Units 3 & 4 Written examination 1 - intranet.cesc.vic.edu.au Maths... · Units 3 & 4 – Written examination 1 ... Chemistry test to achieve the same standard score for both the subjects

TSSM 2013 Page 1 of 27

FURTHER MATHEMATICS Units 3 & 4 – Written examination 1

(TSSM’s 2013 trial exam updated for the current study design)

Reading time: 15 minutes

Writing time: 1 hour and 30 minutes

MULTIPLE-CHOICE QUESTION BOOK

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

24

24

24

B 32 16 4 2 16

Total 40

Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners,

rulers, one bound reference, one approved graphic calculator or approved CAS calculator or CAS software

and if desired, one scientific calculator

Students are NOT permitted to bring into the examination room: blank sheets of paper and/or white out

liquid/tape.

Materials supplied

Question book of 27 pages.

Instructions

Print your name in the space provided on the top of this page.

All written responses must be in English.

Students are NOT permitted to bring mobile phones and/or any other unauthorised

electronic communication devices into the examination room.

Figures

Words

‘2016 Examination Package’ -

Trial Examination 3 of 5

Letter

STUDENT NUMBER

THIS BOX IS FOR ILLUSTRATIVE PURPOSES ONLY

FURMATH EXAM 1


This page is blank

FURMATH EXAM 1


SECTION A

Instructions for Section A

Answer all 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.

Core: Data analysis

Question 1

The mean weight of nine blocks of chocolate is 170g. The total weight of these nine chocolates is

closest to:

A. 0.2 kg

B. 1.3 kg

C. 1.5 kg

D. 1.6 kg

E. 1.8 kg

Question 2

The following information was recorded for a class about test results in Biology and Chemistry.

The test results were normally distributed.

subject mean standard deviation

Biology 54 15

Chemistry 78 5

If Tara obtained a mark of 81 in the Biology test, the mark that she needs to obtain on the

Chemistry test to achieve the same standard score for both the subjects is:

A. 81

B. 82

C. 83

D. 87

E. 9

SECTION A - continued

TURN OVER

FURMATH EXAM 1


Question 3

The table below shows the percentage of students in two-age groups who regularly eat food

cooked at one or more of three locations.

Location Age group

15-19 years 20-24 years

home 95% 95%

cafes 85% 18%

restaurants 38% 74%

For the students surveyed, which one of the following statements, supports the argument that the

location of food cooked is associated with the age group of the students?

A. 95% of students aged 15-19 years ate home cooked food, but only 38% of 15-19 year olds ate

at restaurants.

B. 85% of students aged 15-19 years ate food at a café.

C. 95% of students aged 15-19 years ate home cooked food, but only18% of 20-24 year olds ate

at restaurants

D. The percentage of students who ate food at a café decreased from 85% for those aged 15-19

year olds to 18% for those aged 20-24 years.

E. The percentage of students who ate home cooked food was 95% for both the age groups.

Question 4

The number of siblings in each of the 20 households is recorded in the frequency table below.

Number of siblings Frequency

0 6

1 9

2 3

3 1

4 0

5 1

For this sample of households, the percentage of households with at least one sibling is:

A.

B.

C.

D.

E.


FURMATH EXAM 1


The following information relates to Questions 5 and 6

The following data shows the change in blood pressure of a rabbit over time.

0.5, 4, 10, 26, 37, 32, 1.25, 0.75, 4, 9, 25, 37

A log scale is used to represent the above data in a histogram.

Question 5

The data represented on a log scale is:

A. positively skewed

B. negatively skewed

C. symmetric

D. bimodal

E. approximately symmetric

Question 6

The value of 0.6 on a log scale is closest to:

A. 4.5

B. 9

C. 32

D. 26

E. 4

Question 7

For a set of bivariate data, involving the variables x and y, the following information was

obtained.

The equation of the least squares regression line is closest to:

A.

B.

C.

D.

E.


TURN OVER

FURMATH EXAM 1


Question 8

The number of bikes parked in a 30-space bike shed is counted each day for a month. Which one

of the following would be an appropriate representation to display the data recorded?

A. a dot plot

B. a bar chart

C. a stem plot

D. a histogram

E. a frequency table

Question 9

For the time series given in the table below, the three-moving mean centred at x = 5 is:

x 1 2 3 4 5 6 7 8 9 10

y 4 5 4 4 8 6 9 10 9 12

A. 4

B. 5

C. 6

D. 7

E. 8

Question 10

For the histogram shown below, which of the following statements is most likely to be true?

A. The mode would exceed the mean.

B. The mean would exceed the mode.

C. The mean would equal the mode.

D. The lower quartile would equal the median.

E. The interquartile range would exceed the range.


FURMATH EXAM 1


Question 11

The graph below shows a plot of the residuals against the x-values for a particular data set (x, y).

The residuals were determined after a least squares regression line was fitted to the data.

Which of the following is true?

A. An x2 transformation should be carried out on the original data set.

B. A log transformation should be carried out on the original data set.

C. The actual y-value for the first x-value falls above the least squares regression line.

D. The actual y-values for the last two x-values are the same distance from the least squares

regression line.

E. There are equal numbers of points above and below the least squares regression line.

Question 12

The quarterly sales for a cheese producing company and seasonal indices are as follows.

quarter (2000) Q1 Q2 Q3 Q4

sales ($1000s) 3600 3200 3100 3800

seasonal index 1.04 0.8 1.2

The deseasonalised figure in $1000s for the second quarter is closest to

A. 3072

B. 3200

C. 3333

D. 3462

E. 3875


TURN OVER

FURMATH EXAM 1


Question 13

The product moment correlation, r, for the relationship between police expenditure and the crime

rate is – 0.54. This means that

A. only 54% of crime is solved

B. increased police expenditure has a 54% chance of decreasing the crime rate.

C. there is no relationship between police expenditure and the crime rate.

D. there is a strong negative relationship between police expenditure and the crime rate.

E. police expenditure and the crime rate are moderately negatively related.

Question 14

The coefficient of determination between two variables is 0.8674. The least squares regression

line describing the association between these two variables is given by

The value of product moment correlation coefficient between the two variables is closest to

A. 0.9313

B. – 0.4317

C. 0.4317

D. – 0.9313

E. 12.56

Question 15

The distribution of weights of items produced by a manufacturing process can be approximated

by a normal distribution with a mean of 90 grams and a standard deviation of 1 gram. The

percentage of the items will either weigh less than 88 grams or more than 93 grams is

A. 2.5%

B. 2.65%

C. 5.0%

D. 0.15%

E. 16.0%


FURMATH EXAM 1


Question 16

The following data shows the relationship between number of cigarettes smoked and life

expectancy.

Number of cigarettes Life expectancy

5 80

23 78

25 60

48 53

17 85

8 84

4 73

26 79

11 81

19 75

14 68

35 72

29 58

4 92

23 65

The least squares regression line is used to predict life expectancy from number of cigarettes

smoked. The slope of this line indicates

A. life expectancy increases as the number of cigarettes smoked increases

B. life expectancy decreases by 85.7 as the number of cigarettes smoked increases

C. life expectancy decreases by 0.63 year with every increase in number of cigarettes

D. increase in number of cigarettes causes life expectancy to decrease by 0.63

E. increase in life expectancy tends to decrease the number of cigarettes by 0.63

Core: Recursion and financial modelling

Question 17

A businessman aims to increase profits by 10% each year. The profit, , in dollars, after n years,

would be modelled by the rule:

A.

B.

C.

D.

E.


TURN OVER

FURMATH EXAM 1


Question 18

A tank contains 18 000 litres of water. The water flows out at a constant rate of 120 litres per

minute. The amount of water left in this tank after three hours is:

A. 0 L

B. 3600 L

C. 7200 L

D. 10 800 L

E. 14 400 L

Question 19

Rachelle decides to improve her fitness level by cycling each day. The time in minutes Mn that

Rachelle cycles on the nth day is modelled by the recurrence relation where

. The number of minutes Rachelle cycles on day 4 is closest to:

A. 23

B. 25

C. 26

D. 27

E. 68

Question 20

A sequence is defined by the recurrence relation . The rule that

defines the nth term of this sequence is:

A.

B.

C.

D.

E.

Question 21

Shelly invests $45000 at 4% per annum for 5 years compounded annually. The total amount of

interest earned is closest to:

A. $1800

B. $2100

C. $9000

D. $9750

E. $54750


FURMATH EXAM 1


Question 22

Jane borrows $80 000 for 10 years at 5.6% per annum, compounded monthly, with monthly

repayments of $555. Which one of the following is true?

A. The loan will be fully paid out in 10 years.

B. Weekly repayments of $132 compounded weekly would reduce the period of the loan.

C. The amount of interest paid each month during the loan increases.

D. The balance of the loan will be $40 000 at the end of five years.

E. The loan will be fully paid out in 12 years.

Question 23

An investment of $1200 for one year returns $140.38 interest. The simple interest rate per annum

for this investment is closest to:

A. 0.88%

B. 3.21%

C. 4.38%

D. 11.70%

E. 15.99%

Question 24

Shia buys a new television. The advertised price was $2700. He chooses to pay a deposit of $500

and monthly repayments of $115 over 2 years.

The total cost of the television under this arrangement is closest to:

A.

B.

C.

D.

E.

END OF SECTION A

TURN OVER

FURMATH EXAM 1


SECTION B

Instructions for Section B

Select two modules and answer all questions within the modules.

Choose the response that is correct or best answers the question and mark this response on the

multiple-choice response sheet.

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

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

Marks will not be deducted for incorrect answers.

Module Page

Module 1: Matrices...................................................................................... 13

Module 2: Networks and Decision Mathematics......................................... 17

Module 3: Geometry and measurement……………................................ 21

Module 4: Graphs and relations................................................................... 24

SECTION B - continued

FURMATH EXAM 1


Module 1: Matrices

Question 1

If

00

46

31

A and the matrix product

53

41

14

XA then order of matrix X is:

A. 22 B. 32

C. 13

D. 23

E. 33

Question 2

If

14

28A and

26

13B then the matrix

26

1236AB

The element “6” in the matrix AB is correctly obtained by:

A. 6134

B. 6134

C. 4286

D. 6134

E. 6134

SECTION B – continued

TURN OVER

FURMATH EXAM 1


Question 3

Consider the following system of three simultaneous equations

63

234

123

zx

zyx

zyx

The solution of the simultaneous equations above is given by:

A.

6

2

1

536

404

112

8

1

z

y

x

B.

6

2

1

536

404

112

z

y

x

C.

6

2

1

103

341

123

z

y

x

D.

6

2

1

103

341

123

8

1

z

y

x

E.

6

2

1

113

341

123

z

y

x

Question 4

Which one of the following is not true for the matrix equation CAB , where

4

6,

42

31Cand

x

yBA

A. 2|| A

B. The product AB is defined.

C. The product AC is defined.

D. A is a singular matrix.

E. y = -6 and x = -4


FURMATH EXAM 1


Question 5

Let

66

10,

12

55,

54

32CBA

The matrix X such that CABX can be found by:

A. CABX 1

B. CBAX 1

C. CBAX 1)(

D. 1)( ABCX

E. CABX 1)(


A railway knows that 250 goods wagons will be needed to carry goods from point A to point B.

At the end of each week, it finds that 10% of the wagons that started at A, ended at point B, and

8% of the wagons that started at point B ended at point A.

Question 6

A transition matrix that could represent this situation is:

A.

2.01.0

8.09.0

B. 0.9 0.08

0.1 0.92

C.

92.09.0

08.01.0

D.

2.09.0

8.01.0

E.

08.09.0

92.01.0


TURN OVER

FURMATH EXAM 1


Question 7

If equal number of wagons started at both points, the number of wagons located at point B at the

end of two weeks is:

A. 120

B. 121

C. 129

D. 130

E. 131

Question 8

If RTSP , matrix P is of order 33 and

1009

841

323

T then the order of R is:

A. 23

B. 32

C. 33

D. 22

E. cannot be found

END OF MODULE 1

FURMATH EXAM 1


Module 2: Networks and decision mathematics

Question 1

The sum of the degrees of all the vertices in the network below is:

A. 6

B. 7

C. 8

D. 9

E. 10

Question 2

Which one of the following statements is true regarding the network shown below?

A. ABCDEFG is a Hamiltonian circuit.

B. Only one Hamiltonian path exists.

C. CBAGFEDC is an Eulerian circuit.

D. At least two Eulerian paths exist.

E. There are no circuits.


TURN OVER

G F

E

D

C B

A

FURMATH EXAM 1


Question 3

A connected planar graph has 12 edges. This graph could have:

A. 5 vertices and 6 faces.

B. 5 vertices and 8 faces.

C. 6 vertices and 8 faces.

D. 6 vertices and 9 faces.

E. 7 vertices and 9 faces.


Consider the following table.

Activity Time Immediate predecessor

A 12 -

B 11 A

C 13 -

D 24 A, C

E 11 D, B

F 21 E

Question 4

The activity/ies that come before activity E is/are:

A. D and B.

B. A, D and B.

C. A, C and D.

D. A, B, C and D.

E. F.

Question 5

The earliest completion time for the network is:

A. 55

B. 56

C. 68

D. 69

E. 70


FURMATH EXAM 1


Question 6

Consider the network flow diagram below representing the flow of water between a reservoir (A)

and a town (H). The other nodes (B…G) represent pumping stations. One of the four dotted lines

shown on the diagram is the minimum cut for this network.

The maximum flow of water from A to H is:

A. 100

B. 110

C. 120

D. 130

E. 140

Question 7

Which of the following statements is true?

A. A Hamiltonian circuit is a tree.

B. A tree can contain multiple edges or loops.

C. A Hamiltonian path is not a tree.

D. A tree can visit the same vertex more than once.

E. A tree can have one edge.


TURN OVER

FURMATH EXAM 1


Question 8

What additional edge should be added to the planar graph in the figure below to make an Euler

circuit possible?

A. CA

B. FA

C. FD

D. EB

E. none of the above

END OF MODULE 2

F

A B

E

C E

D

FURMATH EXAM 1


Module 3: Geometry and measurement

Question 1

Which one of these can be used to find the value of in the diagram on the right?

A. ( )

B. ( ) ( )

C. ( )

D. ( ) ( )

E. ( )

35°

Question 2

If the value of ( )

then the area of the triangle is:

A. 27 square units

B. 55 square units

C. 88 square units

D. 110 square units

E. 176 square units

Question 3 The combined total surface area of a hemisphere of radius 28mm mounted on top of a right

circular cone, with slant height 40mm is closest to:

A. 8444.6 mm2

B. 9221 mm2

C. 14146.5 mm2

D. 50271.1 mm2

E. 16609.5 mm2


TURN OVER

θ

16

11

6

θ B

C A 9

FURMATH EXAM 1



A girl scout walks on a bearing of for 10km. Another scout starts from the same initial

position and walks due west until she is due north of the 1st scout.

Question 4

How far did the 2nd

scout walk?

A. 3.7 km

B. 4.2 km

C. 5.8 km

D. 6.7 km

E. 7.4 km

Question 5

The distance between the two scouts is closest to:

A. 7.4314 km

B. 6.6913 km

C. 4.4832 km

D. 4.9791 km

E. 11.1061 km

Question 6

The arc length of a circle with radius 4.2 cm is 4π cm. The angle that this arc subtends at the

centre is closest to:

A.

B.

C.

D.

E.


FURMATH EXAM 1


Question 7

If the height of a rectangle with diagonal equal to 76 cm is x cm, then a similar rectangle with

diagonal equal to 38 cm has a height given by:

A.

cm

B.

cm

C.

cm

D.

cm

E.

cm

Question 8

The length of the side of an equilateral triangle with area 0.4 cm2 is closest to:

A.

B.

C.

D.

E.

END OF MODULE 3

TURN OVER

FURMATH EXAM 1


Module 4: Graphs and relations

Question 1

At a café, one sandwich costs $2.40 and one drink costs $3.00. A customer purchased five

sandwiches and a number of drinks at a total cost of $24.00. The number of drinks purchased

was:

A. 4

B. 5

C. 6

D. 9

E. 10

Question 2

The shaded area in the graph below represents the feasible region for a linear programming

problem.

The minimum value of the objective function for this feasible region is:

A.

B.

C.

D.

E.


FURMATH EXAM 1


Question 3

The graph of y against

is shown below:

The rule connecting x and y is:

A.

B.

C.

D.

E.

Question 4

The confectionery store makes both dark and white chocolates. It makes at least twice as many

dark chocolates as white chocolates. If x represent the number of dark chocolates and y represent

the number of white chocolates, an inequality representing the situation is:

A. 2 xy

B. xy 2

C. xy 2

D. yx 2

E. yx 2


TURN OVER

(2, 5)

1/x

y

FURMATH EXAM 1


Question 5

Which of the following rules could be used to describe the graph above?

A.

64,12

40,532

x

xxy

B.

64,12

40,532

xx

xxy

C.

64,12

40,532

xx

xxy

D.

64,12

40,5.232

xx

xxy

E.

64,12

40,5.232

x

xxy

Question 6

A linear inequation has an x-intercept of 5 and a y-intercept of 6. Also, the point (0, 0) is not

included in the solution region. The linear inequation is:

A. 3065 xy

B. 3065 xy

C. 3056 xy

D. 3056 xy

E. 30 xy


FURMATH EXAM 1


Question 7

The required region shown in the following graph is best described by:

A. 0,0,032,842 yxxyyx

B. 0,0,023,024 yxxyyx

C. 0,0,032,842 yxxyyx

D. 0,0,032,842 yxxyyx

E. 0,0,032,842 yxxyyx

Question 8

A manufacturer produces 2 softwares, Playpal (x) and Playshow (y), and requires two stages in

the production of the software, programming and manufacturing.

The programming stage requires 4 workers per hour to build a Playpal, but 6 workers per hour to

build Playshow. There are up to 72 workers per hour available. The manufacturing stage requires

8 workers per hour for Playpal but 5 workers per hour for Playshow with up to 88 workers per

hour available.

The constraint regarding the programming of each software is:

A.

B.

C.

D.

E.

END OF MULTIPLE-CHOICE QUESTION BOOK

Documents

Units 3 & 4 Written examination 1 - intranet.cesc.vic.edu.au Maths... · Units 3 & 4 – Written examination 1 ... Chemistry test to achieve the same standard score for both the subjects