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PRELIMINARY EXAMINATION 2011
Name of Pupil : ________________________ ( )
Class : _______
Subject / Code : Mathematics / 4016
Paper : 1
Level : Sec 4 Express / 5 Normal Academic
Date : 22 August 2011
Duration : 2 hours
Setter : Tai KS, Tan YL, Wong MC
READ THESE INSTRUCTIONS FIRST
Write your name, class and class register number on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all questions.
If working is needed for any question it must be shown with the answer.
Omission of essential working will result in loss of marks.
You are expected to use a scientific calculator to evaluate explicit numerical expressions.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the
answer to three significant figures. Give answers in degrees to one decimal place.
For , use either your calculator value or 3.142, unless the question requires the answer in terms of
.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 80.
This question paper consists of 16 printed pages, including this Cover Page.
Marks
80
Frequency density
For Examiner's Use
L
6
Y
2
Sec 4E_5N_EM_P1 YYSS_PRELIM_2011
Mathematical Formulae
Compound interest
Total amount =
nr
P
1001
Mensuration
Curved surface area of a cone = rl
Surface area of a sphere = 4r2
Volume of a cone = hr 2
3
1
Volume of a sphere = 3
3
4r
Area of triangle ABC = Cabsin2
1
Arc length = rθ, where θ is in radians
Sector area = 2
2
1r , where θ is in radians
Trigonometry
C
c
B
b
A
a
sinsinsin
Abccba cos2222
Statistics
Mean = f
fx
Standard deviation =
22
f
fx
f
fx
3 For
Examiner’s
Use
Sec 4E_5N_EM_P1 [Turn Over
1. (a) Simplify
3
4
263
xx .
(b) Factorise yzxy .
Answer (a) ……….………….… [1]
(b) ……….……...……... [1]
2. Darika sold a computer for $1568. If she made a profit of 110%, how much was the cost
price of the computer?
Answer $……...……………. [2]
3. The distribution of the ranks of members in an Uniform Group is shown in the table.
Rank Staff Sergeant Sergeant Corporal Lance Corporal
Frequency 4 6 13 7
(a) Write down the median rank.
(b) This distribution is to be shown in a pie chart. Calculate the angle representing the
modal rank.
Answer (a) ……....……………. [1]
(b) ..……………….....° [1]
4 For
Examiner’s
Use
Sec 4E_5N_EM_P1 YYSS_PRELIM_2011
4. (a) In a marathon, there were 2365 participants comprising of 1890 adults and the rest
were youths. Express the number of youths participating as a percentage of the total
number of participants.
(b) 4
1 of the 1890 adult participants finished the marathon within 2 hours and
5
3 of them
finished between 2 hours to 4 hours, while the rest pulled out of the race. Find the
fraction of participants who pulled out of the race.
Answer (a) …….………..………[1]
(b) ………...….…..…… [1]
5. (a) Given that 81
13 n , find n.
(b) Simplify m
mm 3.
Answer (a) n = ...……………… [1]
(b) ..…..………………. [2]
6. In the diagram, FA is parallel to EB and
DC. Given the angle shown and that
ABEF is congruent to CBED, find
(a) ABE,
(b) obtuse ABC.
Answer (a) .….…..……………° [1]
(b) .….…..……………° [1]
(b) ..……..……………° [1]
75°
A
B
C
F E
D
5 For
Examiner’s
Use
Sec 4E_5N_EM_P1 [Turn Over
7. Solve 223513 x .
Answer……..………………. [2]
8. Elvin invests $x in a special account that pays him compound interest at the rate of 2.5%
per year. Calculate the total interest earned in 5 years, leaving your answer in terms of x.
Answer $…..…..…………… [3]
9. The diagram shows a log whose cross section is a circle.
Given that the radius is 20 cm, find
(a) the area of the circular cross section (leave your answer in terms of ),
(b) the length of the log if the volume is 60 000 cm3.
Answer (a).……...…..…… cm2 [1]
(b) ...……………….cm [1]
20 cm
6 For
Examiner’s
Use
Sec 4E_5N_EM_P1 YYSS_PRELIM_2011
10. The first term in a sequence is 5.
Each following term is found by adding 6 to the previous term.
(a) Write down the second and third terms.
(b) Write down an expression, in terms of n, for the nth term.
Answer (a) …….…… , …..………[1]
(b) ..………...….…..…… [1]
11. Two different sizes of bottles of oil are shown below.
The mass of the oil and the price are stated below the bottles.
Which size of bottle gives the better value?
You must show all your working clearly.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
Answer The…..…..……………bottle gives the better value. [2]
Answer (a).……...…..…… cm2 [1]
SMALL
0.5 litres
$8.50
LARGE
1.0 litres
$16.50
7 For
Examiner’s
Use
Sec 4E_5N_EM_P1 [Turn Over
12. The diagram shows the speed-time graph of a motorcycle’s journey.
(a) Find the acceleration when 5t .
(b) Find the total distance travelled by the motorist.
Answer (a) …….……....……… m/s2 [1]
(b) ...………...….…..…… m [1]
13. The container shown in the diagram is a prism.
The cross-section consists of a triangle.
The height of the prism is 12 cm.
Water is poured into the empty container at a constant rate.
It takes 18 seconds to fill the container.
On the axes in the answer space, sketch the graph showing how the depth of the water, d
centimeters, in the container varies over the 18 seconds.
Answer [2]
Speed
(m/s)
Time (s)
12
10 18 30 0
12 cm
Answer [2]
Depth of
water (d cm)
Time (seconds)
0 4 8 12 16
4
12
8
20
8 For
Examiner’s
Use
Sec 4E_5N_EM_P1 YYSS_PRELIM_2011
14. In the figure below, AC = AE, ACB = AED, CAD and BAE are straight lines.
State with reasons whether the two triangles are congruent.
[3]
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
15. The diagram shows two geometrically similar alarm clocks.
The ratio of the area of the clock face is 4 : 9.
(a) The area of the clock face of the smaller alarm clock is 80 cm 2 .
What is the area of the clock face of the larger alarm clock ?
(b) Write down the ratio of the lengths of their hour hands.
(c) The mass of the larger clock is 540g. What is the mass of the smaller clock ?
Answer (a) ………..………cm2 [1]
(b) ………………….. [1]
(c) .............................g [1]
A
E
B D
C
9 For
Examiner’s
Use
Sec 4E_5N_EM_P1 [Turn Over
16. During a thunderstorm, a tree cracked into two parts. The top part fell and
hinged onto the slope. The two parts of the tree and the slope formed a triangular
shaped ABC as shown in the diagram. By measurement, AB = 13 m, AC = 18 m
and BAC = 68o. Find
(a) BC and
(b) the area of triangle ABC.
Answer (a) …..……………m [3]
(b)…..……………m2 [1]
17. Solve the simultaneous equations:
1725
2138
yx
yx
Answer x = _________ y = _________ [3]
D
B
13m
6
8o
A
13 m
B
C
68o
18 m
10 For
Examiner’s
Use
Sec 4E_5N_EM_P1 YYSS_PRELIM_2011
18. Given that 693 = 32 7 11.
(a) Express 1176 as the product of its prime factors.
(b) Find the HCF of 693 and 1176,
(c) Find the smallest integer value of m such that 693m is a perfect square.
(d) Find the smallest integer value of n such that 1176n is a multiple of 693.
Answer (a) .……..…………… [1]
(b) ……………………[1]
(c) m=......................... [1]
(d) n = ..…………….. [1]
19. (a) Estimate the value of 07.585.49
78.996
by changing and writing down each of the figures.
[2]
(b) Given that 90ABC , AC =10 cm and AB = 8 cm, evaluate
(i) CB,
(ii) cos ACD ,
(iii) tan ACD
Answer (i) .……..…...cm [1]
(ii) ……..……….[1]
(iii) ..…..………. [1]
B
C D
A
8 cm
10 cm
11 For
Examiner’s
Use
Sec 4E_5N_EM_P1 [Turn Over
20.
The cumulative frequency graph below shows the marks obtained by 120 students in
a Science test. Use the graph to find
(a) the median mark,
(b) the interquartile range,
(c) the number of students who score more than 50 marks.
Answer (a) .……..…………… [1]
(b) ……………………[1]
(c)……......................... [1]
12 For
Examiner’s
Use
Sec 4E_5N_EM_P1 YYSS_PRELIM_2011
21.
2009 Country A Country B Country C
Population 4.51 million 7.26 million 83.1 million
Land area (km2) 1.83 million 2.59 million 36.4 million
Using information from the table above for year 2009, find
(a) how many more people live in Country C than Country B, giving your answer in
standard form,
(b) the population of Country B in 2010 if its population was 10% lesser than 2009,
giving your answer in ordinary notation,
(c) the average number of people per square kilometer living in Country A.
Answer (a) …..…..…………… [2]
(b) ……...……………. [1]
(c) ……...……………. [1]
13 For
Examiner’s
Use
Sec 4E_5N_EM_P1 [Turn Over
22. (a) A and B lie on a circle, centre O with radius 8 cm.
If AOB = 1.1 radians, find the area of major sector AOB.
(b) Find one value of z, in radians, such that tan z =4
3.
Answer (a) …...…...….….. cm2 [2]
(b) z = .......... ……..…. [1]
23. Five shirts and three pants cost $242 while three shirts and five pants cost $284.40.
(a) Write down two equations using the information given above.
(b) Solve the equations to find the cost of a shirt and a pair of pants.
Answer (a) …..…..………………..
…..…..…………… [2]
(b) shirt = $ .....…………...
pants = $ ...….……. [2]
O
B
1.1
A
14 For
Examiner’s
Use
Sec 4E_5N_EM_P1 YYSS_PRELIM_2011
24. (a) Express x2 + 2x – 1 in the form bax 2)( .
(b) Sketch the graph of y = x2 + 2x – 1.
Answer (b)
[2]
(c) Write down the coordinates of the turning point of y = x2 + 2x – 1.
Answer (a) …..…..…………… [2]
(c) …………………… [1]
x
y
15 For
Examiner’s
Use
Sec 4E_5N_EM_P1 [Turn Over
25. A security guard has to go through checkpoints OABC during his patrol.
A is 700 m due East of the starting point O. B is 600 m away from A on a bearing of 50o
and C is 1200 m away from O on a bearing of 20o.
(a) Using a scale of 1 cm to represent 100m, make an accurate scale drawing of the
patrol area.
(b) On your diagram, construct
(i) the bisector of COA ,
(ii) the perpendicular bisector of AB.
(c) A new checkpoint, D is to be added into the patrol area such that it is equidistant
from OA and OC and equidistant from A and B. On your diagram, mark clearly the
position of checkpoint D.
Answer (a), (bi), (bii), (c)
[5]
North
O A 700 m
16 For
Examiner’s
Use
Sec 4E_5N_EM_P1 YYSS_PRELIM_2011
26. If OB =
5
2 and AB =
8
15, find
(a) (i) 2 AB – 3OB ,
(ii) OA ,
(iii) AB .
(b) Given that BC = OBp and BC =
15
q, find the value of p and q.
Answer (a)(i) ………….………… [1]
(ii) ..….…….....………. [1]
(iii) .………...…………. [2]
(b) p = …….….………...….
q = .……..………….. [2]
- END OF PAPER -
Marking Scheme 4 Express / 5 Normal (Acad) Prelim Paper 1 2011
Qn Details Marks Remarks
1(a)
3
4
263
xx = 833 xx
= 8
A1
1(b) zxy
A1
2. 100
210
1568
= $746.67
M1
A1
3(a) Corporal
A1
3(b) 156360
30
13
A1
4(a) %1.20%100
2365
475
A1
4(b)
20
3
A1
5(a) n = 4
A1
5(b) 2
7
m
A1
6(a) 105°
A1
6(b) 150°
A1
7. x2 and x<5
combine 52 x
M1
A1
8. xx
5
100
5.21
= $0.13x
B2
A1
9(a) 400
A1
9(b) 150 cm
A1
10(a) 11, 17
A1
10(b) -1 + 6n or 6n − 1 A1
11. $8.50 2 = $17.00 for one litre (Small)
Comparing, LARGE bottle gives the better value.
M1
A1
12(a) 2.1
10
12 m/s2
A1
12(b) Distance traveled = Area under graph
123082
1
228 m
A1
13.
M1
A1
M1 given for
correct
curvature of
graph.
A1 given for
accuracy of
curve.
14.
)(
).)((
))((
))((
ASAAEDACB
soppvertADAEBAC
givenSAEAC
givenAAEDACB
M1
M1
A1
Must write
reason
15(a) 2180804
9cm
A1
15(b)
9
42 : 3
A1
15(c) g160540
3
23
A1
Depth of
water (d cm)
Time (seconds)
0 4 8 12 16 20
4
8
12
16(a)
m8.17
68cos13181318 022
M1
A1
16(b)
2
0
108
68sin18132
1
cm
M1
A1
17. Use either elimination or substitution method
x = 3 y = 1
M1
A1, A1
18(a) 23 732 A1
18(b) 37 = 21 A1
18(c) m = 711 = 77 A1
18(d) n = 3 11 = 33 A1
19(a) 4
550
1000
M1, M1 1 mark each
for two figures
written
correctly.
19(b)(i) cmCB 6810 22 A1
19(b)(ii)
5
3
A1
19(b)(iii)
3
4
A1
20(a) 35 marks A1
20(b) 42 – 27 =15 marks
A1
20(c) 8 students
A1
21(a) (83.1 – 7.26)106
=75.84106
= 7.584107
M1
A1
21b 6534000
B1
21c 2.46 (3 s.f.)
B1
22a
2
1(8)2(2 – 1.1)
= 166 cm2
M1
A1
22b Acute =0.644
z = 0.644 rad
M1
A1
23a 5s + 3p = 242
3s + 5p = 284.4
B1
B1
23b p = $43.50
s = $22.30
B1
B1
24a x2 + 2x – 1 = (x + 1)2 – 1 – 1
= (x + 1)2 – 2
M1
A1
24b
B2 B1: Correct
Shape
B1: Correct
y–intercept
24c (–1, – 2)
B1
25 Drawing B5 1 mark for
each correct
line;
1 total mark
deducted for
any number of
unlabelled
points
26ai
31
24
B1
26aii
13
13
B1
26aiii 22 )8(15
= 17 units
M1
A1
26b p = – 3
q = – 6
B1
B1
x
y
–1
PRELIMINARY EXAMINATION 2011
Name of Pupil : _______________________________ ( )
Class : _______
Subject / Code : MATHEMATICS/ 4016
Paper No. : 2
Level : Sec 4 Express/ 5 Normal Academic
Date : 24 August 2011
Duration : 2 hours 30 minutes
Setter : Tan Yurn Long/ Chia Kah Kheng/ Larry Phoon
READ THESE INSTRUCTIONS FIRST
Write your name, class and class register number on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all questions.
Write your answers on the writing paper provided. Begin each question on a new page.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in
the case of angles in degrees, unless a different level of accuracy is specified in the
question.
The use of a scientific calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part
question.
The total number of marks for this paper is 100. ______________________________________________________________________
This question paper consists of 10 printed pages, including this Cover Page.
Marks
100
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
2
Mathematical Formulae
Compound interest
Total amount =
nr
P
1001
Mensuration
Curved surface area of a cone = rl
Surface area of a sphere = 4r2
Volume of a cone = hr 2
3
1
Volume of a sphere = 3
3
4r
Area of triangle ABC = Cabsin2
1
Arc length = rθ, where θ is in radians
Sector area = 2
2
1r , where θ is in radians
Trigonometry
C
c
B
b
A
a
sinsinsin
Abccba cos2222
Statistics
Mean = f
fx
Standard deviation =
22
f
fx
f
fx
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
3
20
A B C
D
E
F
G
O
Answer all the questions.
1. Ali bought three bicycles, A, B and C for a total of $608. He paid for the
bicycles in the ratio of 4 : 5 : 7.
(a) Calculate how much he paid for bicycle B. [2]
(b) He sold bicycle B at a 10% loss. What was his selling price? [2]
(c) Ali then sold bicycles A and C for a total of $480.70.
Find
(i) the profit he made from selling the two bicycles, [2]
(ii) the profit as a percentage of the two bicycles. [2]
(d) Ali bought bicycle D which was 30% more than the total he paid
for the three bicycles. With the money made from selling the 3
bicycles, how much more did he have to pay? [2]
2.
The diagram shows a circle with centre O and angle 20EFD . The
straight lines AC and AE are tangents to the circle at the points B and E
respectively.
(a) Calculate
(i) angle BFD , [1]
(ii) angle GBD , [1]
(iii) angle BAE , [1]
(iv) angle EDB . [1]
(b) Identify two similar triangles and explain why they are similar. [2]
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
4
3. (a) (i) Factorise 432 yy . [1]
(ii) Express as a single fraction in its simplest form
4
3
43
72
yyy
. [3]
(b) Given that1
5
w
wuv ,
(i) find v when u = 10 and w = 2.4, [1]
(ii) express w in terms of u and v. [3]
4.
In the diagram, aOA and bOB . OEOF3
2 and CDOA . B and E
are midpoints of OC and OD respectively.
(a) Express the following vectors in terms of a and/or b,
(i) AC , [1]
(ii) OE , [1]
(iii) AB , [1]
(iv) AE . [1]
(b) Show that ba3
2
3
2AF . [1]
(c) Make 2 statements about the points A, F and B. [2]
(d) Find OCE
OAF
triangleof area
triangleof area. [2]
O A
B
C
E
D
F
a
b
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
5
5. (a) }121: integers{ xx
}numbers prime are that integers{A
Given that sets A and B are such that }2 { BA and
9,1'BA .
(i) Draw a Venn Diagram representing sets , A and B. [2]
(ii) Write down )'(An . [1]
(iii) List the elements contained in the set BA . [1]
(b) The sales of Yearly Pass for the 3 categories in two successive
years to the Zoo and Bird Park are given in the table below.
2010 2011
Category Child Adult Senior
Citizens Child Adult
Senior
Citizens
Yearly Pass $50 $120 $75 $50 $120 $75
Zoo 20 40 10 16 50 10
Bird Park 12 35 12 20 43 8
The information for 2010 sales can be represented by the matrix,
12
10
35
40
12
20Q and the cost of Yearly Pass for each category
can be represented by the matrix
75
120
50
M .
(i) Represent the sale of Yearly Pass in 2011 by a matrix R. [1]
(ii) Evaluate S = (Q + R). [1]
(iii) State what S represents. [1]
(iv) Evaluate the matrix ][2
1MSA . [1]
(v) State what the elements of A represent. [1]
(vi) Evaluate AP 11 . [1]
(vii) State what P represents. [1]
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
6
6. Answer the whole of this question on a sheet of graph paper.
The temperature of a cave is recorded by a scientist at different heights
above or below the sea level. The table below shows some of the values
recorded.
h ( km ) –1.4 –1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0 0.2 0.4
t ( C ) 1.50 2.43 3.00 3.25 3.22 2.55 2.0 1.37 0.70
(a) Using a scale of 2 cm to represent 0.2 km, draw a horizontal h-axis
for 4.04.1 h . Using a scale of 2 cm to represent 0.5 C , draw
a vertical axis t-axis for 41 t . On your axes, plot the points
given in the table and join them with a smooth curve. [3]
(b) Use your graph to estimate
(i) the temperature of the cave at 0.4 km below the sea level, [1]
(ii) the heights, h above or below the sea level at the
temperature of 1.7 C , [2]
(iii) the range of values of heights above or below the sea level
for which the temperature is greater than or equal to 2 C . [2]
(c) By drawing a tangent, find the gradient of the curve at 3,1 . [2]
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
7
7.
A, B and C are ships in the sea. The bearing of Ship A from Ship C is 303o
and the bearing of Ship B from Ship C is 052o. It is given that AC is 520 m
and BC is 470 m.
(a) Find
(i) AB, [4]
(ii) BAC, [2]
(iii) the bearing of B from A. [2]
(b) An eagle is flying directly above Ship C. The angle of depression
of Ship B from the eagle is 50o. Find
(i) the height of the eagle above the ship, [2]
(ii) the shortest distance from C to AB. [2]
North
A
C
B
470 m 520 m
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
8
E
C D B A
42 cm
63 cm
F
8.
The diagram shows a kite which is made of wire. The kite consists of a
large semicircle with diameter AB of 63 cm and two small semicircles of
diameter 42 cm each. C and D are the centres of the two small semicircles
and = 7
22.
(a) Explain why EDC is 60o. [1]
(b) Find
(i) DE, [1]
(ii) arc DFE, [2]
(iii) the perimeter of the shaded region. [2]
(c) A special fabric is used to make the shaded region. Find
(i) the area of sector CED, [2]
(ii) the area of segment DEF. [2]
(d) Show that the area enclosed by the fabric is 444 cm2, correct to 3
significant figures. [2]
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
9
9.
The diagram above shows the top view of two cylinders fitted exactly into
a box PQRS. The larger circle, centre X and radius 6 cm, touches the
rectangle at three points. The small circle, centre V and radius x cm,
touches the rectangle at two points. It is given that RS = 20 cm and
QR = 12 cm.
(a) Find, in terms of x,
(i) the length of XY, [1]
(ii) the length of VX, [1]
(iii) the length of VY. [1]
(b) Form an equation in x and show that it reduces to
0196522 xx . [3]
(c) Solve the equation 0196522 xx , giving both answers correct
to two decimal places. [3]
(d) Find the area of the trapezium XZUV. [2]
P Q U
X
Z
V
6 cm x cm
20 cm
12 cm
Y
S R
Sec 4E_5N_EM_P2 YYSS_PRELIM_2011
10
10. (a) A group of 20 old folks from New Valley House nursing home was
selected to participate in a medical examination. Their ages are
recorded and listed as follows:
80 71 72 80 76
75 90 80 87 92
85 74 98 82 74
82 71 74 76 78
(i) Copy and complete the frequency table shown below. [1]
(ii) Calculate the mean score. [1]
(iii) Calculate the standard deviation. [2]
(b) A school band consists of 15 male students and 10 female students.
The instructor selects a student from the band at random to be
nominated as the drum major. The teacher-in-charge then selects
another student at random to be nominated as the drum secretary.
(i) Draw a tree diagram to show the probabilities of the
possible outcomes. [2]
(ii) Find, as a fraction in its simplest form, the probability that
(a) the instructor and teacher-in-charge both select a
male student, [1]
(b) the teacher-in-charge selects a female student, [2]
(c) one of them selects a male student and the
other selects a female student. [2]
- THE END -
Age (x) Frequency
70 < x ≤ 80
80 < x ≤ 90
90 < x ≤ 100
Sec 4E5NA-Prelim-P2-2011
Marking Scheme
1 (a)
(b)
(ci)
(cii)
(d)
60816
5
= $190
0.9 190
= $171
608 – 190 = $418
480.70 – 418 = $62.70
100418
7.62
= 15%
1.3608 = $790.40
790.40 – 480.70 – 171
= $138.70
M1
A1
M1
A1
M1
A1
M1
A1
M1
A1
2 (ai)
(aii)
(aiii)
(aiv)
(b)
90
20
40
70
Δ EGF is similar to ΔDGB (AAA).
A1
A1
A1
A1
A2
3 (ai)
(aii)
(bi)
(bii)
)1)(4(
432
yy
yy
)1)(4(
34
)1)(4(
337
)1)(4(
)1(37
4
3
)1)(4(
7
4
3
43
72
yy
y
yy
y
yy
y
yyy
yyy
230.0
10
4.1
4.7
14.2
54.2)10(
v
v
v
1
5
5)1(
5
5
5)1(
1
5
1
5
22
22
2222
2222
2222
22
22
vu
vuw
vuvuw
vuwwvu
wvuwvu
wwvu
w
wvu
w
wuv
A1
M1
M1
A1
A1
M1
M1
A1
3
4(ai)
(aii)
(aiii)
(aiv)
(b)
(c)
(d)
b2a OCAOAC
b2a2
1
2
1 ODOE
ba OBAOAB
baOEAOAE
2
1ba
2
1a
b3
2a
3
2
b2a2
1
3
2a
3
2
OEAO
OFAOAF
A, B & F lies on the same straight line & AF =2FB.
3
2
1
1
3
2
triangleof area
triangleof area
OCE
OAF
A1
A1
A1
A1
A1
A2
A2
4
5(ai)
(aii)
(aiii)
(bi)
(bii)
(biii)
(biv)
(bv)
(bvi)
(bvii)
[A2]
1 mistake minus 1 mark
7)'( An
{3, 5, 7, 11}
8
10
43
50
20
16R
12
10
35
40
12
20Q +
207832
209036
8
10
43
50
20
16
S represents the total Yearly Passes sold in 2010 & 2011.
6230
7050
75
120
50
20832
209036
2
1A
$7050 & $6230 represents the average amount of money collected for
the yearly pass for Zoo & Bird Park respectively.
13280SM11P
P represents the total average amount of money collected for the
yearly pass for the Zoo and Bird Park for 2010 & 2011.
A2
A1
A1
A1
A1
A1
A1
A1
A1
A1
A B
3, 5,
7, 11
4, 6,
8, 10,
12
2
1, 9
5
6(a)
(bi)
(bii)
(biii)
(c)
Axes
Correct Points
Smooth Curve
98.2
1.0,36.1x
03.1 t
gradient = 2 (1 mark for calculation)
5
A1
A1
A1
A1
A2
A2
M1, A1
6
7 (ai)
(aii)
(aiii)
(bi)
(bii)
ACB = 52o + (360o – 303o)
= 109o
AB = o109cos4705202470520 22
= 806.4
806 m (3 s.f.)
4.806
109sin
470
sin oBAC
BAC = 33.44o
= 33.4o (1 d.p.)
Bearing = 180 – 57 – 33.44
= 089.5o or 090o
tan 50o = 470
h
h = 560.1
560 m
od 109sin4705202
14.806
2
1
d = 286.5
287 m (3 s.f.)
or
sin33.44o = (shortest distance 520)
shortest distance = 520sin33.44o
= 286.5
287 m (3 s.f.)
M1
M1
M1
A1
M1
A1
M1
A1
M1
A1
M1
A1
M1
A1
7
8
(bi)
(bii)
(biii)
(ci)
(cii)
(d)
EC = ED = CD or ECD = equilateral
21 cm
427
22
360
60
= 22 cm
222427
22
2
1263
7
22
2
1
= 187 cm
221
7
22
360
60
= 231 cm2
231 – 221
2
1
sin 60o
= 40.04
40.0 cm2 (3 s.f.)
2
2
63
7
22
2
1
221
7
22
2
12
+ 231 + 40.04
= 444.29
444 cm2 (3 s.f.)
B1
B1
M1
A1
M1
A1
M1
A1
M1
A1
M1
A1
8
9 (ai)
(aii)
(aiii)
(b)
(c)
(d)
cmxXY )6(
cmxXV )6(
cmx
xVY
)14(
620
)(196520
2302321236
281962361236
)14()6()6(
2
22
222
222
Shownxx
xxxx
xxxxxx
xxx
a = 1, b = –52, c = 196
)1(2
)196)(1(4)52()52( 2 x
91.47x or x 4.09
91.47x (rejected)
Area of Trapezium XZUV )09.4620()609.4(2
1
20.50 cm
A1
A1
A1
M1
M1
A1
M1
A2
M1
A1
9
10(ai)
(aii)
(aiii)
(bi)
(biia)
Age (x) Frequency
8070 x 13
9080 x 5
10090 x 2
5.79
20
)2(95)5(85)13(75
Mean
Standard Deviation
69.6
)5.79(20
)2(95)5(85)13(75 2222
1 Mistake deduct 1 Mark
P(the instructor and teacher-in-charge both select a male student)
20
7
24
14
25
15
A1
A1
M1
A1
A2
A1
25
15
Instructor
Selection
Male
Female 25
10
24
15
24
10
24
14
Teacher
Selection
Male
Female
Male
Female
24
9
10
(biib)
(biic)
P(the teacher-in-charge selects a female student)
5
2
24
9
25
10
24
10
25
15
P(one of them selects a male student and the other selects a female
student)
2
1
24
15
25
10
24
10
25
15
M1
A1
M1
A1