WRT Preliminary 2013 General Maths · Web viewPreliminary Final Examination – General Mathematics 2013. Section I – Multiple Choice Answer Sheet. Name _____. Allow about 15

2013HSC PRELIMINARY COURSEFINAL EXAMINATION

General Mathematics

General Instructions

o Reading Time - 5 minutes

o Working Time – hours

o Write using a blue or black pen. Black pen is preferred

o Board approved calculators may be used

o A table of standard integrals is provided at the back of this paper

o Show all necessary working in Questions 21 – 25

Total marks (70)

Section I

Total marks (20)

o Attempt Questions 1 – 20

o Answer on the Multiple Choice answer sheet provided

o Allow about 30 minutes for this section

Section II

Total marks (50)

o Attempt questions 21 – 25

o Answer on the blank paper provided, unless otherwise instructed

o Start a new page for each question

o All necessary working should be shown for every question

o Allow about 1 hour and 15 minutes for this section

2013 Preliminary Final Examination General Mathematics

Preliminary Final Examination – General Mathematics 2013Section I – Multiple Choice Answer Sheet

Name ______________________________.

Allow about 15 minutes for this sectionSelect the alternative A, B, C or D that best answers the question. Fill in the response oval completely.

Sample: 2 + 4 = (A) 2 (B) 6 (C) 8 (D) 9A B C D

If you think you have made a mistake, put a cross through the incorrect answer and fill in the new answer.

A B C D

If you change your mind and have crossed out what you consider to be the correct answer, then indicate the correct answer by writing the word correct and drawing an arrow as follows.

A B C D

StartHere

1. A B C D 14. A B C D

2. A B C D 15. A B C D

3. A B C D 16. A B C D

4. A B C D 17. A B C D

5. A B C D 18. A B C D

6. A B C D 19. A B C D

7. A B C D 20. A B C D

8. A B C D

9. A B C D

10. A B C D

11. A B C D

12. A B C D

13. A B C D

2


Section ITotal marks (20)Attempt Questions 1-20Allow about 30 minutes for this section

Use the multiple choice answer sheet.

1. A salary of $70 000 pa is equal to:

(A) $2692.31 per fortnight(B) $1400.00 per week(C) $39 per hour in a 38 hour week(D) $5900 per month

2. John invested $5000 in an account which earned 6% p.a. interest compounded each month for 3 years. His final balance was:

(A) $5075.38(B) $5955.08(C) $5983.40(D) $40 736.26

3. Josef’s taxable income for this financial year is $53 893. Using the table below, the tax he is due to pay this year (not including HECS or Medicare) is:

(A) $3572.00(B) $9062.23(C) $10 239.67(D) $17 515.23

4. Suzie records the colour of each car that travels through an intersection for an hour. The data recorded can be classified as:

(A) Colourful(B) Discrete Quantitative(C) Continuous Quantitative(D) Categorical

5. A five number summary of a set of data is 9, 12, 21, 29, 31. Which of the following correctly

3

Taxable income Tax on this income0 - $18,200 Nil$18,201 - $37,000 19c for each $1 over $18,200$37,001 - $80,000 $3,572 plus 32.5c for each $1 over $37,000$80,001 - $180,000 $17,547 plus 37c for each $1 over $80,000$180,001 and over $54,547 plus 45c for each $1 over $180,000


describes the data set?

(A) range = 22, interquartile range = 19.5(B) mean = 9, range = 31(C) median = 21, interquartile range = 20(D) mode = 29, median = 9

6. In a set of data, the highest number (upper extreme) is 57. If the number 256 was added to the set, which measure would it affect the most?

(A) median(B) mode(C) mean(D) all would be effected equally

7. in scientific notation is:

(A)

(B)

(C)

(D)

8. What method could be used to find the area of this composite shape?

4m

3m 6m

14m

(A)

(B)

(C)

(D) All of the above

9. In the following triangle,

4


(A)

(B)

(C)

(D)

10. May has 3 blue, 10 red and 4 green marbles in a bag. If she pulls two marbles out, what is the chance that neither of them are red?

(A)

(B)

(C)

(D)

11. The correct expansion of is:

(A) 12x-15x(B) 5x2-2x(C) 6x3-15x(D) 6x2+15x

12. The gradient and y-intercept of the linear equation when graphed would be:

(A) y-int = -4 , gradient = (B) y-int = -7 , gradient = 3(C) y-int = 3 , gradient = -7

(D) y-int = , gradient = -4

13. James makes about 70 phone calls on his mobile per month. Which plan would suit him better?

5


(A) Unlimited calls for $49 per month(B) 75c per call, unlimited talk time.(C) $29 plan where first 50 calls are free then each call after that $1.50(D) Prepaid card where 150 calls are bought for $119

14. How long would it take to download a file of 160MB with an average download speed of 150kbps? (to the nearest minute)Given that 1kb = 1000bits, 1MB = 220 bytes

(A) 18 minutes(B) 1 hour 4 minutes(C) 2 hours 22 minutes(D) 2 hours 29 minutes

15. The stamp duty payable on a car less than $45 000 is 3%. How much stamp duty would be paid on a car sale of $17 900?

(A) $179.00(B) $537.00(C) $813.00(D) $1350.00

16. A car uses on average 11L/100km in fuel. How much fuel would be used on a trip of 382km?

(A) 9.09L(B) 34.73L(C) 38.20L(D) 42.02L

17. The same trip of 382km took 5hours and 20 minutes. What was the average speed of the trip? (Rounded to the nearest km/h)

(A) 14 km/h(B) 72 km/h(C) 73 km/h(D) 76 km/h

18. A television is being bought for a charitable organisation. As such, the organisation can claim back the GST component of the purchase. How much would they claim if the television cost $2530?

(A) $195(B) $230(C) $253

6


(D) $530

19. How many centimetres are there in a kilometre?

(A) 100(B) 1000(C) 10 000(D) 100 000

20. The solution to the equation is:

(A) x = 2(B) x = 6(C) x = 9(D) x = 18

End of Section I

Section II

Total marks (50)Attempt Questions 21-25Allow about 1 hour and 15 minutes for this section

Answer all questions, starting each question on a new sheet of paper with your name and

7


question number at the top of the page. Do not write on the back of sheets.

In Questions 21 - 25 your response should include relevant mathematical reasoning and/or calculations.

Question 21 (10 marks) Use a separate sheet of paper Marks

a) Sully sells cars at a car yard. He gets a retainer of $200 per week and receives 3% of the sale price of all the cars he sells.

i) If Sully’s sales totaled $50 000 this week, how much would he be paid? 2

ii) If this week was an average week for Sully, how much would he expect to earn over the course of a year?

1

iii) Sully paid $300 a week PAYG tax this year. He was left with a tax bill after he had filed his tax return. Assuming no deductions and that he is exempt from the Medicare levy, use the table in question 3 to determine how much tax he should be putting aside each week so that this does not happen again.

3

b) Bill the Baker buys a bread making oven and a collectable car the same day.

i) Bill wants to declare the depreciation on his bread maker in his tax. If the depreciation is calculated at 10% per year, what is the value of his oven after 3 years if he paid $500 000 for it.

1

ii) Bill paid $240 000 for his collectable car. He anticipates that it will appreciate by 7% per year. What does he think it be worth in 3 years time?

1

c) Gemma earns $2400 per fortnight. She intends to take 4 weeks holiday leave. She is entitled to

leave loading on top of her normal pay. How much does Gemma expect to receive over these four weeks?

2

End Question 21


a) Mohammad decides to survey his school about which band should play at their school. He asks random people at the canteen one lunch time and records their results.

i) Mohammad’s friends decide that this was not a fair way of gathering the information. What might be a better sampling method of finding what the school wants as a whole?

1

ii) What is the advantage of using a sample rather than a census? 1

b) Given the data set: {2, 2, 3, 4, 6, 7, 7, 7, 9, 11, 14, 16, 17, 19, 19}, find:

i) the mean 1

ii) the median 1

iii) the mode 1

8


iv) the range 1

v) the standard deviation (population) 1

vi) create a five number summary 1

vii) create a box and whisker plot using (vi) 1

c) Manfred is moving to a new city and finds that the average (mean) price of a house in that area is $850 000. What measure of central tendency would give Manfred a more accurate indication of what house prices are like explain your reasoning?

1

End Question 22

9



a) The distance between two cities is 85km, measured to the nearest kilometre. What degree of accuracy has this measurement? (answer as a percentage, rounded to 1 decimal place)

1

b) A light year is defined as 9 460 730 472 580 800 km (the distance light travels in a year). Write this number in scientific notation, correct to 4 significant figures.

2

c) A concrete mixture is best prepared in the ratio 1:2:3, when the parts are cement, sand and gravel respectively. If Jonah wished to concrete 0.6m3 :

i) How many litres of concrete would be needed? 1

ii) How many 20L bags of cement would need to be bought? 1

d) i) Convert the rate 20 metres per second into kilometres per hour. 1

ii) Kayleigh measures her pulse for 15 seconds and records 17 beats. What is her pulse rate in beats/minute?

1

e) $240 000 is to be divided in the ratio 3:5. How much money would each person receive? 1

f) i) Find the area of a circle with radius 7cm. (answer to nearest cm2)

1

ii) Hence or otherwise, calculate the volume of a cylinder with diameter 14cm and height 10cm. (answer to nearest cm3)

10cm

1

End Question 23Question 24 (10 marks) Use a separate sheet of paper Marks

a) i) How many different combinations of meals could Mila have at a restaurant where there are 2 entrees, 5 mains and 3 desserts?

1

ii) How many distinct number plates could be made in the style 2 letters, 2 numbers, 2 letters?

1

b) i) A fair six-sided die has been rolled 20 times, the number 6 being rolled 10 times. What is the 1

10


likelihood of rolling a 6 on the next roll?

ii) A weather reporter has stated that there is a 35% chance of rain. Based on this information, what is the chance of fair weather?

1

c) If , find V when r =15cm.

2

d) Solve these equations for x.

i) 1

ii)

1

e)

i) Find the gradient and y-intercept of the above graph. 1

ii) Hence or otherwise, express this linear equation in terms of x and y. 1

End Question 24Question 25 (10 marks) Use a separate sheet of paper Marks

a) A phone call lasts for 3 minutes, 35 seconds. If it costs 40 cents to connect and 45 cents per 30 second block or part thereof, how much does the call cost?

1

b) A 300Mb file is 71% downloaded.

i) How many Mb are left to download? 1

ii) If it took 35 minutes 30 seconds to download 71%, how many minutes more would you expect the download to take?

1

c) It is said a car loses 10% of its value the minute it leaves the shop. If this is the case, how much would a $45 000 car be worth after it left the dealer?

1

d) A kite flies on a string that is 70m long. It is currently 45m from the ground. What is the angle of elevation? (correct to nearest degree)

2

11


70m 45m

e) James pays for a motorcycle with monthly payments of $230. He must make these payments for 4 years after an initial deposit of $3000. If the motorcycle cost $11 990 to buy outright, how much more will he pay by buying it on hire purchase?

2

f) If BACFemale

where N is the number of standard drinks consumed, H is the number of hoursof drinking, and M is the person’s mass in kilograms, calculate the BAC of a woman who has had

4 standard drinks over 2 hours, weighing 65 kg. (to 2 decimal places)

2

End of Examination

FORMULAE SHEET

12


13


FORMULAE SHEET

14

Documents

WRT Preliminary 2013 General Maths · Web viewPreliminary Final Examination – General Mathematics 2013. Section I – Multiple Choice Answer Sheet. Name _____. Allow about 15