preliminary examination 2011 for examiner's use

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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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]


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


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]


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]


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


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]


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


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

preliminary examination 2011 for examiner's use

Documents