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
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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
TSSM 2013 Page 2 of 27
This page is blank
FURMATH EXAM 1
TSSM 2013 Page 3 of 27
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
TSSM 2013 Page 4 of 27
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.
SECTION A - continued
FURMATH EXAM 1
TSSM 2013 Page 5 of 27
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.
SECTION A - continued
TURN OVER
FURMATH EXAM 1
TSSM 2013 Page 6 of 27
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.
SECTION A - continued
FURMATH EXAM 1
TSSM 2013 Page 7 of 27
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
SECTION A - continued
TURN OVER
FURMATH EXAM 1
TSSM 2013 Page 8 of 27
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%
SECTION A - continued
FURMATH EXAM 1
TSSM 2013 Page 9 of 27
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.
SECTION A - continued
TURN OVER
FURMATH EXAM 1
TSSM 2013 Page 10 of 27
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
SECTION A - continued
FURMATH EXAM 1
TSSM 2013 Page 11 of 27
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
TSSM 2013 Page 12 of 27
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.