimetres:

|30.4 |31.1 |31.1 |22.3 |30.6 |37.2 |31.6 |30.8 |

What is the trimmed mean of the data?

A. 30.6 cm

B. 30.9 cm

C. 31.0 cm

D. 31.1 cm

30. Andrew earned the following marks on his unit exams:

|70% |74% |47% |90% |73% |74% |68% |

To calculate his final grade, his teacher removes the outliers, and averages the remaining marks. Which of the following changes will occur as a result of the outliers being removed?

A. The mean increases.

B. The mode increases.

C. The mean decreases.

D. The mode decreases.

31. Paul was in the 80th percentile in Math and in the 25th percentile in English. Which of the following statements can Paul claim with certainty?

A. He passed Math.

B. He passed English.

C. He was below most of his classmates in Math.

D. He was below most of his classmates in English.

32. If Shelley graduated 75th out of a class of 225 students, then 150 students were ranked below Shelley. Assuming there were no ties, what is her percentile rank in her graduating class?

A. 34th

B. 67th

C. 75th

D. 83rd

33. In June 2013, the average hourly wage in each province for all 15-24 year-old workers is shown below:

|Province | Average hourly wage |

|British Columbia |$13.83 |

|Alberta |$16.69 |

|Saskatchewan |$15.75 |

|Manitoba |$13.35 |

|Ontario |$13.50 |

|Quebec |$13.36 |

|New Brunswick |$12.49 |

|Nova Scotia |$12.82 |

|Prince Edward Island |$12.22 |

|Newfoundland and Labrador |$14.12 |

Into what range does the percentile ranking for Saskatchewan fall?

A. between the 10th and 19th percentile

B. between the 20th and 29th percentile

C. between the 70th and 79th percentile

D. between the 80th and 89th percentile

34. A local service club has 723 members. Each week, all 723 members are entered into a draw for a single prize. If Maureen won this week, what is her probability of winning next week?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

35. The probability of a factory manufacturing a defective power steering pump was determined to be 0.015. If 3000 power steering pumps are produced, what is the expected number of defective pumps?

A. 15

B. 45

C. 150

D. 450

36. Which one of the following comparisons between “the odds of an event occurring” and “the probability of an event occurring” is true?

A. If the odds are 1 : 1, the probability will be 50%.

B. If the odds are 2 : 3, the probability will be 66%.

C. If the odds are 4 : 1, the probability will be 40%.

D. If the odds are 20 : 1, the probability will be 21%.

37. There are 25 lockers and 25 students in a certain Grade 12 class. In a strange school spirit activity, the principal asks:

• the 1st student to open all the lockers;

• the 2nd student to close every 2nd locker;

• the 3rd student to stop at every 3rd locker, and:

o if the locker door is open, to close it.

o if the locker door is closed, to open it.

If the pattern that began with the 3rd student continues in the same way with the 4th, 5th, 6th students and so on until the 25th student completes the task, how many of the 25 locker doors will be open?

A. 0

B. 5

C. 10

D. 15

38. Complete the following Sudoku puzzle. The basic rules of Sudoku are:

• There is only one valid solution to each Sudoku puzzle. The only way the puzzle can be considered solved correctly is when all 81 boxes contain numbers and the other Sudoku rules have been followed.

• When you start a game of Sudoku, some blocks will be pre-filled for you. You cannot change these numbers in the course of the game.

• Each column must contain all of the numbers 1 through 9 and no two numbers in the same column of a Sudoku puzzle can be the same.

• Each row must contain all of the numbers 1 through 9 and no two numbers in the same row of a Sudoku puzzle can be the same.

• Each [pic] block must contain all of the numbers 1 through 9 and no two numbers in the same block of a Sudoku puzzle can be the same. 

|4 |

Record your answer in the Numeric Response section of the “Student Examination Form.”

39. Graham is negotiating a 3-year lease on a new truck. The dealership offers him a purchase price of $40 000 with a residual value at the end of the lease of $20 200. He estimates taxes, lease fees, and interest charges will be $100 per month. What is Graham’s anticipated monthly payment? (Round to the nearest dollar.)

40. As a fundraiser, the student council carved pumpkins at the Harvest Festival. To get ready for the day, they bought 5 pumpkin carving kits at $5.00 per kit plus GST and PST, paid the festival organizers $50.00 for the booth, and had parents donate 100 pumpkins. They charged $15.00 per pumpkin and made a profit of $1182.50. How many pumpkins did they have left at the end of the festival?

41. Shane’s gym has a $55.00 initial registration fee plus a monthly fee. He knows the total cost of the gym for the first 6 months is $187.00. What is Shane’s monthly gym fee? (Round to the nearest dollar.)

42. A stop sign is a regular polygon. What is the sum of the measures of the interior angles of a stop sign?

43. A triangular island is shown below. The distance between point A and point B is 123 km, the distance between point B and point C is 58 km, and the measure of [pic] is 68°.

What is the measure of [pic] (Round to the nearest degree.)

44. A light bulb manufacturer randomly selected 40 bulbs from the production line. They found 3 of these bulbs were defective. They manufactured 10 000 bulbs in total. Based on the sample, how many light bulbs would be expected to be defective?

45. A teacher announced that final marks will be calculated by taking 30% of the term 1 mark, 30% of the term 2 mark, and 40% of the final exam mark. If Jill scored 82% in term 1, 70% in term 2, and 88% on her final exam, what is her final mark? (Round to the nearest percent.)

GRADE 12 DEPARTMENTAL EXAMINATION

WORKPLACE AND APPRENTICESHIP MATH 30

PROTOTYPE EXAM — Answer Key

(See Explanation of Answers)

|1. |D |

|Alberta |$16.69 |

|Saskatchewan |$15.75 |

|Newfoundland and Labrador |$14.12 |

|British Columbia |$13.83 |

|Ontario |$13.50 |

|Quebec |$13.36 |

|Manitoba |$13.35 |

|Nova Scotia |$12.82 |

|New Brunswick |$12.49 |

|Prince Edward Island |$12.22 |

Eight provinces have a lower hourly wage than Saskatchewan. Therefore, [pic] Using the correct percentile ranking formula provided with the exam:

[pic]

Using the incorrect percentile ranking formula found in the textbook:

[pic]

34. C.

The outcome of one draw doesn’t change the probability of the next.

The probability will still be [pic]

35. B.

[pic]

[pic]

36. A.

The option A, the odds of 1 : 1 translates to a probability of 50%.

The option B, the odds of 2 : 3 translates to a probability of 40%, not 66%.

The option C, the odds of 4 : 1 translates to a probability of 80%, not 40%.

The option D, the odds of 20 : 1 translates to a probability of 95.24%, not 21%.

37. B

Various strategies could be used to solve this problem such as a list or a table similar to the one shown below:

| |Locker Number |

|Student |1 |2 |3 |

|Numbers (Financial decisions) |6, 7 |1 – 5 |39 – 40 |

|Algebra (Linear Relationships) |8 |6 – 10 |41 |

|Measurement and Geometry |2 – 5 |11 – 26 |42 – 43 |

|Statistics & Probability; Logic |1, 9 – 11 |27 – 38 |44 – 45 |

-----------------------

t

E

Income

Earned

($)

lighthouse

10 km

20 km

•

•

•

Coast Guard

boat A

x

a

b

c

B

Option 2

Option 1

Option A

Option B

Option D

Option C

1

2

Legend:

Ï% = Open Door

X = Closed Door

1

2

Legend:

● = Open Door

X = Closed Door

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