Workplace and Apprenticeship Math 30
- 1 -
- i -
=
=
°°
=
=
sinsin
40cm
sin45sin67.5
30.6147cm
30.6 cm
ca
CA
c
c
c
November 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.ABCD
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.)
What is 10% of $248.50? (Round to the nearest dollar.)
What is 10% of 24 125? (Round to the nearest whole number.)
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
21
21
yy
m
xx
-
=
-
Direct and Partial Variation Formulas
ymx
=
ymxb
=+
Angles and Polygons
Sum of the Measures of the Interior Angles of a Polygon with n-sides:
(
)
1802
°-
n
Central Angle of a Regular Polygon with n-sides:
360
n
°
Sine Law and Cosine Law
sinsinsin
abc
ABC
==
222
2cos
cababC
=+-
+-
=
222
cos
2
bca
A
bc
Percentile Rank
æö
+
=´
ç÷
èø
0.5
100
LF
PR
n
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 2016
VALUE
(45 ( 2)
Answer the following 45 questions on the computer sheet entitled “Student Examination Form.”
MULTIPLE - CHOICE QUESTIONS
1.Whether buying or leasing a new vehicle, there are additional costs, taxes, and fees. Which of the following applies only to leases?
A.down payments
B.over-mileage costs
C.sales taxes such as GST and PST
D.administration and registration fees
2.Monica leases a new car from a dealership under the following terms and conditions:
Term
3 years
Monthly payment
$478
Security deposit
$500
Delivery charge
$399
Residual value
$11 000
Kilometre allowance
24 000 km/year
At the end of her lease term, the car is in excellent condition, has a market value of $17 000, and has been driven a total of 28 000 km. After considering her options, Monica decides to lease another new car. However, rather than returning the car to the dealership, she sells the car privately. Which of the following best describes why a private sale is a good option for Monica?
A.The car’s market value is significantly higher than its residual value.
B.Buying out the lease allows her to get a full refund on her security deposit.
C.Selling the car privately is easier and less problematic than returning it to the dealership.
D.She would have had to pay the car’s market value to the dealership in order to return it.
Use the following information to answer questions 3, 4, and 5.
Marshmallow Factory fights frozen yogurt with warm, fluffy treats!
When visiting the Marshmallow Factory, don’t expect the normal, puffy white campfire variety. The house specialty is smooth marshmallow cream which customers use as a base for craving satisfying flavour experimentation.
“Everything is made the way you want it”. Customers choose a shell out of a wide selection, ranging from molded chocolate to pastries. They pick one of over 20 flavoured creams, from coca-cola to mint, of which samples are eagerly provided before decisions are made. Toppings, such as fruit or chocolate chips are chosen from a toppings bar. Powders, sugars, mocha, sour and more, are used for the finishing touch.
The Marshmallow Factory sign was up for several years while the owner mortgaged the building that was already owned to renovate and experiment until the product was perfected. Owner Chris assumed children would be the target market, but finds the shop gets more business from adventurous adults in their 20s and 40s.
Unlike the already established frozen yogurt franchises, he has relied on trial and error to set up the shop. Admittedly business has been slow – so far. In an effort to increase sales, Chris used various free-advertising web sites to distribute “2 Marshmallows for the Price of 1” coupons, but has seen mixed results. He hoped the offers would create return customers and generate word of mouth, but users were only interested in one-time, cheap deal.
The business has a website, but it lacks the passion and enthusiasm needed. A future suggestion is to set up a YouTube Channel to demonstrate the product for customers. The videos could then be shared via social media platforms such as Facebook and Twitter.
Tourists impressed with his product have encouraged him to expand his business and open other stores. More exposure might make this a possibility. In the meantime, Chris is content watching customers enjoy the unusual treat.
(Adapted from: Jamie Bradburn, “New Danforth Food: Toronto’s Marshmallow Factory fights frozen yogurt with warm, fluffy treats” Special to the Star, Monday May 6, 2013)
3.The Marshmallow Factory provides customers with a selection of toppings for their marshmallows. Which of the following best describes the toppings that Chris purchases for his business?
A.sales
B.profit
C.a fixed expense
D.a variable expense
4.Which of the following measures ensure Chris’s business will not experience a loss by introducing the 2-for-1 coupon?
A.expand the menu by adding other dessert choices for customers
B.put an expiry date on the coupons and restrict the use to weekdays
C.have a unit sale price that is more than double the unit production cost
D.restrict the coupons to one per customer and distribute only a limited number
5.Six months after opening, Chris meets with his financial advisor to review his business plan and complete a viability study for the Marshmallow Factory. Which of the following factors indicate his business is viable?
A.All his loans are paid and his business is debt free.
B.His total unit sales continue to show an increase from the previous month.
C.His total monthly revenue consistently exceeds his total monthly expenses.
D.People like his product and his customer–base grows via word of mouth and social media.
__________________________________________________________________
6.Which of the following situations would have a graph with connected data points?
A.the number of text messages sent each day for a month
B.the number of kilometres travelled as time passes on a trip
C.the number of people on a school bus as it picks up students for school
D.the number of a particular item in a store’s inventory each month of the year
7.Tom is a truck driver who will haul hay bales for farmers. He charges a flat rate of $450.00 to load and deliver the bales, plus $2.62 per kilometer when he travels loaded with bales. Tom charges one farmer $1293.64. How far did Tom haul the hay?
A.150 km
B.322 km
C.494 km
D.666 km
Use the following information and graph to answer questions 8 and 9.
Kaleb has a small residential plumbing business. He charges a base rate for his service call, and then a variable rate depending on the number of hours he is at the job site. The graph below shows the line of best fit for 3 recently completed jobs:
8.How could Kaleb use the graph to determine the fee to charge for a job that took 4 hours to complete?
A.interpolate using a value outside the data
B.extrapolate using a value outside the data
C.interpolate using a value from within the data
D.extrapolate using a value from within the data
9.What is the fee for a job that takes 10 hours to complete?
A.$750
B.$840
C.$900
D.$975
__________________________________________________________________
10.SaskEnergy bills its customers a basic monthly charge plus an amount based on the volume of natural gas consumed. The amounts for October 2008 and September 2013 are shown in the table below:
Date
Basic monthly charge
Cost per cubic metre
October 2008
$12.50
$0.3195
September 2013
$18.85
$0.1453
Which of the following graphs represents the 2008 and the 2013 rates?
A.
B.
C.
D.
11.Which transformation creates a figure that is similar but not congruent to the original figure?
A.dilation
B.reflection
C.rotation
D.translation
12.For safety reasons, the provincial government reports the horizontal and vertical clearance of all overhead structures on Saskatchewan highways. An overhead light near Balgonie has a vertical clearance of 6.30 m. What is the precision of this measurement?
A.0.005 m
B.0.01 m
C.0.05 m
D.0.1 m
13.A contractor needs
2
13.5 m
of tile for a shower. He orders
2
15 m
to account for cutting the tiles and allow for possible tile breakage. What does the extra
2
1.5 m
represent?
A.nominal value
B.precision
C.tolerance
D.uncertainty
14.A surveyor positioned at point X wants to determine the distance,
AB
, across a pond. Her distance from point A and point B is shown in the diagram below:
Which of the following shows the correct substitution for her to solve for length
AB
using the sine law?
A.
160m
sin40sin110
AB
=
°°
B.
160m
sin30sin110
AB
=
°°
C.
85m
sin110sin30
AB
=
°°
D.
85m
sin30sin40
AB
=
°°
15.Ryland has an outboard motor that uses fuel consisting of a specific gas to oil mixture ratio. For each 15.0 L of gas, he needs to add 0.3 L of oil with a tolerance of
5
±
mL. What are the minimum and maximum amounts of oil he can add to a 30.0 L tank of gas?
A.290 mL to 310 mL
B.295 mL to 305 mL
C.595 mL to 605 mL
D.590 mL to 610 mL
16.Sandra is installing 3 underground sprinklers in her backyard. She sets sprinkler #3 so that it rotates back and forth between sprinklers #1 and #2, spraying the triangular area shown below:
How many degrees does sprinkler #3 turn as it rotates between sprinkler #1 and sprinkler #2?
A.
24
°
B.
28
°
C.
52
°
D.
67
°
17.Greg wants to determine the height of the building. When he stands 50 m from the base of the building, the angle of elevation to the top of the building is 45° as shown below:
Which of the following properties of triangles could he use to determine the height of the building?
A.The legs of an isosceles triangle are equal.
B.The sum of the angles in any triangle is 180°.
C.The legs of all right triangles are perpendicular.
D.The base angles of an isosceles triangle are equal.
18.James is designing a dining room light fixture. The base of the fixture is a circle with a diameter of 80.0 cm. James needs to place 8 lights on the circle, equal distance from each other. What is the distance between any 2 consecutive lights?
A.20.0 cm
B.30.6 cm
C.40.0 cm
D.61.2 cm
19.The chart below shows some Cree syllabics and their associated sounds. The third row has been enlarged.
Which of the following transformations is performed on the symbol for ke to form the symbol for kaa?
A.a vertical reflection of the ke symbol
B.a horizontal reflection of the ke symbol
C.a 90° rotation clockwise of the ke symbol
D.a 180° rotation clockwise of the ke symbol
20.Kaitlyn is on an archealogical dig. Her team is currently working within a roped-off area of 21 square units as shown in the grid below:
Each time her team changes their working area, they move it 1 unit right and 3 units up. After 6 such moves, what are the coordinates of one corner of the work area?
A.(6, 20)
B.(18, 6)
C.(25, 6)
D.(13, 18)
21.Which of the following thermometers has the highest degree of uncertainty for measuring the temperature?
A.
B.
C.
D.
22.Which of the following objects has the most planes of symmetry?
A.
B.
C.
D.
23.Sarah is sketching tile patterns for her living room floor. Each of her patterns begins with a starting tile in the lower left corner as shown below:
Which of the following tile patterns was completed using only translations of the starting tile?
A.
B.
C.
D.
24.The quilting pattern shown below contains grey and white quadrilaterals combined to form an eight pointed star.
When cutting the material for this pattern, what measurements would be necessary when cutting out the quadrilaterals?
A.the perimeter
B.the length of the diagonals
C.the side lengths and the interior angles
D.the angle formed by the intersection of the diagonals
25.Madison is taking measurements of a building to prepare a quote for replacing its shingles. To determine the building’s total height, she makes and records the measurements shown in the diagram below:
What is the height from the ground to the top of the building?
A.18 m
B.27 m
C.31 m
D.36 m
26.Carol is sketching a design using patio brick for a customer’s new driveway. To start the design, she wants to select a 4-sided brick-shape that, when cuts are made along BOTH diagonals of a single brick, 2 pairs of congruent triangles are produced, where:
· one pair of triangles are acute and isosceles; and,
· the other pair of triangles are obtuse and isosceles.
Carol considers a parallelogram-shaped brick similar to the one shown below but decides it does not meet her criteria.
Why is this parallelogram-shaped brick NOT an option?
A.The resulting pairs of triangles are equilateral rather than isosceles.
B.The resulting pairs of triangles would be scalene rather than isosceles.
C.The cuts along the diagonals will not produce 2 pairs of congruent triangles.
D.The cuts along the diagonals will produce 2 pairs of triangles that are both acute.
27.Based on their study of shopping trends, a grocery store chain makes the claim, “Most purchases occur between 4:30 p.m. and 6:30 p.m.” What measure of central tendency are they using?
A.mode
B.median
C.trimmed mean
D.weighted mean
28.On a final math exam written by students throughout Saskatchewan, Bill’s score was at the 80th percentile of his classmates but at the 20th percentile of all Saskatchewan students who wrote the exam. Which of the following statements accurately compares Bill’s score to his classmates and the other students in the province who wrote the exam?
A.Bill, along with 20% of his classmates, will definitely pass this exam.
B.Bill, along with 80% of the students in the province, will definitely pass this exam.
C.Bill scored lower than most of his classmates but scored higher than most of the students in the province.
D.Bill scored higher than most of his classmates but scored lower than most of the students in the province.
29.A weather forecast states, “There is a 20% chance of rain on Saturday.” Which of the following statements communicates the same forecast?
A.The probability of rain on Saturday is 0.2.
B.The chance of rain on Saturday is 20 to 1.
C.The probability of rain on Saturday is 2.0.
D.The chance of rain on Saturday is 2 out of 100.
30.A restaurant’s survey asks customers to rate their satisfaction with different aspects of their dining experience on a scale of 1 to 5. The average ratings for 10 surveys are shown below:
3.2
2.5
4.5
5.0
1.9
4.8
3.9
3.8
4.4
4.1
The restaurant manager determines the average customer rating using a trimmed mean that disregards 20% of the surveys. Using this method, what is the average customer satisfaction rating?
A.3.1
B.3.8
C.3.9
D.4.0
31.Maria works for an oil company. In addition to her base salary, she is paid a daily bonus that depends on the risk level of the job assigned to her that day. The table below shows the number of days she earned different bonuses during a recent 10-day shift:
Level
Daily bonus
Number of days at this level
1
$52.50
0
2
$65.00
0
3
$100.00
0
4
$145.00
4
5
$160.00
0
6
$190.00
0
7
$230.00
3
8
$300.00
1
9
$390.00
0
10
$475.00
2
Based on this information, what was Maria’s mean daily bonus for the 10‑day shift?
A.$210.75
B.$252.00
C.$258.00
D.$287.50
32.In a factory assembly line, 200 bottles were randomly selected each day to see how many labels were applied incorrectly. The results for 1 work week are shown below:
Day
Number of bottles with an incorrect label
Monday
5
Tuesday
6
Wednesday
9
Thursday
2
Friday
4
What is the experimental probability that a label is applied incorrectly?
A.2.3%
B.2.6%
C.13.0%
D.26.0%
33.The chart below shows the percentage of Canadians with each blood type:
Blood Type
Percent of Canadians
A+
36.0%
A–
6.0%
O+
39.0%
O–
7.0%
B+
7.6%
B–
1.4%
AB+
2.5%
AB–
0.5%
People with blood type O– are called universal donors because their red blood cells are compatible with all other blood types. In a blood drive with 182 Canadians, how many universal donors would be expected?
A.7
B.13
C.14
D.26
34.The probability that Katie’s hockey team will win an upcoming game is 2 out of 5. Which of the following teams has the same chance of winning as Katie’s hockey team?
A.a team whose odds of winning are 2 : 3
B.a team whose odds of winning are 2 : 5
C.a team whose probability of losing is
2
3
D.a team whose probability of losing is
2
5
35.Paige is the manager of a clothing store. At the end of each month, the sales of all the stores in the city are compared to find out which location is the most successful. Out of 15 stores, Paige’s store is the only one in the 30th percentile. How many stores were more successful than Paige’s?
A.4
B.5
C.10
D.11
36.Aimee, Kelsey, Pete and Ryan played 4 games of bowling. They decide the winner will be the player with the highest mean score of all 4 games.
Scores
Name
Game 1
Game 2
Game 3
Game 4
Aimee
120
140
125
140
Kelsey
160
140
170
140
Pete
115
130
160
160
Ryan
150
150
160
165
Ryan had the highest mean score of 156.25. Which one of the following scoring changes would have resulted in a different winner?
A.Aimee scoring an additional 25 points total.
B.Kelsey scoring an additional 5 points in each game.
C.Pete scoring an additional 15 points in his two lowest scoring games.
D.Ryan scoring 5 points lower in each of his two highest scoring games.
37.Daisy is a 2-player game where players take turns colouring the petals of a daisy. When a player’s turn begins, he or she can colour:
· a single petal; or,
· 2 adjacent petals (2 petals which are right next to each other.)
The winner is the person who colours the last petal.
Which of the following statements is TRUE?
A.You can always win if you go 1st and colour 1 petal.
B.You can always win if you go 1st and colour 2 petals.
C.You can always win if you go 2nd and colour 2 petals across from a single petal shaded by your opponent.
D.You can always win if you go 2nd and you colour 1 petal beside a single petal shaded by your opponent.
38.The puzzle shown below is a
44
´
grid that has been further subdivided into 7 regions consisting of 2 or 3 cells. Complete the puzzle by entering a digit from 1 to 4 in each cell, in such a way that:
· each horizontal row contains each digit exactly once;
· each vertical column contains each digit exactly once; and
· each region has the sum indicated within it.
Sum = 6
Sum = 8
Sum = 3
Sum = 7
Sum = 5
Sum = 4
Sum = 7
What digit belongs in the shaded cell?
A.1
B.2
C.3
D.4
NUMERIC RESPONSE QUESTIONS
Record your answer in the Numeric Response section of the “Student Examination Form.”
39.Brad bought a new truck that costs $34 599, plus 5% GST and 5% PST. After his $2500 down payment, his monthly payments on the 5-year loan are $658. What is the total interest charged on his loan? (Round to the nearest dollar.)
40.Brody is shopping for a used car. The first car he considers is being sold privately for $1400, taxes included. However, the car needs the following repairs, taxes included:
· new brakes ($400);
· new windshield ($375); and,
· new tires ($660).
A similar car that does not need any repairs is for sale at a used car dealership. If 5% GST is added to the dealership’s sale price, which sale price would result in the same total cost as the first car? (Round to the nearest dollar.)
41.Ruth had 20 L of gasoline in her motorcycle. She drove 200 km and had 8.8 L left. If the motorcycle uses fuel at a constant rate, how many more kilometres can she travel before filling up? (Round to the nearest kilometre.)
42.Karen delivers supplies to fly-in fishing camps in northern Saskatchewan. On her regular route, she flies from her home base to Otter Camp, then to Eagle Camp, and then returns to her home base.
Given the information in the above diagram, what is the total distance of Karen’s route? (Round to the nearest kilometre.)
43.Mr. Ryan’s carpentry class is using wooden boards to construct a picnic table in the shape of a regular hexagon. Sara is cutting the boards for the top of the table.
At what angle, x, should she make cuts on the board shown above?
44.Maureen works as a human resource officer. Below is a graph that shows the number of job vacancies over a 12-month period.
What is the median number of job vacancies for this business? (Round to the nearest whole number.)
45.Chad is working with his real estate agent to determine a reasonable listing price for his home. The prices of 12 similar houses that were recently sold in his area are:
$157 000
$159 750
$161 800
$162 000
$162 000
$166 000
$168 000
$170 000
$174 000
$176 000
$176 500
$184 000
After appraising Chad’s house, the real estate agent recommends a listing price of $165 000. If Chad’s recommended list price is included with the 12 other prices, what is its percentile rank? (Round to the nearest percentile rank.)
GRADE 12 DEPARTMENTAL EXAMINATION
WORKPLACE AND APPRENTICESHIP MATH 30
PROTOTYPE EXAM — Answer Key
(See Explanation of Answers)
1.
B
11.
A
21.
A
31.
B
41.
157
2.
A
12.
B
22.
D
32.
B
42.
636 − 638
3.
D
13.
C
23.
D
33.
B
43.
60
4.
C
14.
A
24.
C
34.
A
44.
13
5.
C
15.
D
25.
C
35.
C
45.
38 − 43
6.
B
16.
A
26.
B
36.
B
7.
B
17.
A
27.
A
37.
C
8.
C
18.
B
28.
D
38.
C
9.
B
19.
D
29.
A
39.
3920
10.
D
20.
D
30.
C
40.
2700
Explanation of Answers
1.B.
A kilometre allowance is applied to all leased vehicles. It protects the dealership by limiting the number of kilometers the vehicle is driven during the term of the lease. This helps control the vehicle’s depreciation, ensuring it is not returned having a value that is significantly below its residual value. If the vehicle’s mileage exceeds the kilometre allowance, the leaser must pay an over-mileage fee to the dealership. This fee or cost only applies to leased vehicles.
Each of the other options apply to both purchases and leases.
2.A.
The market value of Monica’s car is significantly higher than its residual value, most likely due to its mint condition and low mileage. Rather than returning the car, Monica could buy-out the car for $11 000, sell the car for market value, and pocket $6000. This is far better than simply returning the vehicle to the dealership, and giving away the equity in the vehicle.
3.D.
A variable expense is one that changes either in its value or its frequency. The cost for topping will not be the same from month to month. They will depend on the sales for that month, and which toppings the customers select that month. Thus, the toppings are a variable expense.
4.C.
2 marshmallows (units) are included in each sale, the selling price is determined as:
ProfitSellingpriceProductioncost
0Selling price(2Unit cost)
2Unit costSelling Price
=-
£-´
´£
Thus, to ensure a loss is not incurred, the selling price of each marshmallow must be at least double the cost of producing a single marshmallow.
5.C.
The surest way to know if a company is ‘viable’ is to examine its profitability. The company needs to be profitable in order to be viable. If the company’s monthly revenue is consistently greater than its expenses, the company is profitable. (If revenue is consistently less than the expenses, the company is losing money each month and is therefore not viable.)
6.B.
Continuous data is represented by a graph with connected data points. Distance is a measured value which may include a part or fraction of a kilometre. Thus, the number of kilometres travelled is continuous data. The number of texts messages, the number of people, and the number of items, however, are all whole-number (discrete) data and therefore would not be graphed with connected data points.
7.B.
Where: charge$1293.64
variable rate (slope) = $2.62/km
distance travelled
flat rate (-int) = $450
1293.642.62450
843.612.62
321.9885
322km
ymxb
OR
CrdfC
r
d
fy
d
d
d
d
=+
=+==
=
=
=
=+
=
=
=
8.C.
Data is given for 3 different times: 1.4 h, 3 h, and 5 h. A time of 4 hours is within this data and thus a charge could be determined by interpolation.
9.B.
Find the rate of change:
465315150
$75/
532
mh
-
===
-
Find the fixed cost:
46575(5)
465375
90
ymxb
b
b
b
=+
=+
=+
=
The equation of the line is:
OR
7590
ymxb
Ft
=+
=+
The fee for 10 hours is:75(10)9075090$84
0
F
=+=+=
10.D.
SaskEnergy’s natural gas rates are partial variations where the Basic monthly charge is the value of the y-intercept and the Cost per cubic metre is the rate of change (slope). Thus:
· the graph for October 2008 has a y-intercept of $12.50;
· the graph for September 2013 has a y-intercept of $18.85; and
· the cost per cubic metre in October 2008 is greater and will therefore have a steeper slope.
11.A.
A dilation will either enlarge or reduce the original object in proportion, creating a similar, non-congruent figure. A reflection, rotation, or translation will change the orientation of the object but not the size. Subsequently, the transformed figure is congruent to the given one.
12.B.
The precision of a measurement is determined by the limitations of the device used to make the measurement. The smallest division on the measuring device determines the precision. For a recorded measurement, the smallest, right-most decimal is the least precise.
A distance of 6.30 m is given to the nearest hundredth of a metre. Therefore, the precision of this measurement is 0.01 m.
13.C.
Tolerance is the measurement variation. The
2
1.5m
represents the maximum amount of tile to order.
14.A.
Using the Law of Sines, we have:
sinsinsin
160m85m
sin110sin30sin40
abx
ABX
AB
==
==
°°°
The only correct ratio among the response options is:
160m
sin40sin110
AB
=
°°
15.D.
Convert litres to millilitres:
0.3L300 mL
=
To make 30 L of fuel, twice that much oil is needed.
300 mL 2600 mL
\´=
Minimum oil:
600 mL2(5 mL)590 mL
-=
Maximum oil:
600 mL2(5 mL)610 mL
+=
Therefore: 590 mL to 610 mL
16.A.
Let
#3
C
Ð=
1
2030
sinsin38
(20)(sin38)
sin
30
(20)(sin38)
sin
30
24.23253971...
24
C
C
C
C
C
-
=
°
°
=
æö
°
=
ç÷
èø
=°
=°
17.A.
As the given reference triangle is isosceles (
454590
°-°-°
), its legs are equal in length and thus the building’s height is 50.0 m. The properties in the other three response options do not give information about a side length and thus do not give the building’s height.
18.B.
The 8 equally distanced lights form a regular octagon. The diameter of the circle is equal to a diagonal that joins opposite vertices. By drawing each of these diagonals, 8 congruent triangles are formed.
You can find the angles of one triangle using the properties of a regular octagon.
(2)180
Each interior angle
(82)180
8
(6)180
8
135
n
n
-°
=
-°
=
°
=
=°
A
°
=
°
=
=°
=Ð
360
The central angle
360
8
45
n
CB
Each diagonal cuts each interior angle in half. Thus, the base angle of
D
CAB
has a measure of:
135
67.5
2
°
=°
As the octagon’s diagonal is 80 cm, the side length of each triangle is 40 cm.
Thus, in
D
ABC
we have:
Ð=°
45,
ACB
Ð=Ð=°
67.5,
CABCBA
and
==
40cm
CBCA
Thus, the distance between adjacent lights is 30.6 cm.
19.D.
A
180
°
rotation of the ke symbol will transform it into the symbol for kaa.
20.D.
Each x-coordinate will increase by
(616)
´=
after 6 moves and each y-coordinate will increase by
(6318)
´=
after 6 moves. Therefore:
(0,0)(06,018)(6,18)
(7,0)(76,018)(13,18)
(0,3)(06,318)(6,21)
(7,3)(76,318)(13,21)
®++=
®++=
®++=
®++=
The four new vertices will be:
(6,18),(13,18),(6,21),and(13,21).
21.A.
Uncertainty is half the precision of the measuring device and precision is the smallest unit marked.
· Thermometer A has markings every
5C.
°
\
Uncertainty =
2.5C.
±°
· Thermometer B has markings every
2C.
°
\
Uncertainty =
1C.
±°
· Thermometer C has markings every
4C.
°
\
Uncertainty =
2C.
±°
· Thermometer D has markings every
1C.
°
\
Uncertainty =
0.5C.
±°
Thermometer A has the greatest amount of uncertainty.
22.D.
Option A has 1 plane of symmetry.
Option B has 5 planes of symmetry.
Option C has 4 planes of symmetry.
In Option D, any vertical plane passing through the tip of the cone is a plane of symmetry. Therefore, there are an infinite number of planes of symmetry.
23.D.
Tile patterns in A, B and C all require rotations of the original tile in order to create the pattern. Only pattern D can be made using translations (slides).
24.C.
The centre of the star is the meeting point for 8 vertices. Thus, the acute interior angle for each quadrilateral (parallelogram) must equal and have a measure of:
360360
45
8
x
n
°°
===°
In addition, once a side length has been determined for 1 quadrilateral, each of the other 7 quadrilaterals must have the identical side lengths.
Thus, the measurements that must be known are the side lengths and the interior angles.
25.C.
First find the angles of the triangles created by the two measurements.
BCD
Ð
is a straight angle
(180).
°
18060120.
Then, in :
1804812012
BCA
ABC
BAC
\Ð=°-°=°
Ð=°-°-°=°
V
Using the Sine Law to determine side
,
AC
we have:
10.0m
sin12sin48
35.74329m
AC
AC
=
°°
=
Finally, to determine the building’s height,
,
AD
we can use the basic trig ratio for sine:
°=
=°
=
=
sin60
35.74329
(sin60)(35.74329)
30.9545m
31m
AD
AD
\
The building's height is 31 m.
26.B.
The diagonals of a parallelogram bisect each other, thereby creating 2 pairs of congruent triangles.
D@DD@D
and
AOBCODAODCOB
One pair of triangles is acute and the other pair is obtuse. However, both pairs of triangles are scalene NOT isosceles.
27.A.
The time period with the greatest number (frequency) of purchases would be the mode.
28.D.
Being in the 80th percentile in his class means that 80% of the students in the class had a score lower than Bill (and 20% of the students in the class had a score as high or higher than Bill). Since most (80%) of the students in his class had a mark lower than Bill’s mark, he did better on the test than many of the students in his class.
Being in the 20th percentile for Saskatchewan means that 20% of the students in Saskatchewan had a score lower than Bill (and 80% of the students in the province had a score as high or higher than Bill). Since most (80%) of the students in the province had mark greater than Bill’s, he did not do as well on the test as many of the students in the province.
29.A.
20
20%0.20
100
==
30.C.
There are 10 pieces of data, so 20% would mean 2 pieces of data out of 10. Taking off the lowest and the highest values: 1.9, 2.5, 3.2, 3.8, 3.9, 4.1, 4.4, 4.5, 4.8, 5.0, gives a trimmed mean of:
+++++
=
++
2.53.23.83.94.14.44.54.8
8
x
=
=
31.2
3.9
8
x
\
trimmed mean
3.9
=
31.B.
(4145)(3230)(1300)(2475)
10
2520
10
$252.00
x
x
x
´+´+´+´
=
=
=
32.B.
Number of favorable outcomes
P(incorrect)
Total number of outcomes
56924
200(5)
26
0.0262.6%
1000
=
++++
=
===
33.B.
Number of favorable outcomes
P()
Total number of outcomes
7%
182
0.07182
12.74
O
x
x
x
-=
=
=´
=
\
13 O− donors would be expected in a group of 182 people.
34.A.
“2 out of 5” represents a probability. Probability is part-whole whereas odds are part-part. The results can be compared by converting each to a probability in percent form.
Katie: 2 out of 5 is a probability of:
2
0.4040%
5
==
Option A: Odds of winning of
22
2:3P(winning)0.4040%
(32)5
Þ====
+
Option B: Odds of winning of
22
2:5P(winning)0.286740%
(25)7
Þ===¹
+
Option C: If
221
P(losing)P(winning)10.333333.33%40%
333
=Þ=-===¹
Option D: If
223
P(losing)P(winning)10.6060%40%
555
=Þ=-===¹
35.C.
Using the correct percentile ranking formula provided with the exam:
0.5
100
(0.5(1))
30100
15
30(15)
0.5
100
4.50.5
4
LF
PR
n
L
L
L
L
æö
+
=´
ç÷
èø
+
=´
=+
=+
=
OR
Using the incorrect formula from the textbook:
100
30100
15
30(15)
100
4.5
L
PR
n
L
L
L
=´
=´
=
=
Since 4 stores are ranked lower, and her store is the only one in the 30th percentile, then there are:
154110
--=
stores that are ranked higher and are more successful.
36.B.
Initial Mean
Adjusted Mean
Aimee
525
131.25
4
=
52525550
137.5
44
+
==
Kelsey
610
152.5
4
=
6105(4)630
157.5
44
+
==
Pete
565
141.25
4
=
5652(15)595
148.75
44
+
==
Ryan
625
156.25
4
=
6255(2)615
153.75
44
-
==
If Kelsey had scored an additional 5 points per game, she would have won.
37.C.
You can always win if you let your opponent go first (i.e. you go second.)
If your opponent colours 1 petal, you colour 2 petals across from the single petal.
e.g. If your opponent colours petal #1, you colour petals #3 and #4, leaving one petal for your opponent and then then you colour the last petal.
or
If your opponent colours 2 petals, you colour 1 petal across from those 2.
e.g. If your opponent colours petals #1 and #2, colour petal #4, leaving one petal for your opponent and then then you colour the last petal.
Both of these options leave your opponent with a 2nd move that does not win (single petal), but will allow you to win on your 2nd move (single petal).
38.C.
In the bottom row, to get a sum of 7, the digits 4, 2 and 1 must be used. The remaining digit is 3, which is the value of the shaded cell.
Sum = 6
Sum = 8
Sum = 3
Sum = 7
Sum = 5
Sum = 4
Sum = 7
39.Numeric Response: 3920
Cost of truck with taxes:
´=
$346001.10$38060
=-
=
=´´
=
=-
=
Total owing after down payment$38060$250
0
$35560
Total paid on loan$658125
$39480
Interest$39480$35560
$3920
40.Numeric Response: 2700
Private sale car cost$1400repairs
$1400$400$375$660
$2835
=+
=+++
=
Then,
Dealership car cost1.05$2835
$2835
Dealership car cost
1.05
Dealership car cost$2700
´=
=
=
41.Numeric Response: 157
Fuel used20 L–8.8 L11.2L
==
200kmkm
17.857
11.2LL
Then,
km
17.8578.8L157.08km
L
=
´=
\
She can drive the motorcycle for 157 km before running out of fuel.
42.Numeric Response: 636 − 638
Let x = the distance from Eagle Camp to Home Base
222
2
2
2151852(215)(185)cos72
4622534225(24582.3019)
55867.6981
236.36km
236km
x
x
x
x
x
=+-°
=+-
=
=
=
The total distance is:
215185236636km
++=
43.Numeric Response: 60
Each interior angle of a regular hexagon has a measure of:
180(2)
180(62)
6
120
n
z
n
z
z
°-
=
°-
=
=°
Segments joining the opposite angles of the regular hexagon bisect each angle. Therefore:
120
60
22
z
x
°
===°
OR
The central angle for a regular hexagon has a measure of:
360360
60
6
z
n
°°
===°
Then, using the sum of the angles of any triangle is
180,
°
we have:
260180
2120
60
x
x
x
+=
=
=°
44.Numeric Response: 13
The number of job vacancies arranged from least to greatest is:
9
9
10
11
12
13
13
13
14
14
14
14
With 12 data points, the median is the average of the 6th and 7th data points.
131326
median13
22
+
\===
45.Numeric Response: 38 − 43
There are 5 houses with a listing price lower than $165 000. Therefore,
5.
L
=
Using the correct percentile ranking formula provided with the exam:
0.550.5(1)
10010042.342nd
13
LF
PR
n
æö
++
=´=´=@
ç÷
èø
Using the incorrect percentile ranking formula found in the text book:
5
10010038.4638th
13
L
PR
n
=´=´==
Question by Outcome
1.
WA30.6
16.
WA30.3
31.
WA30.9
2.
WA30.6
17.
WA30.4
32.
WA30.11
3.
WA30.7
18.
WA30.4
33.
WA30.11
4.
WA30.7
19.
WA30.5
34.
WA30.11
5.
WA30.7
20.
WA30.5
35.
WA30.10
6.
WA30.8
21.
WA30.2
36.
WA30.9
7.
WA30.8
22.
WA30.5
37.
WA30.1
8.
WA30.8
23.
WA30.5
38.
WA30.1
9.
WA30.8
24.
WA30.4
39.
WA30.6
10.
WA30.8
25.
WA30.3
40.
WA30.6
11.
WA30.5
26.
WA30.4
41.
WA30.8
12.
WA30.2
27.
WA30.9
42.
WA30.3
13.
WA30.2
28.
WA30.10
43.
WA30.4
14.
WA30.3
29.
WA30.11
44.
WA30.9
15.
WA30.2
30.
WA30.9
45.
WA30.10
Content Area
Outcomes
Multiple-choice Questions
Numeric Response Questions
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
x
x
board
Number
of Job
Vacancies
Month
Job Vacancies Over Time
C
A
B
c
a
b
Then, using the Sine Law, we have:
� EMBED Equation.DSMT4 ���
O
A
B
D
C
5
2
4
1
3
3
1
4
2
3
1
4
1
3
2
2
4
3
4
2
1
(October 1999)
- OVER -
October 1997