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Unformatted text preview: GOSFORD HIGH SCHOOL 20 1 0
GENERAL MATHEMATICS YEAR 12 HSC Assessment Task 2 General Instructions Time Allowed: 1 hour 30 minutes. Attempt all questions. Approved calculators may be used. Write using blue or black pen. Start each Section on a new page. Full marks may not be awarded where necessary working is not shown.
A formula sheet is provided I O O O O O SECTION I. CREDIT AND BORROWING.
1.Which of the following is the highest interest rate?
A. 0.02% / day. B. 0.13% / week. C. 0.6% / month. D. 7.25% / annum. 2. The amount of ﬂat interest on a loan of $10000 at 8.4% p.a. over 4 years is:
A. $840. B. $10840. C. $3360. D. $13360. 3. Michelle borrows $3300 over 11 months. If she repays a total of $4022, the ﬂat rate
of interest per annum correct to 1 decimal place is: A. 23.9%. B. 20.4%. C.18.5%. D. 17.0%. 4. The outstanding balance on a credit card is $2563.75. If the full balance is not paid
by the due date one months interest will be added at the rate of 18% pa. Calculate the
outstanding balance (to the nearest cent) if the full balance is not paid by the due date. A. $38.46. B. $461.48. C. $2602.21. D. $3025.23. 5. F .I.D. is a government charge on all payments made to a credit card provider. It is
calculated at a rate of 0.06% of the payment. The RID. on a payment of $17 85.44 is: A. $1.07. B. $10.71. C. $107.12. D. $107.13. 6. Sarah borrows $15000 from a credit union and is charged an annual ﬂat interest
rate of 7.5% p.a. She agrees to repay the loan in equal monthly payments over 3 years. (a) Calculate the interest Sarah is charged each year. (1)
(b) What is the total amount to be repaid on the loan? (2)
(0) Calculate the amount of each monthly repayment. (1) 7. Mark buys a used car with a cash price of $12000 on the following terms:
0 20% deposit.
0 $89.23 per week for 3 years. Calculate
(a) the deposit. (1)
(b) the total cost of the car. (2) (c) the annual ﬂat rate of interest charged. . (2) 8. Mr. And Mrs. Murphy borrowed $130000 to purchase a home unit. The interest
rate is 9% pa. reducible over a 20—year term. The monthly repayments are $1087.37. (a) Complete the following table. (3) M ONTH PRINCIPAL (P) INTEREST (I) BALANCE
OWING
$130000 $975 $129887.63
2 $129837.63 $974.16 —
—
(b) How much money has Mr. and Mrs. Murphy paid off their mortgage after 3
months? (1) SECTION I]. PROBABILITY (Start a new page) 1. A bag containing only,r red and blue discs has twice as many red ones as blue ones.
If one disc is selected at random the probability that it is blue is: B Al .1 0.3 13.1
2 3 3 6 2. In how many ways can 5 people be seated in a single row?
A. 5 B. 120 C. 25 D. 3125 3. The expected number of times a four appears on the uppermost face when a die is
rolled 300 times is: A. 4 B. 50 C. 100 D. 24 4. The 8 cards shown above are shufﬂed and placed face down on a table. What is the
probability that 2 randomly selected cards will both have a star image printed on them? (note: the selected card is M replaced on the table)
5 3 1 A. —. 13.2. C.—. D. —.
14 9 5 28 5.
'. A company tests the salt content in a sample of food packets. Manufacturers have labelled the food packets as either “containing salt” or “salt free”. The results of the tests are shown in the following twoway table. TEST FOR SALT IN FOOD SAMPLES Negative Total
Content Positive Containing Salt What percentage of food packets were incorrectly labelled, according to the test results? A. 3.3. B. 5.6. C. 7.5. D. 26.7.
6. An Ice—cream Parlour offers 10 different ﬂavours. Fiona chooses 2 different
ﬂavours for a double cone. How many different possible choices could she make? (2) 7. At a school Ann, Betty, Craig, David and Emma nominate for the position of
school captain and vice captain. (a) What is the probability that a boy is elected as school captain? (1)
(b) In how many ways can the position of captain and vice captain be filled‘2 (1)
(c) What is the probability that a girl is captain and a boy is vice captain? (1) 8. A bag contains 5 red and 3 white counters. Two counters are selected at random
from the bag. (a) COpy and complete the probability tree below R
R W R
W W _ (2) (b) What is the probability that the colours selected are: (i) both white? (1)
(ii) different colours? (1) 9. Two unbiased dice with faces numbered 1, 2, 3, 4, 5 and 6 are rolled
simultaneously. (a) (i) List the sample space for this multistage event. ~ (1)
(ii) What is the probability that neither dice shows a 6 on the uppermost face? (I) (b) Cooper plays a game with these dice. There is no entry fee. When the dice are
rolled, C00per wins $20 if both dice show a 6 on the uppermost face, he wins $2 if
there is only one 6 and he loses $2 if neither shows a 6. Calculate the ﬁnancial expectation for this game. (2) SECTION III. MEASUREMENT (Start a new page) 1. The area of a sector in a circle with radius 7 cm that is cut off by an angle of 60 0 at
the centre is: 60 x7. B. 2—xele4. C. fO—xxx’Yz. D. ﬂ><2><12'><'7.
360 360 A. ______
360x2x1r 360 2.
The volume of this ﬁgure is:
NOT TO SCALE.
8 cm
A. 112 cm3. B. 672 cm3. C. 336 cm3. D. 62 ems. 3. The diagram shows a circle inside an ellipse. The shaded area, to the nearest cm2 ,7
is: 10 cm +—————+
20 cm A. 79. B. 157. C. 314. D. 550. 4. How many square centimeters are in 0.0075 square metres?
A. 0.75. B. 7.5. C. 75. D. 7500. 5. The surface area of a closed cylinder with radius 7.8 m and height 3.2 m is closest
to A. 539.0m2. 11539.1 m2. C. 1842.7m2. D. 1842.8m2. 6. The side of a square is measured as 39 cm to the nearest cm. What are the lower
and upper limits of the area of the square? (1) 7.Use Simpson’s rule twice to calculate the area of the shape below. All
measurements are in metres. ‘ NOT TO SCALE.
4' 8 52 4———————~———————————>
12 (3) 8. A sphere has a surface area of 25000 cm2 . Calculate its radius correct to 2 decimal
places. (2) 9. Rectangular sheets of thin aluminium are rolled into open cylindrical drums as
shown in the diagram below. 1.25 m
<——————————~——> 1m (i) Show that the drums have a radius of approximately 20 cm. 7 (1) (ii) Calculate the volume of the drums in cubic metres. Give your answer correct to 2
decimal places. (2) (iii) If the drums have atop and bottom added, what is the capacity of a drum? Give
your answer correct to the nearest litre. 7 (1) 10. The diagram below shows a roundabout with the outside portion paved, and with
an inside garden. (i) What is the area 'of the paved portion? (2) (ii) Calculate the cost of paving the roundabout at $27.75 / In2 . (1) SECTION IV. ALGEBRA. (Start a new page.) 1. 4a+8+2a—3= A. 115:. B. 6a2+5_ C. 60—11. D. 6a+5.
2. Evaluate all)2 given that a:2,b=—3. A. 18. B. 36. C. "18. D. —36. 3. If A=7rR_2, what is R equal to? . 2
iii. BE. (3.1. D.‘ 1‘1. J7; 7r ' It ﬁt 3x 4. Which ofthe following is the solution to 2 + 1 = 10?
A. x=6l. B. x=6. C. 32:11. ' D. x=23.
3 3 3 5. Make r the subject of v=u+at. v u—v v—u
A. I=——a. B. t=v—u—a. C. t=—. D. I:
u a a 6. Solve the following equations (i) 2x+1=9. (2)
(ii) 4x3 = —108_ ' (2)
mnx:3=s a (a 7 If T = 2:: JE , ﬁnd L when T = 6, g = 9.8. Give your answer correct to 3
g signiﬁcant ﬁgures. (2) 8. Make a the subject of P = y . (2)
x  a
.2 5—91 9. Given that A = P(1 + r)" , ﬁnd the value of n comestdoQﬂecimal places when
A = 200, P = 40, r = 0.05. (3) 2009 HIGHER SCHOOL CERTIFICATE EXAMINATION
General Mathematics F0 RMULAE SHEET Area of an annulus ‘3 'J
A = Rhine)
R = radius of outer circle
r = radius of inner circle
Area of an ellipse
A = me
a = length of semimajoraxis
b = length of semiminor axis
Area of a sector
9 a
A = 7—3:"
.360
6 = number of degrees in central angle
Arc length of a circle
6
l = ———’27rr‘
360
9 = number of degrees in central angle Simpson’s rule for area approximation Surface area
Sphere A = dim3 Closed cylinder A = zmh. + 2m? 1' = radius
17. = perpendicular height
Volume
Cone V = jam21':
3
Cylinder V = 7P2]?
. I
Pyramid V = :Ah
.3
Sphere V = gm}
r = radius
h = perpendicularheight
A = area of base
Sine rule
(I b C sin/l sinB sinC h
A‘ '" '3T(df +4dm +di) Area of a triangle
. . i .
l'i = distance between successwe A = gabsmC
measurements —
{I}. = first measurement
rim 2 middle measurement Cosine rule
_  ‘J ’J ’1
(I, — last measurement C = n'+b'—2(ibcosC
or
c 2 +13 2
l‘ P —(.'
eosC = —————————— 2a b FORMULAE SHEET Simple interest I
p ll ll Pm initial quantity
percentage interest rate per period,
expressed as a decimal number of periods Compound interest A
A I? P(l+r)” ﬁnal balance initial quantity number of compounding periods
perCentage interest rate per compounding  period, expressed as a decimal Future value (A) of an annuity 7 A M 11 (l + r)" _1 J" M contribution per period,
paid at the end of the period Present value (N) of an annuity N 01' MJU + r)” —l i r(l + r)" A (l + r)” St ‘aightline formula for depreciation S . S Vu D H V0 — DH salvage value of asset after :2 periods
purchase price of the asset amount of depreciation apportioned
per period
number of periods Declining balance formula for depreciation s = v00 —i)” S salvage value of asset after u periods r percentage interest rate per period. expressed as a decimal ll Mean of a sample _ 2x
.1' =
_, n
Za
= 2
E  mean
A: 2 individual score
n. = number of scores
f = frequency Formula for a zscore X—I .
S {‘1 s = standard deviation Gradient of a straight line vertical change in position
in = ——————'——"——_'__ _ _ .
horizontal change lli POSlLlUl'l Gradient—intercept form of a straight line y = nu+b
m = gradient
(7 = .v—intercept Probability of an event The probability of an event where outcomes
are equally likely is given by: number of favourable outcomes
P(event) = W—
total number of outcomes ...
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