# 2 UNIT

Based on the 2014 syllabus and the BOS specimen paper.

Working time 2 ½ hours

DIRECTIONS TO CANDIDATES

Section 1: 25 marks

 Attempt Questions 1  25

 Allow about 35 minutes for this section

Section II: 75 marks

 Attempt questions 26  30

 Allow about 1 hour and 55 minutes for this section

 A formula sheet is provided at the end of the paper.

 Board approved calculators may be used.

 Answer each question of section II on a separate page.

 In questions 26 to 30 show relevant mathematical reasoning and/or calculations

 You may ask for extra paper if you need it.

### Section I; 25 marks

Attempt Questions 1-25
Allow about 35 minutes for this section.

1 Jordan borrowed \$12000 to buy a car. He repaid the loan at \$580 per month for 2 years. What was the annual rate of simple interest?

A. 4.83%

B. 8.0%

C. 9.67%

D. 16.0%

2. A paperweight is in the shape of a pyramid that is 20cm long, 10cm wide and has a perpendicular height of 9cm?
It is to be packed in a box that is in the shape of a rectangular prism that just contains the pyramid. The space in the box that is not occupied by the pyramid is to be filled with polystyrene.
What volume of polystyrene is required?

A. 600cm3

B. 900cm3

C. 1200cm3

D. 1800cm3

3. If m = 3, find the value of m0 + m1 + m2

A. 10

B. 12

C. 13

D. 27

4. The following cumulative frequency histogram shows the number of hours worked on a Saturday for ten students who had a part-time job at the local hamburger shop. How many of the students worked for 4 hours?

A. 1

B. 2

C. 3

D. 6

5. There are 8 girls and 10 boys in the school debating club. Two boys and 2 girls are to be chosen to represent the school. How many combinations of 2 girls and 2 boys are possible?

A. (8 x 7) + (12 x 11)

B. (8 x 7) x (12 x 11)

C. (8 x 7 ÷ 2) + (12 x 11 ÷ 2)

D. (8 x 7 ÷ 2) x (12 x 11 ÷ 2)
.
6. Two fire lookouts at A and B are 10km apart. A fire is observed at point F.
The attendant at lookout A measures the angle BAF as 67o and the attendant at lookout B measures the angle ABF as 73o. How far is the fire from the closest lookout?

A. 10 sin 67o / sin 40o

B. 10 sin 73o / sin 40o

C. 10 sin 40o / sin 67o

D. 10 sin 40o / sin 73o

7. A fieldbook entry for an offset survey of a block of land is shown below. What is the shape of the block of land?

B. Parallelogram

C. Rhombus

D. Trapezium

8. The manufacturer of Lollywater soft drink labels the contents of bottles as 500mls.
The factory produces bottles of Lollywater where the contents are normally distributed with a mean of 520mls and a standard deviation of 10mls.
What percentage of bottles of Lollywater contain less than the stated contents of 500ml?

A. 2.5

B. 5

C. 13.5

D. 27

9. The following table shows the future value of an annuity with a contribution of \$1.

Future Value of \$1
Period 2% 4% 6% 8% 10% 12% 14%
6 6.31 6.63 6.98 7.34 7.72 8.12 8.54
12 13.41 15.03 16.87 18.98 21.38 24.13 27.27
18 21.41 25.65 30.91 37.45 45.60 55.75 68.38
24 30.42 39.08 50.82 66.76 88.50 118.16 158.66
30 40.57 56.08 79.01 113.28 164.49 241.33 337.83

Izabella contributes \$100 per month for 18 years at 4% per annum compounded annually.
What is the future value (in dollars) of her annuity?

A. 25.65 x 18 x 100

B. 25.65 x 18 x 4 x 100

C. 25.65 x 18 x 12 x 100

D. 25.65 x 18 x 12 x 4 x 100

10. Students were asked to rate their teachers as good, bad or average on a survey.
When analysing this data, which of the following could be found?

A. Mean

B. Range

C. Mode

D. Median

11. Nathan sells cakes at a market stall for \$20 each. It costs him \$15 to make each cake. The cost of the market stall is \$50 per day.
If Nathan sells x cakes in a day, which of the following equations is the equation that shows the number of cakes that Nathan has to sell to break even.

A. 20x  15x = 50

B. 20x + 15x = 50

C. 20  15x = 50

D. 20x  15 = 50

12. There are 12 black socks and 8 brown socks in a drawer. Chiara went to the drawer in the dark and chose 2 socks at random. What is the probability that she chose 2 socks of the same colour?

A. 8/20 x 7/19 + 12/18 x 11/17

B. 12/20 x 11/19 + 8/18 x 7/17

C. 12/20 x 11/20 + 8/20 x 7/20

D. 12/20 x 11/19 + 8/20 x 7/19

13. Chris lives in Sydney (time = GMT + 10) and receives a phone call from his daughter in Calgary, Canada (time = GMT  7).
The time is 6pm Tuesday in Calgary. What is the time in Sydney?

A. 11am Tues

B. 11am Wed

C. 1am Tues

D. 1am Wed

14. The distance d, for a car to stop after the brakes have been applied is proportional to the square of the speed, s.
If it takes 30 metres for a car to stop when travelling at 20 km/h, how far does it take the same car to stop from 40 km/h?

A. 60m

B. 120m

C. 225m

D. 400m

15. Izabella uses a 1200 watt vacuum cleaner to clean the house. It takes 3 hours to clean the house and she cleans once a week.
She decides to save money on electricity by only cleaning the house once a fortnight.
How much does she save (to nearest \$1) in a year if electricity costs 30cents per kilowatt hour?

A. \$3

B. \$28

C. \$56

D. \$94

16. The formula for the blood alcohol content for males is given as:
B = (10N  7.5H) /6.8M where
B = blood alcohol content
N = number of standard drinks
H = number of hours over which the drinks were consumed
M = mass of drinker

Which of the following shows the formula rearranged with N the subject.

A. M = (10N  7.5H) /6.8B

B. N = (6.8M + B) / 75H

C. N = 0.68MB + 0.75H

D. N = 6.8MB / 75H

17. Jordan was planning to go to the United States and noted that 1 Australian dollar could be exchanged for 75 US cents. The bank charges a fee of \$10 (Australian) to change currencies regardless of the amount changed. If A is the number of Australian dollars and U is the number of US dollars, which of the following equations shows the conversion of Australian dollars to US dollars?

A. A = 0.75U + 10

B. A = (1.00U/0.75) + 10

C. A = (1.00U/0.75) - 10

D. A = 0.75U - 10

18. What is the value of; (x3 + x) (x2  1)?

A. x5 + 2x3 - 1

B. x5 + x3  x2 - x

C. x5  x3 + x2 - x

D. x5 - x

19. The pie chart below shows the percentage of water used by the Smiff household for different purposes. The family bought a pump and a grey-water tank so that the laundry water could be recycled and used for the garden.
The Smiff household used 450kL of water per year before they bought the grey-water tank.
What is their annual water usage after they bought the grey-water tank?

A. 81kL

B. 180kL

C. 270kL

D. 369kL

20. Morgan scored the following marks out of 20 for his first 4 tests: 12, 14, 16, 16.
He needs a mean of 15/20 after the fifth test to be promoted to the A class.
What is the minimum score that Morgan can achieve in his fifth test to be promoted to the A class?

A. 16

B. 17

C. 18

D. 20

21. Jordan used a metre rule graduated in centimetres to measure the length of a sheet of cardboard. He measured the length as 57cm.
How should Jordan record the length of the cardboard?

A. 57 cm.

B. 57 ± 1 cm.

C. 57 ± 0.5 cm.

D. 57 ± 1/57 cm.

22. Leah has a credit card that charges an annual interest rate of 20%, compounded daily, including the date of purchase and the date of repayment. If she buys a computer for \$850 on the 27th May and makes no other purchases, and pays off her credit card in full on 14th June, how much does she have to pay?

A. A = 850(1 + 20/36500)19

B. A = 850(1 + 20/365)19

C. A = 850(1 + 20/36500)18

D. A = 850(1 + 20/365)18

23. Chiara ran for a distance of 2.0 km in a direction 30o south of east from her home. What is the compass bearing of her home from her present position?

A. 030oT

B. 060oT

C. 150oT

D. 330oT

24. The heights of members of a class are measured and recorded.
How would you describe the data collected?

A. qualitative, continuous

B. qualitative, discrete

C. quantitative, continuous

D. quantitative, discrete

25. The net below is folded to form a pyramid. What is the surface area of the pyramid?

A. 84 units2

B. 96 units2

C. 57 units2

D. 69 units2

### Question 26 (15 marks)

(a) Morgan bought a second-hand car to travel from Sydney to Cairns for a running festival. He paid \$5400 after receiving a 10% discount for paying cash.

(i) What was the asking price before the discount was applied? (1 mk)

It costs \$30 to transfer the registration to your name if you do so within 14 days of purchase or \$137 of you transfer the registration after 14 days.
As well as paying for the transfer of registration the buyer also has to pay stamp duty on the purchase.
Stamp duty is 3% on the first \$45000 and 5% on the amount over \$45000.

(ii) How much did Morgan have to pay (including stamp duty) to transfer the registration to his name on the day of purchase? (1 mk)

Morgan is 18 and has had his licence less than a year and has applied to take out a comprehensive policy with Phantasmic Car Insurance.
Phantasmic Car Insurance applied the following formula to determine the price of Morgans policy:

Basic Policy Cost: \$1000 + 10% of the cars value.
Postcode loading (where the car is garaged) +2% on basic policy cost.
Morgan does not have a no-claim bonus but has a loyalty bonus of 5% since his green slip is with Phantasmic.
The loyalty bonus is calculated on the final price of the policy, before GST and stamp duty. GST: 10% Stamp Duty: 5% of final price including GST.

(iii) Determine the amount that Morgan has to pay for his insurance policy before GST and Stamp Duty are added. (1 mk)

(iv) Determine the amount that Morgan has to pay for his insurance policy after GST and Stamp Duty are added. (1 mk)

Morgan travelled 6800kms on his trip to Cairns and back and his total driving time was 200 hours. He stopped for a rest every 2 hours (stop, revive, survive).

(v) What was the average distance travelled between rest stops? (1 mk)

The fuel consumption on Morgans car is 7.2L per 100km.

(vi) How many litres of fuel did the car use on the total trip (to nearest litre)? (1 mk)

Morgan spent \$719 on fuel for the trip.

(vii) What was the average price per litre for fuel (nearest cent)? (1 mk)

Morgan has a reaction time of 1.2 seconds.

(viii) Given that 10m/s = 36km/h, find the distance Morgan would travel in his reaction time if he was travelling at 54km/h. (1 mk)

The braking distance for a car to stop is directly proportional to the square of its speed. Morgans car has a braking distance of 28m from a speed of 36km/h.

(ix) What is the braking distance from a speed of 54km/h? (1 mk)

Morgan, who weighs 75kg, won the main event and to celebrate he drank 2 bottles of Runners Brew in 2 hours.
(x) What was Morgans BAC at the end of the 2 hours? (1 mk)

Because Morgan has a provisional licence he must have a BAC of zero to legally drive. The body eliminates alcohol at approximately 0.015g/100ml per hour, regardless of the weight or gender of the person.

(xi) How long after he stopped drinking could Morgan legally drive? (1 mk)

(b) Izabella bought a 16m roll of chicken wire to construct a chicken run i.e. a fenced area to contain live chickens. She wanted the maximum area that could be enclosed by the 16m of wire but was unsure whether to construct a square or a circular chicken run.

(i) What area would be enclosed by a square chicken run constructed from 16m of chicken wire? (1 mk)

(ii) What is the radius of a circular chicken run constructed from 16m of chicken wire? (1 mk)

(iii) What is the area of a circular chicken run fenced by 16m of chicken wire? (1 mk)

(iv) By what factor is the bigger area greater than the smaller area? (1 mk)

### Question 27 (15 marks)

(a) The table below shows the height and weight of Dolores between her first and second birthdays while the graph plots Dolores age and height.

Age (Months) Height (cm) Weight (kg)
12 69 7.0
15 72 7.6
18 75 8.1
21 78 8.6
24 80 9.0 (i) What is the gradient of the graph? (1 mk)

(ii) Calculate the mean of the ages. (1 mk)

(iii) Calculate the standard deviation of the ages. (1 mk)

(iv) Calculate the mean of the heights. (1 mk)

(v) Calculate the standard deviation of the heights. (1 mk)

(vi) Calculate the correlation coefficient. (1 mk)

(vii) What would you predict Dolores height to be at birth? (1 mk)

The adult dose of Stopcough is 20 mls. What is the dose that Dolores should be administered (all answers to nearest 0.1 ml) when she is 18 months old according to:

(viii) Frieds Formula: Dosage for children 1-2 years = {age (months) x adult dosage} / 150 (1 mk)

(ix) Youngs Formula: Dosage for children 1  12 years = {age (years) x adult dosage} / age in years + 12 (1 mk)

(x) Clarks Formula: Dosage for children = {weight (kg) x adult dosage} / 70 (1 mk)

If the concentration of the active ingredient in the medicine is 5 grams per litre, calculate the number of mg of active ingredient in;
(xi) The adult dose (1 mk)

(xii) Dolores dose as calculated by Clarks formula. (1 mk)

(xiii) How many Dolores-size doses (as calculated by Clarks formula) are in a 200ml bottle of Stopcough and what percentage of a dose remains? (2 mks)

(b) A phone company charges a 45 cent connection fee and then 30 cents per minute or part thereof.

What is the cost of a phone call that lasts for 3 minutes and 30 seconds? (1 mk)

(c)
A hospital tried a new test on 1000 patients to determine if the patient had cancer. The results are summarised in the incomplete table below.

Tested Positive Tested Negative Total
Did Not Have Cancer 69 764
Total 745 1000

(i) How many patients were correctly diagnosed as not having cancer? (1mk)

(ii) What is the percentage of patients that were incorrectly diagnosed? (1 mk)

### Question 28 (15 marks)

An industrial chute is 10m long and tapers from having an area of cross-section of 6m2 at one end to 4m2 in the middle and 2m2 at the other end. Use Simpsons rule to find the volume of the chute. (2 mks)

(b)
Cataract Dam was 82.8% full on 17th August 2015. It has a storage capacity of 97190ML and the lake area is 8.5km2.

(i) What extra volume of water has to be added to the dam to reach its full capacity? (1mk)

(ii) What is the average depth of the lake when the dam is 100% full? (1mk)

(iii) The catchment area of Cataract Dam is 130km2. If 3mm of rain fall evenly over the catchment area, what volume of water (in ML) is added to the dam? (1mk)

(c)
(i) Rons electricity bill for the quarter (91 days) was \$223.86 before his customer discount and GST were included. If the cost of electricity is 70cents per day for the home supply charge plus 22cents per kWh, how many kilowatt hours of electricity did Ron use over the 91 days? (1mk)

(ii) How much did Ron have to pay after his 12% customer discount was applied and then 10% GST was added? (1mk)

(d)
Solve the following algebraic equation:     (m + 2)/3  + 7 = (m - 5) / 2    (2mks)

(e)

(i) Convert 720MB to bits and give your answer in scientific notation to four significant figures. (3 mks)

(ii) If the download speed is 256 kb/s, how long (to the nearest second) does it take to download the movie? (1 mk)

(f)
A running track consists of two parallel sections joined at each end by two semicircular sections as shown in the diagram below. The length of each straight section is 2r and the diameter of each semicircle is 2r where r is the radius of the semicircular sections. The distance around one lap of the track is 400 metres. br /> Calculate the value of r to the nearest centimetre. (2 mks)

### Question 29 (15 marks)

(a)
The cost per person, C, to attend a school formal varies inversely to the number of people attending, N. If 80 people attend then the cost per person is \$100.

(i) What is the cost per person if only 60 people attend? (1 mk)

(ii) Write an equation linking the cost per person, C, with the number of people attending, N. The value of any constant should be included. (1 mk)

(iii) How many people have to attend for the price per person to drop to \$60? (1 mk)

(b)
A bag contains a large number of marbles. Izabella withdrew 40 marbles from the bag and marked them with a permanent marker. She then returned the marbles to the bag and mixed them thoroughly. She then withdrew 30 marbles from the bag and noted that 12 of them had been marked.
Predict the number of marbles in the bag and justify your prediction with suitable mathematics. (2 mks)

(d)
Hobart (43oS, 147oE) and Townsville ((19oS, 147oE) are both cities in Australia.

(i) Given that the radius of the Earth is 6400km, what is the distance, to the nearest 10km, that a plane would fly from Hobart to Townsville? (2 mks)

(ii) If the plane flies at an average speed of 670 km/h, how long does it take to fly from Hobart to Townsville? (1 mk)

(iii) If the plane leaves Hobart at 10.00am (Hobart time), at what time (Townsville time) will it land in Townsville? (1 mk)

(e) A class consists of 12 girls and 6 boys. Four girls and two boys are chosen at random to complete a survey.

(i) How many different combinations of girls are possible? (1 mk)

(ii) Bill is chosen as one of the boys. What is the probability that his friend Joseph is also chosen? (1 mk)

(iii) How many combinations of 4 girls and 2 boys are there in which Bill is one of the members? (1 mk)

(f) The table shows present value interest factors for some monthly interest rates (r) and loan term in months (N).

Table of present value interest factors
r 0.005 0.006 0.007 0.008 0.009 0.010
N
30 27.794054 27.380070 26.974646 26.577578 26.188663 25.807708
31 28.650800 28.210805 27.780185 27.35870826.946148 26.542285
32 29.503284 29.036585 28.580124 28.133639 27.696876 27.269589
33 30.351526 29.857441 29.374503 28.902419 28.440908 27.989693
34 31.195548 30.673400 30.163359 29.665100 29.178303 28.702666
35 32.035371 31.484493 30.946732 30.421725 29.909121 29.408580
36 32.871016 32.290749 31.724659 31.172346 30.633420 30.107505
37 33.702504 33.092196 32.497179 31.917010 31.351259 30.799510
38 34.529854 33.888862 33.264329 32.655764 32.062695 31.484663
39 35.353089 34.680778 34.026146 33.388655 32.767785 32.163033
40 36.172228 35.467970 34.782667 34.115723 33.466585 32.834686

Jordan borrowed \$12000 for a car and arranged to repay the loan with monthly repayments over 3 years. He is charged 7.2% per annum interest.

(i) Using the table, calculate the amount of each monthly repayment. (1 mk)

(ii) What is the total amount that Jordan has to repay on the loan?(1 mk)

(iii) What is the amount that Jordan will pay in interest over the period of the loan? (1 mk)

### Question 30 (15 marks)

(a) The diagram below shows a radial survey of a block of land. (i) Show that ∠ BOC = 117o. (1 mk)

(ii) Find the shortest distance between B and C. (2 mks)

(iii) Find the area of ΔBOC. (1 mk)

(b)
A teacher gave his class a quick quiz and the marks for the 19 students are shown below:
0, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10,

(i) What mark is the upper quartile, Q3? (1 mk)

(ii) What is the interquartile range? (1 mk)

(iii) Sketch a box-and-whisker plot showing the above data. (2 mks) (iv) Morgan said that the score of 0 was an outlier. Show why you agree or disagree with him. (1 mk)

(c)
Anastasia decided to sell belts. The initial set-up cost was \$40 and each belt cost an extra \$5 to make. Anastasia sold the belts for \$10 each.

(i) Draw a graph of the cost of belts (vertical axis) against the number of belts. (3 mks) (ii) On the same axes, draw a graph of income against the number of belts. (1 mk)

(iii) Write an equation linking the cost of the belts (C) to the number of belts made (N). (1 mk)

(iv) What does the point of intersection on the graph indicate? (1 mk)