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Letter

Reading Time: 15 minutes Writing Time: 1 hour 30 minutes

Student Number:

Structure of Book

Section Number of questions

Number of questions to be

answered

Number of Modules

Number of modules to be

answered

Number of marks

A – Core B – Modules

24 32

24 16

4

2

24 16

Total 40

• Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners, rulers, one bound reference, one approved technology (calculator or software) and, if desired, one scientific calculator. Calculator memory DOES NOT need to be cleared. For approved computer-based CAS, full functionality may be used.

• Students are NOT permitted to bring into the examination room: blank sheets of paper and/or correction fluid/tape.

Materials Supplied

• Question and answer book of 34 pages.

• Formula sheet.

• Answer sheet for multiple choice questions.

• Working space is provided throughout the book.

Instructions

• Write your name in the space provided above on this page.

Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room.

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The School For Excellence 2018 Units 3 & 4 Further Mathematics – Written Examination 1 Page 1

SECTION A – Core

Instructions for Section A

Answer all questions in pencil on the answer sheet provided for multiple-choice questions.

Choose the response that is correct for the question.

A correct answer scores 1, an incorrect answer scores 0.

Marks will not be deducted for incorrect answers.

No marks will be given if more than one answer is completed for any question.

Unless otherwise indicated, the diagrams in this book are not drawn to scale.

Data Analysis

Use the following information to answer Questions 1 and 2: The graph below shows the number of people living in each house in a street that has fifty houses.

QUESTION 1 The mean number of people living in each house in this street would be

A. 3

B. 3.5

C. 4

D. 4.5

E. 5


QUESTION 2 A box and whisker plot that represents the same information would be A.

B.

C.

D.

E.


The following information is used in Questions 3 and 4: At a large local football club the heights of the players is normally distributed with a mean of 182.1 cm and a standard deviation of 6.3 cm.

QUESTION 3 The percentage of players with heights between 175.8 cm and 194.7 cm is

A. 68%

B. 95%

C. 81.5%

D. 18.5%

E. 47.5% QUESTION 4 Two new players are recruited, one with a height of 179.1 cm and one with a height of 185.1 cm. Which of the following statements about the mean and standard deviation of the height would be true?

A. The mean would remain the same, but the standard deviation would decrease.

B. Both the mean and standard deviation would decrease.

C. Both the mean and standard deviation would increase.

D. Both the mean and standard deviation would remain the same.

E. The mean would remain the same, but the standard deviation would increase. QUESTION 5 A study recorded the performance of a number of battery brands to determine how long in hours that each battery brand lasted. It was found that the recorded times were normally distributed. The z-score for the Evercell battery brand has a value of 2. Given this information, which of the following statements is true?

A. Evercell batteries last twice as long as other batteries.

B. Evercell batteries last two hours longer than the average of the other batteries.

C. Evercell batteries last two hours less than the average battery.

D. 2.5% of the batteries tested last longer than Evercell batteries.

E. Evercell batteries last as long as the top 2% of batteries.


QUESTION 6 The boxplot below shows the logarithm of the balances of savings accounts held by students at a particular bank. All balances are recorded correct to the nearest whole dollar.

The range of balances for these accounts based on the information displayed in the boxplot is

A. $1000

B. $999

C. $990

D. $90

E. $3


The table and information shown below are used in Questions 7 and 8: The table below records the percentage of people who have 20 or more teeth remaining (not

removed) in a number of age groups and the highest education level that they have

received:

Final year of school completed

Year 7 or less Year 8 or 9 Year 10 or 11 Year 12

Ag

e g

rou

p

25 to 44 years 88% 97% 98% 99%

45 to 64 years 56% 81% 90% 96%

More than 65 20% 38% 57% 66%

QUESTION 7 The variables “Final year of school completed” and “age group” in this table are

A. Both nominal categorical variables.

B. A nominal categorical variable and an ordinal categorical variable respectively.

C. An ordinal categorical variable and a nominal categorical variable respectively.

D. Both ordinal categorical variables.

E. An ordinal categorical variable and a continuous numerical variable respectively. QUESTION 8 Which of the following statements is a valid conclusion from the information shown in this table?

A. Having a higher education level will ensure that a person retains 20 or more teeth.

B. There is a positive association between tooth retention and education level in all age groups.

C. 20% of people aged more than 65 only had an education level of Year 7 or less.

D. The association between tooth retention and education level is coincidental.

E. If a person loses their teeth it will affect their educational achievement.


QUESTION 9 The equation of the least squares regression line for the relationship between the number of people attending a particular outdoor event and the maximum daily temperature is

15000 750Number attending maximumtemperature

The value of the correlation coefficient for this relationship is 0.75. Which of the following statements is true?

A. The mean of the number attending must be 1000 times the standard deviation of the maximum temperature.

B. The mean of the number attending must be 1000 times the mean of the maximum temperature.

C. The standard deviation of the number attending must be 1000 times the mean of the maximum temperature.

D. The standard deviation of the maximum temperature must be 1000 times the standard deviation of the number attending.

E. The standard deviation of the number attending must be 1000 times the standard deviation of the maximum temperature.

QUESTION 10 The correlation coefficient for the relationship between a student’s school results and the student’s attendance at school is 0.85r .

A conclusion that can be drawn from the correlation coefficient is

A. There is a moderate, positive relationship between results and attendance.

B. Not attending school causes a student’s results to be lower.

C. Students who attend school regularly tend to have better results.

D. 85% of the variation in school results can be explained by the variation in attendance.

E. Students learn more if they attend school regularly.


The graph and information below are used in Questions 11 and 12: The scatterplot below shows the least squares regression line for the relationship between the cost of a number of people’s monthly gas bill in dollars and the size in squares of their house.

QUESTION 11 The equation of the least squares regression line for this relationship is closest to

A. 8.40 6.05Gasbill in$ sizeof house

B. 6.05 8.40Gasbill in$ sizeof house

C. 68.50 6.05Gasbill in$ sizeof house

D. 69.50 8.40Gasbill in$ sizeof house

E. Sizeof house Gasbill in $8.40 6.05


QUESTION 12 The residual plot that would result from this relationship would be A.

B.

C.

D.

E.


QUESTION 13 The time series plot below shows the number of people dining in a restaurant that is open every day of the week, over a three week period. On this time series day 1 is Sunday Week 1, day 2 is Monday Week 1, etc.

This time series plot is best described as

A. Seasonal with irregular fluctuations.

B. Seasonal with an increasing trend and irregular fluctuations.

C. Cyclic with irregular fluctuations.

D. Cyclic with an increasing trend and irregular fluctuations.

E. An increasing trend with structural changes and irregular fluctuations. QUESTION 14 The monthly takings in thousands of dollars at a restaurant over a one year period are given in the table below:

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Takings in $1000

5.1 4.9 5.4 3.5 3.4 2.9 2.4 2.8 3.5 4.1 5.2 6.3

The four point moving mean centred at August would be

A. 3.2

B. 2.9

C. 3.05

D. 3.1

E. 6.1


The information below is used in Questions 15 and 16: A surfboard retailer’s sales are seasonal. The seasonal indices for the four seasons of the year shown below:

Summer Autumn Winter Spring

1.6 0.9 0.4 1.1

The deseasonalised sales of surfboards is given by the equation

120 11.7deseasonalised sales time period

Where time period 1 = Summer 2015, time period 2 = Autumn 2015 etc.

QUESTION 15 Which of the following statements is not true?

A. Autumn 2017 would be time period 10.

B. Predicted sales in Summer 2020 would be unreliable due to extrapolation.

C. The deseasonalised sales are predicted to rise by 11.7 surfboards per year.

D. Average Summer sales are four times as great as average Winter sales.

E. When correcting for seasonality, Winter sales would be multiplied by 2.5. QUESTION 16 The actual sales in Spring 2018 is predicted to be closest to

A. 279

B. 296

C. 307

D. 325

E. 338


Recursion and Financial Modelling

QUESTION 17 The balance of an investment after n years is given by the recurrence relation

1000 1.050 n+1 nL L L

The balance of this investment after five years would be closest to

A. $1250

B. $1050

C. $1216

D. $1276

E. $1340 QUESTION 18 Which of the following recurrence relations could model the balance of a reducing balance loan of $20 000?

A. A 20000 A 1.025 A 6000 n+1 n

B. A 20000 A 1.025 A 6000 n+1 n

C. A 20000 A 1.025 A 5000 n+1 n

D. A 20000 A A 16000 n+1 n

E. A 20000 A 1.03 A 6000 n+1 n

QUESTION 19 A commercial printing press is purchased for $20 000. The press is depreciated using the unit cost method. The value of the press depreciates by $4.00 for every 5000 sheets printed. The press will have a book value of $15 000 when it has printed

A. 1250 sheets

B. 6 250 000 sheets

C. 625 000 sheets

D. 3750 sheets

E. 18 750 000 sheets


The amortisation table and information below is used for Questions 20 and 21: Amelia takes out a $4000 loan to renovate her kitchen. She will pay the loan off over an eight month period with equal monthly payments of $540 for the first seven months, followed by a smaller final payment that will reduce the balance to zero. An incomplete amortisation table is shown below of the monthly transactions for Amelia’s loan:

Payment Number

Payment Interest Charged Principal Reduction

Balance of Loan

- - - - $4000

1 $540 $30 $510 $3490

2 $540 $26.18 $513.82 $2976.18

3 $540 $22.32 $517.68 $2458.50

4 $540 $18.44 $521.56 $1936.94

5 $540 $14.53 $525.47 $1411.47

6 $540 $10.59 $529.41 $882.06

7 $540 $6.62 $533.38 $348.68

8 $0

QUESTION 20 The per annum rate of interest charged on Amelia’s loan is

A. 9%

B. 0.75%

C. 0.9%

D. 7.5%

E. 9.75% QUESTION 21 The values in the shaded cells would be

A. $537.38, $2.62, $537.38 respectively

B. $540, $2.62, $348.68 respectively

C. $542.62, $2.62, $348.68 respectively

D. $351.30, $2.62, $353.92 respectively

E. $351.30, $2.62, $348.68 respectively


QUESTION 22 The graph below shows the depreciation on a laptop computer over a ten year period:

A recurrence relation that could model this graph would be:

A. 6000 1.20 n+1 nC C C

B. 6000 0.90 n+1 nC C C

C. 6000 0.8 12000 n+1 nC C C

D. 6000 0.80 n+1 nC C C

E. 6000 12000 n+1 nC C C

QUESTION 23 Cam takes out a $20 000 loan at 7.8% per annum compounding weekly to purchase a car. The car is to be paid off with equal weekly payments over a three year period. Correct to the nearest dollar, how much has Cam paid off the principal at the end of 18 months?

A. $10 000

B. $10 584

C. $9 416

D. $17 924

E. $11 223


QUESTION 24 Nathan is planning for his retirement. He currently has $25 000 in his superannuation

account and he will deposit $1500 every month for the next 25 years. His superannuation

account receives 5.3% per annum interest compounding monthly during the course of the 25

years.

After 25 years Nathan intends to retire. He will change his balance over to an annuity. He

wants to draw $5200 every month and he will receive 5.3% per annum compounding

monthly in the annuity.

How long will Nathan be able to draw the full amount of $5200 from his annuity?

A. 197 months

B. 198 months

C. 273 months

D. 468 months

E. 469 months

END OF SECTION A


SECTION B – Modules

Instructions for Section B

Select two modules and answer all questions within the selected modules in pencil on the answer sheet provided for multiple-choice questions.

Show the modules you are answering by shading the matching boxes on your multiple-choice answer sheet and writing the name of the module in the box provided.

Choose the response that is correct for the question.

A correct answer scores 1; an incorrect answer scores 0.

Marks will not be deducted for incorrect answers.

No marks will be given if more than one answer is completed for any question.

Unless otherwise indicated, the diagrams in this book are not drawn to scale.

Contents Page

Module 1 – Matrices ……………………………………………………………….….……… 18

Module 2 – Networks and decision mathematics………………………………..………… 22

Module 3 – Geometry and measurement……….……………………………..…………… 26

Module 4 – Graphs and relations……………….…….…………………………..………… 32


Module 1: Matrices Before answering these questions, you must select the “Matrices” module on the answer sheet for multiple choice questions and write the name of the module in the space provided.

QUESTION 1

The transpose of matrix A0 2 3

5 4 6

is

A.

3 6

2 4

0 5

B. 5 4 6

0 2 3

C.

5 0

4 2

6 3

D. 6 4 5

3 2 0

E.

0 5

2 4

3 6

QUESTION 2 The element in row i and column j of matrix P is

ijp .

The elements in matrix P are determined using the rule ijp i j3 .

A matrix that could not be P is

A. 2 1

B. 2

5

C. 2 1

5 4

D.

2

5

10

E. 2 1 0


QUESTION 3

The inverse D 1 of matrix D

6 3

11 6

is

A. 6 31

11 63

B. 2 1

3.7 2

C. 6 31

11 63

D. 6 111

3 63

E. 6 11

3 6

QUESTION 4 Matrix C represents the number of new (N) and used (U) cars sold in January (J), February

(F) and March (M) at a car dealer:

C

J F M

10 12 16 N

23 18 31 U

New cars make a profit of $4000 each and used cars make a profit of $2000 each.

A matrix equation that would calculate the total profit made at the car dealer during the three given months would be:

A. C4000 2000

B. C4000

2000

C. C1 4000

1 2000

D. C

1

1 4000 2000

1

E. C

1

4000 2000 1

1


QUESTION 5 Which of the following matrix equations would represent a set of inconsistent simultaneous

equations?

A. x

y

1 2 13

3 4 29

B. x

y

1 2 13

2 4 29

C. x

y

1 2 13

2 4 26

D. x

y

3 2 7

6 4 14

E. x

y

3 2 17

3 4 21

QUESTION 6 In a laundromat there are three washing machines, A, B and C. A large number of people

use the laundromat on a regular weekly basis and in the first week an equal number of

people use each machine. Over time the machines that people use will change week by

week as per the following transition matrix:

this week

A B C

A

B next week

C

0.2 0 0.6T

0.4 1 0.1

0.4 0 0.3

Which of the following statements is not true?

A. Eventually only machine B will be used.

B. The steady state matrix proportions would be the same regardless of the initial state

matrix values.

C. Of the people who use machine A each week, the same number of people change to

each of machines B and C the next week.

D. The number of people who change from machine A to machine B every week is four

times the number of people changing from machine C to machine B every week.

E. Of the people using machine C each week 10% change to machine B.


QUESTION 7 The matrix product PQR exists, but the matrix product PR does not exist. Which of the

following statements is not true?

A. Both PQ and QR must exist.

B. The inverse of Q, Q -1, does not exist.

C. PQ + QR could exist.

D. PQR -1 – PQR could exist.

E. RP could not exist.

QUESTION 8 People who go on cruise holidays can choose from interior (I), oceanview (O) or balcony (B)

cabins. The number of people choosing each option on a popular cruise line is changing

from year to year. The rule that gives the matrix containing number of people choosing each

option is

I

C C C O

B

n 1 n 2015

0.3 0.1 0.2 200 1000

0.2 0.5 0.4 500 where 2000

0.5 0.4 0.4 100 3000

.

The number of people choosing each option in 2017 would be given by

A.

C C2017 2015

0.3 0.1 0.2 200

2 0.2 0.5 0.4 2 500

0.5 0.4 0.4 100

B.

C C

2

2017 2015

0.3 0.1 0.2 200

0.2 0.5 0.4 2 500

0.5 0.4 0.4 100

C.

C C2017 2015

0.3 0.1 0.2 0.3 0.1 0.2 200 200

0.2 0.5 0.4 0.2 0.5 0.4 500 500

0.5 0.4 0.4 0.5 0.4 0.4 100 100

D.

C C2017 2016

0.3 0.1 0.2 200

0.2 0.5 0.4 2 500

0.5 0.4 0.4 100

E.

C C2017 2015

0.3 0.1 0.2 0.3 0.1 0.2 200

0.2 0.5 0.4 0.2 0.5 0.4 2 500

0.5 0.4 0.4 0.5 0.4 0.4 100


Module 2: Networks and decision mathematics Before answering these questions, you must select the “Networks and decision mathematics” module on the answer sheet for multiple choice questions and write the name of the module in the space provided.

QUESTION 1 Consider the following graph.

Which of the following statements is not true? A. The graph is a connected, planar graph. B. The graph has four regions. C. The graph is a simple graph. D. There is a bridge in this graph. E. There are four vertices in this graph with a degree of three. QUESTION 2 A connected, planar graph has twice as many edges as vertices. The number of regions will be A. Two more than the number of vertices B. Two C. Two more than the number of edges D. Two less that the number of vertices E. Two less than the number of edges


QUESTION 3 A network is shown in the diagram below:

For the graph shown above, there is A. An Eulerian circuit and a Hamiltonian cycle only. B. An Eulerian trail and a Hamiltonian path only. C. An Eulerian circuit and a Hamiltonian path only. D. An Eulerian trail and a Hamiltonian cycle only. E. An Eulerian trail and both a Hamiltonian cycle and path. QUESTION 4 An activity network for a large projects is shown below. The duration of each activity in hours is also shown.

Which of the following statements about this network is not true? A. The shortest time in which the project could be completed is 24 hours.

B. There are two critical paths for this network.

C. If activity B was reduced by two hours, there would be no reduction in the minimum time.

D. Activity F has the greatest float time of all activities.

E. Activity G cannot be started until activity E is completed.


The directed graph below shows the capacities, in litres per minute, of a series of water pipes that connect a source to a sink. The diagram is used in Questions 5 and 6:

QUESTION 5 The capacity of Cut 1 shown on the diagram in litres per minute is A. 118 B. 108 C. 98 D. 88 E. 78 QUESTION 6 The pipe that has a capacity of 18 litres per minute is to be replaced with a pipe of capacity of 40 litres per minute. This would result in A. No change to the maximum flow through the network. B. An increase in the maximum flow by 22 litres per minute. C. An increase in the maximum flow by 15 litres per minute. D. An increase in the maximum flow by 1 litre per minute. E. An increase in the maximum flow by 5 litres per minute.


The following information is used in Questions 7 and 8:

A minimal spanning tree is to be drawn for the weighted graph below:

QUESTION 7 The weight of the minimal spanning tree is A. 24 B. 26 C. 22 D. 25 E. 28 QUESTION 8 The number of different minimal spanning trees that can be drawn is A. 5 B. 6 C. 7 D. 8 E. 9


Module 3: Geometry and measurement

Before answering these questions, you must select the “Geometry and measurement”

module on the answer sheet for multiple choice questions and write the name of the module

in the space provided.

QUESTION 1

Consider the following right angled triangle.

The length of the side marked x is closest to

A. 8 cm

B. 13.1 cm

C. 12.6 cm

D. 20 cm

E. 15.2 cm

QUESTION 2

Triangle PQR is shown below. PQ is 12.2 cm, PR is 19.6 cm and angle PQR is 131⁰.

The size of angle QPR, labelled b⁰, is closest to

A. 28⁰

B. 21⁰

C. 23⁰

D. 52⁰

E. 19⁰


QUESTION 3 The perimeter of the sector shown below is 14 m. The length of the radius r is closest to

A. 3.41 m B. 4.32 m C. 4.75 m D. 6.25 m E. 11.30 m QUESTION 4 A 4 metre high solid concrete stage is shaped as a truncated cone as shown below. The radius of the base is 9 metres and the radius of the top is 6 metres.

The volume of concrete used to make the stage, in cubic metres, would be closest to A. 2149 m3

B. 867 m3

C. 716 m3

D. 528 m3

E. 339 m3


QUESTION 5 The position of Edinburgh, Scotland (56⁰N, 3⁰W) is shown on the diagram of the Earth below. Assume that the radius of the Earth is 6400 km.

Based on this information which of the following statements is not true? A. The shortest distance from Edinburgh to the equator is 6255 km correct to the nearest

km.

B. The sun would rise approximately 12 minutes later in Edinburgh than in Greenwich on the prime meridian.

C. The radius of the small circle that passes through Edinburgh would be 3579 km correct to the nearest km.

D. The radius of the parallel of latitude at Edinburgh in km is calculated using 6400 sin(56) .

E. The distance from Edinburgh to the Greenwich prime meridian would be 187 km correct to the nearest km.

QUESTION 6 Karl goes on a hike with a compass. He walks 3.90 km on a bearing of 040⁰ and then he walks 2.42 km on a bearing of 114⁰. The bearing that he should take to walk directly back to his starting point is closest to A. 067⁰ B. 247⁰ C. 223⁰ D. 207⁰ E. 227⁰


QUESTION 7 Consider the diagram below:

In this diagram angle ADB is equal to angle ACD. The length AB is 5 cm and the length AD is 9 cm. The ratio of the unshaded to shaded area is A. 5:9 B. 25:81 C. 4:5 D. 25:56 E. 16:25


QUESTION 8 Sam is approaching a tall building on horizontal ground. He walks 100 m in a direct line from his starting position towards the building. From his second position his angle of elevation to the top of the building is 61⁰. The top of the building is 45 metres above his horizontal line of sight. This is shown in the diagram below.

The angle of elevation to the top of the building from his original position is closest to

A. 20⁰

B. 13⁰

C. 24⁰

D. 29⁰

E. 70⁰


Module 4: Graphs and relations Before answering these questions, you must select the “Graphs and relations” module on the answer sheet for multiple choice questions and write the name of the module in the space provided.

QUESTION 1 The equation of the line shown below is:

A. x y3 7

B. x y3 7

C. x y3 7 1

D. x y7 2.5 14

E. x y3 7

QUESTION 2 The point (-7, -5) satisfies the inequality

A. y x

B. x y5 7 0

C. x y10

D. x6 3

E. y x2


QUESTION 3 Annika goes for a bike ride. The graph below shows the distance in metres, d, that Annika is from home after t minutes.

Annika was cycling fastest between

A. 0 to 5 minutes

B. 5 to 8 minutes

C. 8 to 12 minutes

D. 12 to 20 minutes

E. Both 0 to 5 minutes and 12 to 20 minutes as she is running at the same speed QUESTION 4 David is a teacher taking a large group of students to see a Star Wars movie. Altogether the tickets for the 3 adults and 25 children will cost $315.90. An adult ticket costs $4.80 more than a child’s ticket.

If the cost of an adult ticket is A and the cost of a child ticket is C , then a set of

simultaneous equations that could be used to determine A and C is

A. A C3 25 315.9 and A C 4.8

B. A C25 3 315.9 and A C 4.8

C. A C3 25 315.9 and C A 4.8

D. A C3 25 315.9 and C A 4.8

E. A C25 3 315.9 and A C 4.8


QUESTION 5

The equation of the relationship shown above is

A. y x0.8

B. y x1.25

C. x

y5

4

D. yx

5

4

E. yx

4

5


QUESTION 6 A graph is shown below showing the relationship between the revenue in dollars (R) made at a large function centre and the number of people (n) attending a function. The function centre charges an amount per person that is more for the first 40 people. If more than 40 people attend the function, every person after the first 40 is charged at a lower rate. If 30 people attend a function, then the revenue is $1200. If 40 people attend a function, the revenue is $2000. If 70 people attend a function, the revenue is $2500. These points are shown on the graph.

The function centre have fixed costs of $200 per function, as well as a cost of $30 per person. The function centre will make a profit if

A. n 20

B. n 21

C. n 111

D. n20 110

E. n21 109


The information and graph, including the shaded feasible region below, is used in Questions 7 and 8:

A retailer stocks and sells washing machines and tumble dryers. For this problem, let x be the number of washing machines sold and y be the number of tumble dryers sold. It is

assumed that x 0 and y 0 .

QUESTION 7 Which of the following could be the descriptions of the inequalities for this problem?

A. The retailer can stock a maximum of 30 washing machines and a maximum of 40 tumble dryers with no more than 50 items in total. He stocks at least twice as many washing machines as tumble dryers.

B. The retailer can stock a maximum of 30 washing machines and a maximum of 40 tumble dryers with no more than 50 items in total. The number of tumble dryers is at least half the number of washing machines.

C. The retailer can stock a maximum of 40 washing machines and a maximum of 30 tumble dryers with no more than 50 items in total. He stocks at least half as many washing machines as tumble dryers.

D. The retailer can stock a maximum of 40 washing machines and a maximum of 30 tumble dryers with no more than 50 items in total. He stocks at least twice as many washing machines as tumble dryers.

E. The retailer can stock a maximum of 30 washing machines and a maximum of 40 tumble dryers with no more than 50 items in total. The number of tumble dryers is no more than half the number of washing machines.


QUESTION 8 The profit on each washing machine is $50 and the profit on each tumble dryer is $60. Which of the following statements is not true?

A. If the objective function is maximised, the maximum would be at point B.

B. If the profit on each washing machine increased by $25, the new maximum would be at point C.

C. If the profit on tumble dryers fell by $10 each, the maximum profit would be at any integer point on the line between B and C.

D. If, during a sale, the tumble dryers are reduced by $90, the maximum profit is at point D.

E. If, during a sale, the washing machines are reduced by $60, the maximum profit is at point C.

END OF MULTIPLE-CHOICE QUESTION BOOK

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