Hsc General Mathematics s1

HSC GENERAL MATHEMATICS TERM 2 ASSESSMENT TASK 2012

General Instructions Total marks - 55

Section 1  Working time – 65 minutes 10 marks

 Write using black or blue pen  Board approved calculators may be used  A formulae sheet is provided at the back of this paper Section 2  Write your name and the question 45 marks number on each answer booklet for Questions 11, 12 and 13

Section 1 Question 11 Questions 1-10

Full marks 10 15

Marks awarded

Name:......

12MG6 Mr. Param Teacher: Tick a box

12MG7 Mr. Lachmaiya

12MG8 Mr. Garvey

Year 12 General Mathematics Term 2 Assessment Task - 2012 2 SECTION 1 - 10 marks

Attempt Questions 1 – 10

Use the multiple-choice answer sheet for Questions 1- 10

Q1. If a plane travels 1600 kilometres in 4 hours, its speed in knots is

Q2. The difference in local time between two places with a longitude difference of is

Q3. The distance in nautical miles, between two places with coordinates and is

A. 900 B. 3900 C. 1500 D. 2400

Q4. It is 8 am at P. At which other location (A, B, C or D) is it also 8 am?

A. A B. B

C. C D. D

Year 12 General Mathematics Term 2 Assessment Task - 2012 3 Q5. A new piece of machinery is purchased for $245 000. If its depreciation is calculated by the declining balance method at 12% p.a. each year, then which expression gives the value of the machine at the end of 4 years?

A. $ B. $

C. $ D. $

Michael invested $3000 for 6 years compounded annually at 5% p.a. Which calculation will give the amount of interest he will earn on the investment?

Q7. Peter calculates the present value of (N) of an annuity. The interest rate is 4% p.a., compounded monthly. In five years the future value will be worth $120 000.

Which calculation will result in the correct answer?

Q8. A loan of $25 000 is used to purchase a car. The term of the loan is 3 years and the interest rate is 9% p.a., compounded fortnightly. Which equation should be used to calculate the fortnightly repayments, M?

Year 12 General Mathematics Term 2 Assessment Task - 2012 4 C. D.

Q9. Which of the following graphs shows the lowest rate of depreciation over the given time period?

Q10. Kim lives in Perth . He wants to watch an ice hockey game being played in Torontostarting at 10:00 pm on Wednesday.

What is the time in Perth when the game starts?

A. 9:00 am on Wednesday B. 7:40 pm on Wednesday

C. 12:20 am on Thursday D. 11:00 am on Thursday

SECTION II - 45 marks

Attempt Questions 11-13

Answer each question in a separate writing booklet.

Show necessary working

Question 11 (15 marks) Use a SEPARATE writing booklet. Marks a) A ship sails from an island resort at and heads due east for

Year 12 General Mathematics Term 2 Assessment Task - 2012 5 2100 nautical miles towards its next port.

i) How many nautical miles is one degree along a great circle? 1

ii) Name the great circle the island resort is situated. 1

iii) What are the coordinates of the position of the ship when it

arrives at the port? 2

iv) The ship averaged a speed of 30 knots from the island resort to the port.

If the ship left the resort at 7:30 am local time on Sunday 10th April,

determine the day, date and local time the ship arrived at the port. 4

b) i) Convert 750 nautical miles to kilometres. 1

ii) Convert 25 knots to kilometres per hour. 1

iii) A plane flies along the parallel of latitude. How many nautical

miles is it from the North Pole? 2

iv) What is the length of the equator if the radius of the Earth is 6400 km,

to the nearest metre? 1 c)

Find the length of the arc PQ in the diagram, correct to one decimal place. 2

Question 12 (15 marks) Use a SEPARATE writing booklet. Marks a) The table shows the future value of a $1 annuity at different interest rates

over different numbers of time periods.

Year 12 General Mathematics Term 2 Assessment Task - 2012 6 i) What would the future value of a $5 000 per year annuity at 3% p.a. for

6 years, with interest compounding yearly? 1

ii) What is the value of the annuity that would provide a future value of

$407 100 after 7 years at 5% p.a. compound interest? 1

iii) An annuity of $1000 per quarter is invested at 4% p.a. compounded

quarterly for 2 years. What will be the amount of interest earned? 3

b) Sally decides to put $100 per week into her superannuation fund.

The interest rate quoted is 7.28% p.a., compounded weekly. Calculate

the future value of her superannuation at the end of 35 years. 3

c) Malcolm needs $800 per month for 3 years while he studies at Macquarie

University. What amount of money do his parents need to invest now at

6.6% p.a. compounded monthly to provide the money that Malcolm needs? 3

d) Which is a better result at the end of 25 years: an investment of $100 000 at

12% p.a. compounded monthly or $1 000 invested per month at 12% p.a.

compounding monthly? 4

Question 13 (15 marks) Use a SEPARATE writing booklet. Marks a) Monthly repayments of $2 500 are to be repaid on a loan over a period of 20 years.

The interest charged monthly on the amount owing on the loan is at a rate of 6.9% p.a. Year 12 General Mathematics Term 2 Assessment Task - 2012 7 i) Use the formula to show that the amount borrowed

was $325 000, to the nearest thousand dollars. 3

ii) A Home Loan Table for this loan for the first three monthly repayments(R) is

shown in the spreadsheet below.

Period Principal Interest (I) P + I P + I – R (Months) (P) $324 1 $325 000 $1 868.75 $326 868.75 368.75 $323 2 $324 368.75 $1 865.12 $326 233.87 733.87 3 $323 733.87 A B C

Complete the table by calculating the values represented by A, B and C. 3

b) Computer equipment is purchased for $21 000 and depreciates by $3 000 each year.

Use the straight line method of depreciation to find:

i) the value of the equipment after 3 years 1

ii) when the equipment will be worth $9 000 2

iii) when the salvage value of the equipment will be zero. 1

c) The graphs show the depreciation of a capital item using the straight line and the

declining balance methods.

Year 12 General Mathematics Term 2 Assessment Task - 2012 8 Use the graphs on page 7 to answer the following questions:

i) How much was the purchase price? 1

ii) What was the value of the item after 1 year, using each method? 2

iii) When is the book value equal for both methods? 1

What is the book value at this time? 1

End of Paper

Year 12 General Mathematics Term 2 Assessment Task - 2012 9 Year 12 General Mathematics Term 2 Assessment Task - 2012 10 Name:......

Year 12 General Mathematics Term 2 Assessment Task - 2012 11 12MG6 Mr. Param Teacher: Tick a box

12MG7 Mr. Lachmaiya

12MG8 Mr. Garvey

MULTIPLE CHOICE ANSWER SHEET

Place a cross in the right box corresponding to the correct answer

A B C D

Year 12 General Mathematics Term 2 Assessment Task - 2012 12 Year 12 General Mathematics Term 2 Assessment Task - 2012 13