72
1449/2 1449/2 4 For Examiner’s Use Section A [52 marks] Answer all questions in this section. 1 The Venn diagram in the answer space shows sets K, L and M such that the universal set, = K L M. On the diagrams in the answer space, shade (a) L M , (b) ( K M )’ L. [3 marks] Answer: (a) (b) L K M L K M

# Maths Test 1 SPM 2014

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• 1449/2

1449/2

4

For

Examiners

Use

Section A

[52 marks]

Answer all questions in this section.

1 The Venn diagram in the answer space shows sets K, L and M such that the

universal set, = K L M.

(a) L M ,

(b) ( K M ) L.

[3 marks]

(a)

(b)

L

KM

L

KM

• 1449/2

[Turn over1449/2

5

2(a) Diagram 1 shows a right prism. The base GMND is a horizontal rectangle.

Right angled triangle MFG is the uniform cross-section of the prism.

S is the midpoint of ND.

DIAGRAM 1

Identify and calculate the angle between the line FS and the base GMND.

[4 marks]

For

Examiners

Use

E

G

D

M

S

F

N

5 cm

16 cm6 c

• 1449/2

1449/2

6

For

Examiners

Use 2(b) Diagram 2 shows a right prism with a horizontal rectangular base JKLM .

The isosceles triangle KLH is the uniform cross-section of the prism.

N is the midpoint of KL.

DIAGRAM 2

Identify and calculate the angle between the plane KLG and the plane KLH.

[4 marks]

J

K L

H

G

N

M

6 cm

5 cm

12 cm

• 1449/2

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7

3 Diagram 3 shows a solid, formed by joining a half cylinder to a half cone.

The height of the cone is 6 cm.

By using722

, calculate the volume, in cm3 , of the combined solid.

[4 marks]

For

Examiners

Use

7 cm

12 cm

DIAGRAM 3

• 1449/2

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8

For

Examiners

Use

4 Using factorisation, solve the quadratic equation 3x (2x 1) + 8x = 1.

[4 marks]

5 Using factorisation, solve the quadratic equation pp 5

23 2 .

[4 marks]

• 1449/2

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9

6 Calculate the value of m and of n that satisfy the following simultaneous

linear equations:

1223166

nmnm

[4 marks]

For

Examiners

Use

7 Calculate the value of h and of k that satisfy the following simultaneous

linear equations:

273

6443

hk

hk

[4 marks]

• 1449/2

1449/2

10

For

Examiners

Use 8 Diagram 4 shows two sectors OPQ and ORS, both with centre O.

It is given that POQ = 60.

By using =722 , calculate

(a) the perimeter, in cm, of the whole diagram,

(b) the area, in cm2, of the shaded region.

[ 6 marks ]

(a)

(b)

T

Q 14 cm

7 cm

R

S

O

PDIAGRAM 4

• 1449/2 Form Four

[Turn over1449/2

11

9(a) Write down two implications based on the following statement:

m > 6 if and only if m 6 > 0

(b) State the converse of the following statement and hence determine whether the

converse is true or false.

If x is a factor of 5, then x is a factor of 10.

(c) Make a general conclusion by induction for the sequence of numbers

1 , 6 , 15 , 28, . . . which follows the following pattern.

1 = 2 ( 1 )2 1

6 = 2 ( 2 )2 2

15 = 2 ( 3 )2 3

28 = 2 ( 4 )2 4

=

[6 marks]

(a) Implication 1:

Implication 2:

(b)

...

(c) ...

For

Examiners

Use

• 1449/2 Form Four

1449/2

12

For

Examiners

Use 10 In Diagram 5 , OPQR is a parallelogram and O is the origin.

Find

(a) the equation of the straight line PQ,

(b) y intercept of the straight line PQ.

[4 marks]

(a)

(b)

x

R ( 4 ,12)

DIAGRAM 5

y

P ( 3 , 6 )

O

Q

• 1449/2

1449/2

13

11 In Diagram 6 , O is the origin. KL, PQ and RS are straight lines.

PQ is parallel to RS.

The equation of the straight line KL is 62 xy .

Find

(a) the gradient of the straight line PQ,

(b) the equation of the straight line RS.

[5 marks]

(a)

(b)

For

Examiners

Use

xO

KR

S

L

DIAGRAM 6

y

P

Q (3, 3)

3[Turn over

• 1449/2

1449/

14

For

Examiners

Use

Section B

[48 marks]

Answer any four questions from this section.

12(a) The Venn diagram in the answer space shows the universal set , sets P, Q

and R. On the diagram in the answer space, shade the region for

(i) P Q ,

(ii) ( P Q ) R.

[3 marks]

(i)

(ii)

P

Q

PQ

R

2R

• 1449/2

1449/2

15

12(b) In Diagram 7 , O is the origin. Straight line NR is parallel to straight line OQ .

Find

(i) the equation of the straight line RN,

(ii) the x intercept of the straight line RN .

[5 marks]

(i)

(ii)

For

Examiners

Uses

y

x

R

N ( 4,9 )

Q (3, 4)

O

DIAGRAM 7[Turn over

aCross-Out

• 1449/2

1449/2

16

For

Examiners

Use

12(c) Diagram 8 shows a right prism. The base PQRS is a horizontal rectangle.

Trapezium PQGF is the uniform cross-section of the prism.

U, V, and W are midpoints of PS, FE and QR respectively.

DIAGRAM 8

Identify and calculate the angle between the plane QRV and the base PQRS.

[4 marks]

E

P

G

H

Q

R

F

V

US

W8 cm12 cm

5 cm

• 1449/2

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17

13(a) (i) State whether the following sentences is a statement or

non-statement.

(a) 2x + 5y 6

(b) 4 is a prime number.

(ii) Combine the two statements below to form a false statement.

Statement 1 : 3 13 = 39

Statement 2 : 39 is a prime number.

(iii) Write down Premise 1 to complete the following argument:

Premise 1 :

Premise 2 : 3 is a factor of 15

Conclusion : 3 is a factor of 30

(iv) Fill in the blanks with < or > to form

(a) a true statement,

6 3

(b) a false statement.

8 24

[6 marks]

(i)(a) _________________________________

(b) _________________________________

(ii) ______________________________________________________

(iii) Premise 1 :______________________________________________

(iv) (a) 6 3

(b) 8 24

For

Examiners

Uses

• 1449/2

1449/

18

For

Examiners

Use

13(b) In Diagram 9, ORST is a quadrant and KL is an arc of another circle both

with centre O. ORK and OSL are straight lines.

DIAGRAM 9

OR = RK = 7 cm.

Using722

, calculate

(i) the perimeter, in cm, of the whole diagram,

(ii) the area, in cm 2 , of the shaded region.

. [6 marks]

(i)

(ii)

60

R

S

T

L

K

O

• 1449/2

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19

14(a) Using factorisation, solve the quadratic equation mm 6

52 .

[4 marks]

14(b) Calculate the value of d and of e that satisfy the following simultaneous linear

equations:

144

10213

ed

ed

[4 marks]

For

Examiners

Uses

• 1449/2

1449/2

20

For

Examiners

Use

14(c) Diagram 10 shows a solid cuboid. A semi cylinder is taken out of the solid.

The volume of the remaining solid is 292 cm 3 .

Calculate the width, in cm, of the remaining solid.

(Use =722 )

[4 marks]

2 cm

2 cm

8 cm

7 cm

DIAGRAM 10

• 1449/2

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21

15. The data in Diagram 11 shows the ages of 50 runners who took part in a charity run

event.

14 36 12 16 27 31 27 28 30 28

16 18 23 18 24 32 23 14 18 31

22 30 23 20 25 30 31 22 20 37

12 26 36 23 28 30 34 38 33 36

11 23 27 27 34 38 25 12 17 29

DIAGRAM 11

(a) Based on the data in Diagram 11 and by using a class interval of 5, complete

Table 1 in the answer space.

[4marks]

(b) Based on Table 1 in (a),

calculate the estimated mean of the age of the runners.

[3marks]

(c) For this part of the question, use the graph paper provided on page 23.

By using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 1

runner on the vertical axis, draw a frequency polygon for the data.

[5marks]

For

Examiners

Use

• 1449/2

1449/2

22

For

Examiners

Use

(a)

Age (years) Midpoint Frequency

11 15

TABLE 1

(b) i)

ii)

(c) Refer graph on page 23.

• 1449/2

[Turn over1449/2

23

• 1449/2

1449/2

24

For

Examiners

Use

16. The data in Diagram 12 shows the marks obtained by 40 pupils in a quiz.

67 76 91 79 81 82 87 71

79 82 88 83 72 84 71 89

80 86 70 86 62 83 83 80

75 84 84 77 84 86 85 76

80 75 95 77 73 86 77 68

DIAGRAM 12

(a) Using the data in Diagram 12, and a class interval of 5, complete Table 2 in

[6 marks]

(b) For this part of the question, use the graph paper provided on page 26.

By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the

y-axis, draw an ogive based on the data.

[5 marks]

(c) From your ogive in (b), find the third quartile.

[1 mark]

• 1449/2

[Turn over1449/2

25

a)

Marks Frequency Cumulative Frequency Upper Boundary

61 65

TABLE 2

b) Refer graph on page 26

c)

For

Examiners

Use

• 1449/2

1449/2

26

• 1449/2

[Turn over1449/2

27

INFORMATION FOR CANDIDATES

1. This question paper consists of two sections: Section A and Section B.

2. Answer all questions in Section A and four questions from Section B.

3. Write your answers in the spaces provided in the question paper.

6. The diagrams in the questions provided are not drawn to scale unless stated.

7. The marks allocated for each question and sub-part of a question are shown inbrackets.

8. A list of formulae is provided on page 2 to 3.

9. A booklet of four-figure mathematical tables is provided.

10. You may use a non-programmable scientific calculator.

11. Hand in this question paper to the invigilator at the end of the examination.

• Mathematics Form 4 Final year 2008Section A

[ 52 marks ]

No Marking Scheme Marks

1a)

b)

P1

P2 3

2 a) FSQ

Tan22 86

5

'3426/57.26

b) FSQ

Tan4

12

'3471/57.71

P1

K2

N1

P1

K2

N1

4

4

3 1227

27

722

21

627

27

722

31

21

5.269/21269

627

27

722

31

2112

27

27

722

21

K1

K1

K1

N1 4

L

KM

L

KM

• No Marking Scheme Marks

4

1,61

01160156 2

x

xxxx K1

K1

N1,N1 4

5

31,2

01320253 2

p

pppp K1

K1

N1,N1 4

6

2,36020

48183

mnn

nm K1K1

N1, N1 4

7

8,35117

24163

khh

hk K1K1

N1, N1 4

8 a) 77

2223606021

7222

36045

0

0

0

0

OR

83.65/6565

777

222360601421

7222

3604521

0

0

0

0

b) 22 77

223606021

722

36045

OR

42.174@125174

77217

722

3606021

722

36045 22

0

0

K1

K1

N1

K1

K1

N1 6

• No Marking Scheme Marks

9 a) Implication 1 : If m 6, then m 6 0Implication 2 : If m 6 0, then m 6

b) If x is a factor of 10, then x is a factor of 5False

c) ,2 2 nn .......,4,3,2,1n

P1P1

P1P1

P1P1 6

10 a) 304012

ORPQ mm

15315336

xycORc

b) 15y

K1

K1N1

N1 4

11 a)21

3303

PQm

621

6)0(216

21

xy

cORc

mm RSPQ

K1, N1

K1

K1

N1 5

• Section B[48 marks]

No Marking Scheme Marks

12 a)i

ii.

b)i.34

m

834

)9(344

xy

c

ii. 8340 x

6x

c) VWU

Tan125

P1

P2

K1

K1

N1

K1

N1

P1

K2

P Q

R

PQ

R

'3722/62.22 N1 12

• No Marking Scheme Marks

13 a) i) a) Non-statementb) Statement

ii) andiii) all factors of 15 are factors of 30iv) a )

(b) i) 147222

36060

0

0

OR 77222

36030

0

0

147222

36060

0

0

+ 77222

36030

0

0

+14+7+7

3146 OR 46.34

ii) 1414722

36060

0

0

OR 77722

360300

1414722

36060

0

0

+ 77722

360300

= 89.83 2cm or6589

P1P1

P1P1P1P1

K1

K1

N1

K1

K1

N112

14

5,1051

056)( 2

mmmmma

2362206)(

edd

edb

cm

cmw

wc

6292298

292727

222187

87)(

22

K1N1N1,N1

K1K1N1N1

K1

K1, K1

N112

• No Marking Scheme Marks

15 (a)

Age(years) Midpoint Frequency

11 - 15 13 6

16 20 18 8

21 25 23 10

26 30 28 13

31 35 33 7

36 40 38 6

All values in Column 1 correctAll values in Column 2 correctAll values in Column 3 correct

(b)

5.2550

127550

)6(38)7(33)13(28)10(23)8(18)6(13

(c) Refer to the graph

Axes drawn in the correct direction , uniform scale for 438 xand 130 y .Horizontal axis labeled using midpoint / upper boundary / classinterval6 points plotted correctly(8,0) and (43,0).Straight line passing 8 point.

P1P1P2

K2

N1

K1

P1P1P1P1

12

• No Marking Scheme Marks

16 Marks Frequency Cumulativefrequency

Upperboundary

I55 60

II0

III0

IV60.5

61 65 1 1 65.566 70 3 4 70.571 75 6 10 75.576 80 10 20 80.581 85 11 31 85.586 90 7 38 90.591 - 95 2 40 95.5

All values in Column ( I ) correctAll values in Column ( II ) correct excluding Row I correct.All values in Column ( III ) correctAll values in Column ( IV ) correct

(b) x-axis and y-axis are drawn with the right direction and inuniform scale from 60.5 5.95 x , 110 y

All eight points* plotted correctly.Note : Seven or six points* plotted correctly. 1 P1(60.5, 0) plotted or passed throughAll the right eight points plotted correctly and ogive is drawnsmoothly passing through all the points.

(c) 85 0.5

P1P2P2P1

K1

K2

K1N1

N112

• 8 13 18 23 28 330

2

4

6

8

10

12

14

Graph is not drawn to scale.

38

43

Frequency

Mid-point

Graph for Question 15.

• 655605 705 755 805 855 905

0

5

10

15

20

25

30

35

40

Graph is not drawn to scale.

Graph for Question 16.

95.5

CumulativeFrequency

UpperBoundary

• SULIT 1449/11449/1MatematikKertas1PeraturanPemarkahanOktober2008

SEKTOR SEKOLAH BERASRAMA PENUHBAHAGIAN SEKOLAH

KEMENTERIAN PELAJARANMALAYSIA

PERATURAN PEMARKAHANPEPERIKSAAN AKHIR TAHUN TAHUN 2008

TINGKATAN 4

MATEMATIK

KERTAS 1 & 2

1449/1/2

1 D 21 C

2 C 22 B

3 C 23 D

4 D 24 A

5 A 25 B

6 A 26 B

7 C 27 A

8 D 28 D

9 C 29 D

10 C 30 D

11 A 31 B

12 C 32 B

13 A 33 D

14 B 34 C

15 B 35 D

16 C 36 A

17 B 37 B

18 A 38 A

19 A 39 A

20 B 40 C

• 1449/2 Form Four1

NAMA : ___________________________________

TINGKATAN : _____________________________

BAHAGIAN PENGURUSANSEKOLAH BERASRAMA PENUH / KLUSTER

BAHAGIAN SEKOLAHKEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/2TINGKATAN EMPATMATHEMATICSKertas 2Oktober2 jam Dua jam tiga puluh minit

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian Soalan MarkahPenuhMarkah

Diperoleh

A

1 3

2 8

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

1. Kertas soalan ini mengandungi dua bahagian :Bahagian A dan Bahagian B. Jawab semuasoalan daripada Bahagian A dan empat soalandalam Bahagian B.

2. Jawapan hendaklah ditulis dengan jelas dalamruang yang disediakan dalam kertas soalan.Tunjukkan langkah-langkah penting. Ini bolehmembantu anda untuk mendapatkan markah.

3. Rajah yang mengiringi soalan tidak dilukismengikut skala kecuali dinyatakan.

4. Satu senarai rumus disediakan di halaman2 & 3.

5. Anda dibenarkan menggunakan kalkulatorsaintifik yang tidak boleh diprogram.

3 44 4

5 4

6 4

7 4

8 6

9 6

10 4

11 5

B

12 12

13 12

14 12

15 12

16 12

Jumlah[Turn over1449/2Maths / F4 / P2 /2008

Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak

1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelahSULIT

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

2

MATHEMATICAL FORMULAE

The following formulae may be helpful in answering the questions. The symbols given are theones commonly used.

RELATIONS

1 am an = am + n 12 Pythagoras Theoremc2 = a2 + b2

2 am an = am n 13

12

12

xxyym

3 (am )n = am n 14interceptintercept

xym

4

acbd

5)()()(

SnAnAP

6 )(1)'( APAP

7 Distance = 2122

12 )()( yyxx

8Midpoint,

2,

2),( 2121 yyxxyx

9takentimetravelleddistancespeedAverage

10dataofnumber

dataofsumMean

11sfrequencieofsum

frequency)marks(classofsumMean

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

3

SHAPES AND SPACE

1heightsidesparallelofsum

21trapeziumofArea

2 Circumference of circle = d = 2 r

3 Area of circle = r 2

4 Curved surface area of cylinder = 2 r h

5 Surface area of sphere = 4 r 2

6 Volume of right prism = cross sectional area length

7 Volume of cylinder = r 2 h

8Volume of cone hr 2

31

9Volume of sphere 3

34 r

10Volume of right pyramid heightareabase

31

11 Sum of interior angles of polygon = (n 2)180

12o360

centreatsubtendedanglecircleofncecircumfere

lengtharc

13o360

centreatsubtendedanglecircleofareasectorofarea

14PAPA'k ,factorScale

15 Area of image = k2 area of object

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

4

For

Examiners

Use

Section A

[52 marks]

Answer all questions in this section.

1 The Venn diagram in the answer space shows sets K, L and M such that the

universal set, = K L M.

(a) L M ,

(b) ( K M ) L.

[3 marks]

(a)

(b)

L

KM

L

KM

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

5

2(a) Diagram 1 shows a right prism. The base GMND is a horizontal rectangle.

Right angled triangle MFG is the uniform cross-section of the prism.

S is the midpoint of ND.

DIAGRAM 1

Identify and calculate the angle between the line FS and the base GMND.

[4 marks]

For

Examiners

Use

E

G

D

M

S

F

N

5 cm

16 cm6 cm

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

6

For

Examiners

Use 2(b) Diagram 2 shows a right prism with a horizontal rectangular base JKLM .

The isosceles triangle KLH is the uniform cross-section of the prism.

N is the midpoint of KL.

DIAGRAM 2

Identify and calculate the angle between the plane KLG and the plane KLH.

[4 marks]

J

K L

H

G

N

M

6 cm

5 cm

12 cm

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

7

3 Diagram 3 shows a solid, formed by joining a half cylinder to a half cone.

The height of the cone is 6 cm.

By using722

, calculate the volume, in cm3 , of the combined solid.

[4 marks]

For

Examiners

Use

7 cm

12 cm

DIAGRAM 3

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

8

For

Examiners

Use

4 Using factorisation, solve the quadratic equation 3x (2x 1) + 8x = 1.

[4 marks]

5 Using factorisation, solve the quadratic equation pp 5

23 2 .

[4 marks]

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

9

6 Calculate the value of m and of n that satisfy the following simultaneous

linear equations:

1223166

nmnm

[4 marks]

For

Examiners

Use

7 Calculate the value of h and of k that satisfy the following simultaneous

linear equations:

273

6443

hk

hk

[4 marks]

• 1449/2 Form Four

1449/2Maths / F4 / P2 /2008

10

For

Examiners

Use 8 Diagram 4 shows two sectors OPQ and ORS, both with centre O.

It is given that POQ = 60.

By using =722 , calculate

(a) the perimeter, in cm, of the whole diagram,

(b) the area, in cm2, of the shaded region.

[ 6 marks ]

(a)

(b)

T

Q 14 cm

7 cm

R

S

O

PDIAGRAM 4Form Four

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

11

9(a) Write down two implications based on the following statement:

m > 6 if and only if m 6 > 0

(b) State the converse of the following statement and hence determine whether the

converse is true or false.

If x is a factor of 5, then x is a factor of 10.

(c) Make a general conclusion by induction for the sequence of numbers

1 , 6 , 15 , 28, . . . which follows the following pattern.

1 = 2 ( 1 )2 1

6 = 2 ( 2 )2 2

15 = 2 ( 3 )2 3

28 = 2 ( 4 )2 4

=

[6 marks]

(a) Implication 1:

Implication 2:

(b)

...

(c) ...

For

Examiners

Use

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

12

For

Examiners

Use 10 In Diagram 5 , OPQR is a parallelogram and O is the origin.

Find

(a) the equation of the straight line PQ,

(b) y intercept of the straight line PQ.

[4 marks]

(a)

(b)

x

R ( 4 ,12)

DIAGRAM 5

y

P ( 3 , 6 )

O

Q

• 1449/2 Form Four

1449/2Maths / F4 / P2 /2008

13

11 In Diagram 6 , O is the origin. KL, PQ and RS are straight lines.

PQ is parallel to RS.

The equation of the straight line KL is 62 xy .

Find

(a) the gradient of the straight line PQ,

(b) the equation of the straight line RS.

[5 marks]

(a)

(b)

For

Examiners

Use

xO

KR

S

L

DIAGRAM 6

y

P

Q (3, 3)

3[Turn over

• 1449/2 Form Four

1449/Maths

14

For

Examiners

Use

Section B

[48 marks]

Answer any four questions from this section.

12(a) The Venn diagram in the answer space shows the universal set , sets P, Q

and R. On the diagram in the answer space, shade the region for

(i) P Q ,

(ii) ( P Q ) R.

[3 marks]

(i)

(ii)

P

Q

PQ

R

2/ F4 / P2 /Form Four2008

R

• 1449/2 Form Four

1449/2Maths / F4 / P2 /2008

15

12(b) In Diagram 7 , O is the origin. Straight line NR is parallel to straight line OQ .

Find

(i) the equation of the straight line RN,

(ii) the x intercept of the straight line RN .

[5 marks]

(i)

(ii)

For

Examiners

Uses

y

x

R

N ( 4,9 )

Q (3, 4)

O

DIAGRAM 7[Turn over

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

16

For

Examiners

Use

12(c) Diagram 8 shows a right prism. The base PQRS is a horizontal rectangle.

Trapezium PQGF is the uniform cross-section of the prism.

U, V, and W are midpoints of PS, FE and QR respectively.

DIAGRAM 8

Identify and calculate the angle between the plane QRV and the base PQRS.

[4 marks]

E

P

G

H

Q

R

F

V

US

W8 cm12 cm

5 cm

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

17

13(a) (i) State whether the following sentences is a statement or

non-statement.

(a) 2x + 5y 6

(b) 4 is a prime number.

(ii) Combine the two statements below to form a false statement.

Statement 1 : 3 13 = 39

Statement 2 : 39 is a prime number.

(iii) Write down Premise 1 to complete the following argument:

Premise 1 :

Premise 2 : 3 is a factor of 15

Conclusion : 3 is a factor of 30

(iv) Fill in the blanks with < or > to form

(a) a true statement,

6 3

(b) a false statement.

8 24

[6 marks]

(i)(a) _________________________________

(b) _________________________________

(ii) ______________________________________________________

(iii) Premise 1 :______________________________________________

(iv) (a) 6 3

(b) 8 24

For

Examiners

Uses

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

18

For

Examiners

Use

13(b) In Diagram 9, ORST is a quadrant and KL is an arc of another circle both

with centre O. ORK and OSL are straight lines.

DIAGRAM 9

OR = RK = 7 cm.

Using722

, calculate

(i) the perimeter, in cm, of the whole diagram,

(ii) the area, in cm 2 , of the shaded region.

. [6 marks]

(i)

(ii)

60

R

S

T

L

K

O

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

19

14(a) Using factorisation, solve the quadratic equation mm 6

52 .

[4 marks]

14(b) Calculate the value of d and of e that satisfy the following simultaneous linear

equations:

144

10213

ed

ed

[4 marks]

For

Examiners

Uses

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

20

For

Examiners

Use

14(c) Diagram 10 shows a solid cuboid. A semi cylinder is taken out of the solid.

The volume of the remaining solid is 292 cm 3 .

Calculate the width, in cm, of the remaining solid.

(Use =722 )

[4 marks]

2 cm

2 cm

8 cm

7 cm

DIAGRAM 10

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

21

15. The data in Diagram 11 shows the ages of 50 runners who took part in a charity run

event.

14 36 12 16 27 31 27 28 30 28

16 18 23 18 24 32 23 14 18 31

22 30 23 20 25 30 31 22 20 37

12 26 36 23 28 30 34 38 33 36

11 23 27 27 34 38 25 12 17 29

DIAGRAM 11

(a) Based on the data in Diagram 11 and by using a class interval of 5, complete

Table 1 in the answer space.

[4marks]

(b) Based on Table 1 in (a),

calculate the estimated mean of the age of the runners.

[3marks]

(c) For this part of the question, use the graph paper provided on page 23.

By using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 1

runner on the vertical axis, draw a frequency polygon for the data.

[5marks]

For

Examiners

Use

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

22

For

Examiners

Use

(a)

Age (years) Midpoint Frequency

11 15

TABLE 1

(b) i)

ii)

(c) Refer graph on page 23.

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

23

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

24

For

Examiners

Use

16. The data in Diagram 12 shows the marks obtained by 40 pupils in a quiz.

67 76 91 79 81 82 87 71

79 82 88 83 72 84 71 89

80 86 70 86 62 83 83 80

75 84 84 77 84 86 85 76

80 75 95 77 73 86 77 68

DIAGRAM 12

(a) Using the data in Diagram 12, and a class interval of 5, complete Table 2 in

[6 marks]

(b) For this part of the question, use the graph paper provided on page 26.

By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the

y-axis, draw an ogive based on the data.

[5 marks]

(c) From your ogive in (b), find the third quartile.

[1 mark]

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

25

a)

Marks Frequency Cumulative Frequency Upper Boundary

61 65

TABLE 2

b) Refer graph on page 26

c)

For

Examiners

Use

• 1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

26

• 1449/2 Form Four

[Turn over1449/2Maths / F4 / P2 /2008

27

INFORMATION FOR CANDIDATES

1. This question paper consists of two sections: Section A and Section B.

2. Answer all questions in Section A and four questions from Section B.

3. Write your answers in the spaces provided in the question paper.

6. The diagrams in the questions provided are not drawn to scale unless stated.

7. The marks allocated for each question and sub-part of a question are shown inbrackets.

8. A list of formulae is provided on page 2 to 3.

9. A booklet of four-figure mathematical tables is provided.

10. You may use a non-programmable scientific calculator.

11. Hand in this question paper to the invigilator at the end of the examination.

• Mathematics Form 4 Final year 2008Section A

[ 52 marks ]

No Marking Scheme Marks

1a)

b)

P1

P2 3

2 a) FSQ

Tan22 86

5

'3426/57.26

b) FSQ

Tan4

12

'3471/57.71

P1

K2

N1

P1

K2

N1

4

4

3 1227

27

722

21

627

27

722

31

21

5.269/21269

627

27

722

31

2112

27

27

722

21

K1

K1

K1

N1 4

L

KM

L

KM

• No Marking Scheme Marks

4

1,61

01160156 2

x

xxxx K1

K1

N1,N1 4

5

31,2

01320253 2

p

pppp K1

K1

N1,N1 4

6

2,36020

48183

mnn

nm K1K1

N1, N1 4

7

8,35117

24163

khh

hk K1K1

N1, N1 4

8 a) 77

2223606021

7222

36045

0

0

0

0

OR

83.65/6565

777

222360601421

7222

3604521

0

0

0

0

b) 22 77

223606021

722

36045

OR

42.174@125174

77217

722

3606021

722

36045 22

0

0

K1

K1

N1

K1

K1

N1 6

• No Marking Scheme Marks

9 a) Implication 1 : If m 6, then m 6 0Implication 2 : If m 6 0, then m 6

b) If x is a factor of 10, then x is a factor of 5False

c) ,2 2 nn .......,4,3,2,1n

P1P1

P1P1

P1P1 6

10 a) 304012

ORPQ mm

15315336

xycORc

b) 15y

K1

K1N1

N1 4

11 a)21

3303

PQm

621

6)0(216

21

xy

cORc

mm RSPQ

K1, N1

K1

K1

N1 5

• Section B[48 marks]

No Marking Scheme Marks

12 a)i

ii.

b)i.34

m

834

)9(344

xy

c

ii. 8340 x

6x

c) VWU

Tan125

P1

P2

K1

K1

N1

K1

N1

P1

K2

P Q

R

PQ

R

'3722/62.22 N1 12

• No Marking Scheme Marks

13 a) i) a) Non-statementb) Statement

ii) andiii) all factors of 15 are factors of 30iv) a )

(b) i) 147222

36060

0

0

OR 77222

36030

0

0

147222

36060

0

0

+ 77222

36030

0

0

+14+7+7

3146 OR 46.34

ii) 1414722

36060

0

0

OR 77722

360300

1414722

36060

0

0

+ 77722

360300

= 89.83 2cm or6589

P1P1

P1P1P1P1

K1

K1

N1

K1

K1

N112

14

5,1051

056)( 2

mmmmma

2362206)(

edd

edb

cm

cmw

wc

6292298

292727

222187

87)(

22

K1N1N1,N1

K1K1N1N1

K1

K1, K1

N112

• No Marking Scheme Marks

15 (a)

Age(years) Midpoint Frequency

11 - 15 13 6

16 20 18 8

21 25 23 10

26 30 28 13

31 35 33 7

36 40 38 6

All values in Column 1 correctAll values in Column 2 correctAll values in Column 3 correct

(b)

5.2550

127550

)6(38)7(33)13(28)10(23)8(18)6(13

(c) Refer to the graph

Axes drawn in the correct direction , uniform scale for 438 xand 130 y .Horizontal axis labeled using midpoint / upper boundary / classinterval6 points plotted correctly(8,0) and (43,0).Straight line passing 8 point.

P1P1P2

K2

N1

K1

P1P1P1P1

12

• No Marking Scheme Marks

16 Marks Frequency Cumulativefrequency

Upperboundary

I55 60

II0

III0

IV60.5

61 65 1 1 65.566 70 3 4 70.571 75 6 10 75.576 80 10 20 80.581 85 11 31 85.586 90 7 38 90.591 - 95 2 40 95.5

All values in Column ( I ) correctAll values in Column ( II ) correct excluding Row I correct.All values in Column ( III ) correctAll values in Column ( IV ) correct

(b) x-axis and y-axis are drawn with the right direction and inuniform scale from 60.5 5.95 x , 110 y

All eight points* plotted correctly.Note : Seven or six points* plotted correctly. 1 P1(60.5, 0) plotted or passed throughAll the right eight points plotted correctly and ogive is drawnsmoothly passing through all the points.

(c) 85 0.5

P1P2P2P1

K1

K2

K1N1

N112

• 8 13 18 23 28 330

2

4

6

8

10

12

14

Graph is not drawn to scale.

38

43

Frequency

Mid-point

Graph for Question 15.

• 655605 705 755 805 855 905

0

5

10

15

20

25

30

35

40

Graph is not drawn to scale.

Graph for Question 16.

95.5

CumulativeFrequency

UpperBoundary