<p> HSC GENERAL MATHEMATICS TERM 2 ASSESSMENT TASK 2012</p><p>General Instructions Total marks - 55</p><p>Section 1  Working time – 65 minutes 10 marks</p><p> 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</p><p>Section 1 Question 11 Questions 1-10</p><p>Full marks 10 15</p><p>Marks awarded</p><p>Name:...... </p><p>12MG6 Mr. Param Teacher: Tick a box</p><p>12MG7 Mr. Lachmaiya</p><p>12MG8 Mr. Garvey</p><p>Year 12 General Mathematics Term 2 Assessment Task - 2012 2 SECTION 1 - 10 marks</p><p>Attempt Questions 1 – 10</p><p>Use the multiple-choice answer sheet for Questions 1- 10</p><p>Q1. If a plane travels 1600 kilometres in 4 hours, its speed in knots is</p><p>A. B.</p><p>C. D.</p><p>Q2. The difference in local time between two places with a longitude difference of is</p><p>A. B.</p><p>C. D.</p><p>Q3. The distance in nautical miles, between two places with coordinates and is</p><p>A. 900 B. 3900 C. 1500 D. 2400</p><p>Q4. It is 8 am at P. At which other location (A, B, C or D) is it also 8 am?</p><p>A. A B. B</p><p>C. C D. D</p><p>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?</p><p>A. $ B. $</p><p>C. $ D. $</p><p>Q6.</p><p>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?</p><p>A. B.</p><p>C. D.</p><p>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. </p><p>Which calculation will result in the correct answer?</p><p>A. B.</p><p>C. D.</p><p>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?</p><p>A. B.</p><p>Year 12 General Mathematics Term 2 Assessment Task - 2012 4 C. D.</p><p>Q9. Which of the following graphs shows the lowest rate of depreciation over the given time period?</p><p>Q10. Kim lives in Perth . He wants to watch an ice hockey game being played in Torontostarting at 10:00 pm on Wednesday.</p><p>What is the time in Perth when the game starts?</p><p>A. 9:00 am on Wednesday B. 7:40 pm on Wednesday</p><p>C. 12:20 am on Thursday D. 11:00 am on Thursday</p><p>SECTION II - 45 marks</p><p>Attempt Questions 11-13</p><p>Answer each question in a separate writing booklet.</p><p>Show necessary working</p><p>Question 11 (15 marks) Use a SEPARATE writing booklet. Marks a) A ship sails from an island resort at and heads due east for </p><p>Year 12 General Mathematics Term 2 Assessment Task - 2012 5 2100 nautical miles towards its next port.</p><p> i) How many nautical miles is one degree along a great circle? 1</p><p> ii) Name the great circle the island resort is situated. 1</p><p> iii) What are the coordinates of the position of the ship when it </p><p> arrives at the port? 2</p><p> iv) The ship averaged a speed of 30 knots from the island resort to the port.</p><p>If the ship left the resort at 7:30 am local time on Sunday 10th April, </p><p> determine the day, date and local time the ship arrived at the port. 4</p><p> b) i) Convert 750 nautical miles to kilometres. 1</p><p> ii) Convert 25 knots to kilometres per hour. 1</p><p> iii) A plane flies along the parallel of latitude. How many nautical </p><p> miles is it from the North Pole? 2</p><p> iv) What is the length of the equator if the radius of the Earth is 6400 km, </p><p> to the nearest metre? 1 c)</p><p>Find the length of the arc PQ in the diagram, correct to one decimal place. 2</p><p>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 </p><p> over different numbers of time periods.</p><p>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 </p><p>6 years, with interest compounding yearly? 1</p><p> ii) What is the value of the annuity that would provide a future value of </p><p>$407 100 after 7 years at 5% p.a. compound interest? 1</p><p> iii) An annuity of $1000 per quarter is invested at 4% p.a. compounded </p><p> quarterly for 2 years. What will be the amount of interest earned? 3</p><p> b) Sally decides to put $100 per week into her superannuation fund. </p><p>The interest rate quoted is 7.28% p.a., compounded weekly. Calculate </p><p> the future value of her superannuation at the end of 35 years. 3</p><p> c) Malcolm needs $800 per month for 3 years while he studies at Macquarie </p><p>University. What amount of money do his parents need to invest now at </p><p>6.6% p.a. compounded monthly to provide the money that Malcolm needs? 3</p><p> d) Which is a better result at the end of 25 years: an investment of $100 000 at </p><p>12% p.a. compounded monthly or $1 000 invested per month at 12% p.a. </p><p> compounding monthly? 4</p><p>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. </p><p>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 </p><p> was $325 000, to the nearest thousand dollars. 3</p><p> ii) A Home Loan Table for this loan for the first three monthly repayments(R) is </p><p> shown in the spreadsheet below.</p><p>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</p><p>Complete the table by calculating the values represented by A, B and C. 3</p><p> b) Computer equipment is purchased for $21 000 and depreciates by $3 000 each year. </p><p>Use the straight line method of depreciation to find:</p><p> i) the value of the equipment after 3 years 1</p><p> ii) when the equipment will be worth $9 000 2</p><p> iii) when the salvage value of the equipment will be zero. 1</p><p> c) The graphs show the depreciation of a capital item using the straight line and the</p><p> declining balance methods.</p><p>Year 12 General Mathematics Term 2 Assessment Task - 2012 8 Use the graphs on page 7 to answer the following questions:</p><p> i) How much was the purchase price? 1</p><p> ii) What was the value of the item after 1 year, using each method? 2</p><p> iii) When is the book value equal for both methods? 1</p><p>What is the book value at this time? 1</p><p>End of Paper</p><p>Year 12 General Mathematics Term 2 Assessment Task - 2012 9 Year 12 General Mathematics Term 2 Assessment Task - 2012 10 Name:...... </p><p>Year 12 General Mathematics Term 2 Assessment Task - 2012 11 12MG6 Mr. Param Teacher: Tick a box</p><p>12MG7 Mr. Lachmaiya</p><p>12MG8 Mr. Garvey</p><p>MULTIPLE CHOICE ANSWER SHEET</p><p>Place a cross in the right box corresponding to the correct answer</p><p>A B C D</p><p>1</p><p>2</p><p>3</p><p>4</p><p>5</p><p>6</p><p>7</p><p>8</p><p>9</p><p>10</p><p>Year 12 General Mathematics Term 2 Assessment Task - 2012 12 Year 12 General Mathematics Term 2 Assessment Task - 2012 13</p>