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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 15  Allow about 1—;— hours forthis section Gosford High School Hatf Yearly HSC General Mathematics 2009 r ' Section 1
Total marks (25)
Attempt Questions 125 Allow about 30 minutes for this section Use the multiplechoice answer sheet for Questions 122.
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 2a5 = —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 $1960. 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 425 hours is:
(A) 883300 ' (B) $85750
(C) 888200 (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 stemandleaf 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 semiminor 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) 41 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) 79cm
(C) 67cm (D) 53cm 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 crosssection 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 crosssection. 3 (ii) Estimate the volume of water, in cubic metres, in a 50 metre length
of this river, assuming the crosssection 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 threedigit 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 5155 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 HalfYearly 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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