[2009] Task 2 - Student Name 2009 YEAR 12 HALF YEARLY HSC...

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Unformatted text preview: Student Name: 2009 YEAR 12 HALF YEARLY HSC EXAMINATION GENERAL MATHEMATICS General instructions Total marks — 100 . Reading Time — 5 minutes Section 1 a Working Time — 2 hours 25 Marks . Write using blue or black pen . Attempt Questions 1_25 ‘ Calculators may be used . Allow about 30 minutes for this . A formulae sheet is provided at the back section Of this paper. Section 11 75 Marks . Attempt Questions 1-5 - Allow about 1—;— hours forthis section Gosford High School Hatf- Yearly HSC General Mathematics 2009 r ' Section 1 Total marks (25) Attempt Questions 1-25 Allow about 30 minutes for this section Use the multiple-choice answer sheet for Questions 1-22. 1. Simplify: 12k3 + 4k (A) 3k2 (B) 31:3 (C) 8k2 (D) - Ska 2. Simplify 3m(m — 4) + 6071 — 2) (A) 3m2 —m-—8 (B) 3m2+6m—6 (C) 3m2—6m—12 (D) 9m—6 3. The solution of 2a-5 = —4. is: 1 1 2 1 A a=—8— =—3— C a:—— D :3“ ( ) 2 (B) a 2 ( ) 7 ( ) a 2 15a3b8 4. Sim ii the al ebraic fraction p fy g 25a5b2 31')4 b6 A B ( ) 5a2 ( ) 10a3 . 3b6 54 C _ ( ) 5a3 (D) 10a2 2 5. The formula .5' = M! +%— is rearranged to make a the subject. The result is: ZS—ut (A) a = :2 zs—m (B) a = (12 ) 25+2ut (C) a = 2 t (D) a = t2 (Zr—22:1) Gosford High School Half- Yearly HSC General Mathematics 2009 6. 10. 11. New car registrations plates contain two letters followed by two numerals followed by two more letters eg AC 12 DC. Letters and numerals may be repeated. Which of the following expressions gives the correct number of car registration plates that begin with‘the letter M? (A) 263x102 (B) 253x102 (C) 264x102 (D) 25“><1o2 There are 200 “LEGO” bricks in a bucket. There are 63 blue bricks, 37 green bricks, 59 yellow bricks and the remainder are red bricks. One brick is chosen at random. Find the probability of the brick being blue or red. 41 63 9 13 (A) E (B) E (C) E (D) E Stirling Mortlock kicks a field goal in one out of every six attempts. Today he is planning to kick 300 balls. How many of these would he expect to be successful field goals? (A) 6 (B) 18 (C) 50 (D) 60- There are five contestants left in “So You Think You Can Dance”. Only two will reach the final. In how many ways can the two finalists be chosen? (A) 10 (B) -20 (C) 25 (D) 40 Rugby League and Soccer are the only sports offered at a local boys school. 65% of the boys play Soccer and 18% play soccer and rugby league. 15% of the boys do not play any sport. A boy is selected at random. What is the probability that this boy does not play Rugby League? (A) 15% (B) 38% (C) 47% ' (D) 62% Justin’s bank account has a $5 monthly fee plus an excess transaction fee of 60 cents for every transaction above the free limit of 20 per month. How much does Justin pay in fees in a month if he makes 32 transactions? (A) $7.20 (B) $24.20 (C) $19.20 (D) $12.20 Gosford High School Half- Yearly HSC General Mathematics 2009 12. 13. 14. 15 A MP3 player which costs $100 is increased in price by 25% in December. In the January sales the MP3 is reduced by 25%. , The sale price is (A) $93.75 (B) $100 (C) $119.75 (D) $150 Belinda is paid an hourly rate of $19-60. She is paid at the normal rate for a 40 hour week and is paid time and a half for any overtime. Her gross pay for a week where she works 42-5 hours is: (A) 8833-00 ' (B) $857-50 (C) 8882-00 (D) $897.50 The following table shows the monthly repayments on a personal loan. __ 7% —“- —_-_ 79 158 237 315 The total interest paid on a loan of $10 000 over 20 years at 6% p.a. is: (A) $32480 (B) $3540 (C) $2124 (D) $42480 Rod has $3050 and is going to borrow the rest to buy a second hand car costing $11000. He is going to pay the loan in 36 monthly repayments of $280. What is the annual rate of interest ? (A) 6.5%p.a. (B) 8.9%p.a. (C) 19.4%p.a. (D) 26.8%p.a. Gosford High School Half- Yearly HSC General Mathematics 2009 16. Which data set has a mean of 4, a median of 3 and a mode of 2? (A){2,2,3,2,11} (B){2,3,2,3,3} (C){2,2,4,2,.10} (D){2,3, 7, 6,2} 17. Which of the following sets of scores MUST be positively skewed? (A) Mean =50, Mode = 60, Range =45 (B) Mean =50, Mode = 50, Range =60 (C) Mean =50, Mode = 40, Range =30 (D) Mean =50, Mode = 60, Range =70 18. Calculate the interquartile range for the data set shown in the stem-and-leaf plot. (A) 24 (B) 78 (C) 85' (D) 102 19. This curve shows a normal distribution. Which of the following statements is false? (A) The mean, median and mode lie on the line of symmetry. (B) The number of scores above the mean is the same as the number below. (C) Scores will most probably lie within two standard deviations from the mean. (D) The distribution is skewed. Gosford High School Half— Yearly HSC General Mathematics 2009 20. The scores 4, 3, 7, and y have a mean of 4. What is the value of y. (A)2.5 (B) 2.0 (C) 3.5 (D) 4 21. The following ellipse has an area of 50m2. é————-—-—-———% 12m The length of the semi-minor axis correct to two decimal places is (A) 1.32 (B) 2.66 (C) 2.65 (D) 1.33 22. A small lake has a surface area of 1.5 hectares. Given that 10 mm of rain fell on the lake, then the volume of rainwater in megalitres is (A) 0.15 7 (B) 1.5 (C) 15 (D) 150 23. A prism has a volume of 246L. Its height is 60cm. What is the area of the base? (A) 410 m2 (B) 4-1 m2 (C) 41 m2 (D) 0.41 m2 24. A sphere has a surface area equal to 350cm2. Using the formula S = 421.7”2 the radius of the sphere will be closest to: (A) 10.5cm (B) 7-9cm (C) 6-7cm (D) 5-3cm 25. Convert 400 mm2 to cmz. (A)4 mm2 (B) 40 cm2 (C) , 400 cm2 (D) 4 000 cm2 END OF SECTION 1 Gosford High School Half- Yearly HSC General Mathematics 2009 Section II 75 Marks Attempt Questions 1 -— 5 Allow about 1—:— hours for this section. Answer all questions, starting each question in a new writing booklet. All necessary working should be shown in every question. Question 1 (15 marks) Start a new writing booklet. Marks (a) The diagram shows a vertical cross-section of a river. waterlevel . 2.1 m 2.1 m NOT 3.0 m 3.8 m . TO _ nver bed SCALE five:- had (i) Use two applications of Simpson’s rule to find the approximate area of the river’s cross-section. 3 (ii) Estimate the volume of water, in cubic metres, in a 50 metre length of this river, assuming the cross-section is the same as above and uniform along the 50 metre length of the river. ' 2 Give your answer correct to the nearest cubic metre. (b) A tent was made in the shape of a cone. The radius of the base of the tent is 2 m and the height is 2.8 m. (i) Draw a possible net of the tent. 1 (ii) Calculate l, the slant height of the tent. 1 (iii) The base of the tent was madefrom rubber sheeting. What area of rubber sheeting was used to make the base of the tent? 2 (iv) The curved surface of the tent is made from nylon.- Calculate the area of the curved surface. 1 Given that curved surface area = n X r X l. Gosford High School Half- Yearly HSC General Mathematics 2009 (c) The dimensions of a rectangle, measured with a ruler graduated in millimetres, are found to be 25 mm and 16 mm respectively. Find the lower and upper limits between which the true area of the rectangle lies. 2 (d) The diagram below shows the details of a survey of a council park. All dimensions are in metres. D i) In your answer booklet record the details of this survey as a neat notebook entry . 1 ii) Find the area of the park ABCD 2 End of Question 1. Gosford Hi h School Half— Year] HSC General Mathematics 2009 Question 2 (15 marks) Start a new writing booklet. Marks (a) In the game of “BINGO” numbers between, and including, 1 and 90 are i (b) randomly selected from a barrel and called out. Players then mark numbers that are on their own card as they are called out. The winner is the first person to have a row of numbers marked on their card. An example of 'a Bingo card is shown below. (i) (ii) (iii) (iV) What is'the minimum number of calls needed before a game can be won? 1 What is the probability that the first number called out is one of the numbers on the top line of the card shown above? 1 What is the probability that the first two numbers called out are numbers on the top line of the card shown above? 1 Calculate the chance that a player with one bingo card has of winning in five calls. 2 The menu at the local seafood cafe includes the following items: 0) (ii) (iii) Burgers Fries Drinks Plain Small Coke Cheese Large Orange Bacon Lemonade The Lot Draw a tree diagram to show all the possible menu choices. 2 How many different combinations are there if a person must choose something from each group? . 1 If the person is equally likely tochoose an item from any of the lists, find the probability that the choice includes a bacon burger with large fries and an orange drink. 1 Gosford High School Half— Yearly HSC General Mathematics ‘ 2009 (c) Three digit numbers are formed from five cards labelled 1, 2, 3, 4 and 5. i) How many different three-digit numbers can be formed“.7 ii) What is the probability of randomly selecting a three digit number less than 500 with its digits arranged in descending order? (d) The probability that it will rain on any day over Easter in Byron Bay is 0.8 i) What is the probability it will rain on two consecutive days over Easter in Byron Bay? ii) What is the probability that it will rain on only one of two consecutive days in Byron Bay over Easter? End of Question 2. 1o Gosford High School Half— Yearly HSC General Mathematics 2009 Question 3 (15 marks) Start a new writing booklet. Marks (a) The local cinema ran a horror and comedy movie promotion. Ten movies from each movie type were shown and the attendances for each showing were recorded as follows: HORROR 248 211 250 267 I98 235 227 259 195 220' COMEDY 199 213 208 325 21] 200 215 203 196 210 (i) Calculate the mean and standard deviation for each movie type. ' 2 (ii) Which movie type attracted a more consistent audience? Give reasons for your answer. 2 (iii) Calculate the median for the comedy movies shown. 1 (iv) The cinema would like to run more comedy movies and therefore needs to plan for future audience numbers. ‘ Should they base their planning on the mean or median? Give reasons for your answer. 1 (b) The retirement ages of two million people are displayed in a table. Age (thousands) i) What is the relative frequency of the 51-55 year retirement age? 2 ii) Describe the distribution. 1 11 Gosford High School Half— Yearly HSC General Mathematics 2009 (c) Mrs Evans has a theory that “people always underestimate the length of a line”. A group of students decide to investigate this theory. They each estimate the lengths of several lines and then measure the actual lengths. O 5 10 15 20 25 30 35 40 ‘5 Length of line L. ..- (i) Write down the median of the estimated lengths. 1 (ii) Write down the median of the actual lengths. 1 (iii) What are the range and interquartile range for the estimates? 2 (iv) Would you agree with Mrs Evans’s theory? Justify your answer. 2 End of Question 3. Question 4 (15 marks) Start a new writing booklet Marks (a) The Cribb Building Society publishes the following loan repayment ready reckoner showing the monthly repayment amount for each $1 000 borrowed. $1061 $6.60 _ p... n“— $3.44 $7.16 $7.75 $8.36 $9.00 _ Jason borrows $320 000 to purchase a townhouse. The loan is to be repaid at 9% pa over 25 years. (i) Calculate Jason’s monthly repayment. ' 1 (ii) Find the total amount Jason pays over the term of the loan. - 1 12 Gosford High School Half— Yearly HSC General Mathematics 2009 (b) (C) (iii) How much extra per month would Jason have had to pay if the loan _ were repaid over 15 years? (iv) How much would Jason have paid in total if the loan was repaid in 15 years? (v) How much would Jason have saved by paying the loan over 15 years rather than 25 years? During the 2006 — 2007 financial year, Mr Hickstone earned a gross income of $58 563. His tax instalments amounted to $14 691.42. However, Mr Hickstone earned a fiarther gross income of $5 416 on weekends. Since his expenses in earning the additional income were considerable his allowable deductions amounted to $2 804. (i) Calculate Mr Hickstone’s total gross income. (ii) _ Calculate Mr Hickstone’s total taxable income. (iii) Use the tax table below to calculate Mr Hickstone’s tax payable. Tax payable Taxable income ($) $0 - $10 000 Nil $10 0071 - $28 000 Nil plus 25 cents for each $1 over $10 000 $28 001 - $50 000 $4 500 plus 30 cents for each $1 over $28 000 $50 001 - $100 000 $11 100 plus 40 cents for each $1 over $50 000 over $100 000 $31 100 plus 60 cents for each $1 over $100 000 (iv) Find Mr Hickstone’s refund due or additional tax payable. Clearly explain your answer. Simon has $4000 that he doesn’t need to spend and wants to put it in a bank account for three years. (i) How much interest would Simon earn if he put it in an account earning simple interest of 6% per annum? (ii) How much interest would Simon earn if he put it in an account earning compound interest of 6% per annum compounded quarterly? End of Question 4. 13 Gosford High School Half-Yearly HSC General Mathematics 2009 Question 5 (15 marks) Start a new writing booklet ‘ (a) (b) (0) (d) (6) 5x+l_ Solve 4x — 7 The cost (C) of renting a car is $40 plus 500 per kilometre flc) driven. i) Write an algebraic equation for the cost C in terms of 1: ii) The cost of the rental car is $150. Solve your equation in (i) to find k the distance travelled in the rental car. Solve E+—1 — 2x—8 ' 3 5 =1 Solve 1{532+4 = 9 This is a stick pattern of houses. 666666 1 house uses 2 houses uses 3 houses uses 6 matches 11 matches 16 matches (i) In your answer booklet, copy and complete this table, where h = number of houses and s = number of sticks. (ii) Find the linear function for .s' in terms of h. (iii) How many sticks would be needed to make 40 houses? (iv) If this function is graphed on the number plane, what will be its gradient and vertical intercept? END OF EXANIINATION PAPER 14 Marks...
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