peperiksaan akhir tahun selaras sbp 2008 1449/1 · pdf filepeperiksaan akhir tahun selaras sbp...

SULIT

BAHAGIAN PENGURUSANSEKOLAH BERASRAMA PENUH / KLUSTER

KEMENTERIAN PELAJARAN MALAYSIA

MOZ@C

1449/1 2008 Hak Cipta Sektor SBP [Lihat sebelahSULIT

1

PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/1TINGKATAN EMPATMATHEMATICSKertas 1Oktober

1¼ jam Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini adalah dalam Bahasa Inggeris.

2. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini.

Kertas soalan ini mengandungi 20 halaman bercetak.

SMS MUZAFFAR SYAH , MELAKA

SULIT


2

MATHEMATICAL FORMULAE

The following formulae may be helpful in answering the questions. The symbols given arethe ones commonly used.

RELATIONS

1 am x an = a m+ n

2 am an = a m – n

3 ( am )n = a mn

4 A-1 =bcad

1

ac

bd

5 Distance = 2 22 1 2 1( ) ( )x x y y

6 Midpoint, ( x, y ) =

2,

22121 yyxx

7 Average speed =

8 Mean =

9 Mean =

10 Pythagoras Theorem

c2 = a2 + b2

11 P ( A ) =)(

)(

Sn

An

12 P ( A ) = 1 P(A)

13 m =12

12

xx

yy

14 m =

sum of datanumber of data

sum of (class mark × frequency)sum of frequencies

y-interceptx-intercept

distance travelledtime taken

MOZ@C


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3

SHAPES AND SPACE

1 Area of trapezium =2

1× sum of parallel sides × height

2 Circumference of circle = d = 2r

3 Area of circle = r2

4 Curved surface area of cylinder = 2rh

5 Surface area of sphere = 4r2

6 Volume of right prism = cross sectional area × length

7 Volume of cylinder = r2h

8 Volume of cone =3

1r2h

9 Volume of sphere =3

4r3

10 Volume of right pyramid =3

1× base area × height

11 Sum of interior angles of a polygon = ( n – 2) × 180˚

12360

centreatsubtendedangle

circleofncecircumfere

lengtharc

13360


circleofarea

sectorofarea

14 Scale factor , k =PA

PA'

15 Area of image = k 2 × area of object

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20

INFORMATION FOR CANDIDATES

1. This question paper consists of 40 questions.

2. Answer all questions.

3. Each question is followed by four alternative answers, A, B, C or D. For eachquestion, choose one answer only. Blacken your answer on the objective answersheet provided.

4. If you wish to change your answer, erase the blackened mark that you have done.Then blacken the space for the new answer.

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

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

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

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4

1. Round off 37 285 correct to three significant figures.

A 37 000

B 37 200

C 37 290

D 37 300

2. Express 2·937 × 105 as a single number.

A 2 937

B 29 370

C 293 700

D 2 937 000

3.144

0160

=

A 2·857 210

B 5·6 310

C 2·857 410

D 5·6 210

4 1·3× 610 52 710 =

A 1·2 710

B 1·2 × 610

C 1·05 710

D 1·05 × 610

5. A rectangular floor has a width of 2700 cm and a length of 3200 cm. The floor

will be covered with tiles. Each tile is a square of side 24 cm. Calculate the number

of tiles required to cover the floor fully.

A 1·5 × 104

B 3·6 × 104

C 1·5 × 105

D 3·6 × 105

Answer all questions.

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5

6. )3()2(5 yxyx

A yx 92

B yx 112

C yx 8

D yx 38

7. xxx 314322

A 988 2 xx

B 9816 2 xx

C 9816 2 xx

D 9128 2 xx

8. List all the subsets of set H = { p, q}.

A {p}, {q}

B {p}, {q}, { }

C {p}, {q},{p, q}

D {p}, {q}, {p, q},{ }

9. Given the universal set, ξ = TN , set N = {a, b, c} and set T = {b, c, d, e, f},

find the value of n(ξ).

A 2

B 4

C 6

D 8

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1449/1 2008 Hak Cipta Se

10. Diagram 1 is a Venn diagram showing the universal set, ξ = {Form Four students},

set G = {Students who play badminton} and set H ={Students who play tennis}.

Given n(ξ) = 50,

who do not play t

A 44

B 30

C 24

D 18

11. Diagram 2 shows

The distance of O

Find the gradient

A2

1

B4

3

C 1

D 2

MOZ@C

S
ktor SBP
n(G) = 2

he two g

a straig

Q is 2 u

of PQ.

ξ

MS MU
6
3, n(H) = 9 and n

ames.

ht line PQ on a Car

nits.

O

y

Q

G

DIAGRAM 1

DIAGRAM

ZAFFAR SYAH ,
[Lihat sebelah
SULIT

6 HG , find the number of students

tesian plane.

x

(8, 6)P

H

2

MELAKA

SULIT


7

12. In Diagram 3, MN is a straight line on a Cartesian plane.

Find the gradient of MN.

A 2

B4

3

C4

3

D 2

13. Find the x-intercept of the straight line xy 23 = 12.

A 6

B6

1

C 4

D4

1

14. Diagram 4 shows the score obtained by a group of five pupils in a quiz where x is an

integer. The mode score is 6.

2 x x 4 9

Then another three pupils with scores of 3, 3 and 8 joins the group.

Find the median score of the group.

A 3·5

B 5

C 5125

D 6

N

M

8

6

0

y

x

DIAGRAM 3

DIAGRAM 4

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1449/1 2008 Hak Cipta Sektor SBP 8

15. Diagram 5 is a bar chart showing the number of Mathematics textbooks sold in four

months. The number of textbooks sold in March and May are not shown.

DIAGRAM 5

The total number of books sold in four months is 140. The

March to books sold in May is 3 : 2. Find the number of bo

A 14

B 16

C 24

D 40

16. Diagram 6 is a pie chart which shows the combined results

by two groups of pupils. Table 1 shows the results obtained

is incomplete.

Calculate the number of pupils in the Yellow Group.

A 140

B 146

C 160

D 194

Num

ber

of

textb

ook

10

20

30

40

50

60

Feb Mar Apr May

TABL

156

Qualify

Do notqualify

DIAGRAM 6

Total 130

MOZ@C


ratio of books sold in

oks sold in May.

of a time trial race taken

by the two groups but it

Month

GroupNumber of pupils

Qualify Do not qualify

Yellow

Blue 60 80

[Lihat sebelahSULIT

E 1

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9

17 A number is chosen at random from set P = {x: x is an integer , 2 x 12}.

Find the probability that the number chosen is a prime factor of 15.

A10

1

B5

1

C10

3

D5

2

18. Table 2 shows the types of food bought by 60 students at the canteen.

If a student is chosen at random from the group, the probability of the student

buying fried noodles is1

4. Calculate the value of q.

A 11

B 13

C 15

D 26

19. A container holds 28 red marbles and a number of blue marbles. A marble is picked

at random from the container. The probability of picking a red marble is8

7.

How many blue marbles are there in the container?

A 4

B 8

C 21

D 24

Type of food Number of students

Fried noodles m

Nasi lemak 24

Bread q

Roti canai 10

TABLE 2

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1449/1 2008 Hak Cipta Sektor SBP

20. A student puts 20 cards with serial number 21 to 40 in a box. A card is drawn at

random. Find the probability of drawing a card with a serial number which is a

multiple of 5.

A4

1

B5

1

C10

1

D20

1

21. In Diagram 7, EFG is a tangent to the circle FJH at F.

Find the value of x.

A 64

B 58

C 52

D 26

J

64°

x°

GF

H

E

MOZ@C

SMS MUZAF
[Lihat sebelah
SULIT10

DIAGRAM 7

FAR SYAH , MELAKA

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11

22. In Diagram 8, KLM is a tangent to the circle centre O, at L. KJPO and NPL are

straight lines.

Find the value of y.

A 28

B 34

C 56

D 62

23. In Diagram 9, FGH is a tangent to the circle centre O, at G.

Find the value of z.

A 77

B 55

C 45

D 35

F G H

PQ

O

13°

68° z°

M

N

O

28°

y°J

L

K

P

DIAGRAM 8

DIAGRAM 9

O

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12

24. In Diagram 10, PQRS is a rectangle and PM = NR = 3 cm.

Find the value of tan .

A12

5

B12

5

C13

5

D13

5

25. It is given that sin x =25

24and 90° ≤ x ≤ 180°.

Find cos x.

A25

7

B25

7

C7

24

D7

24

P

S

M

N R

Q

13 cm

M15 cm

DIAGRAM 10

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1449/1 200

26. Diagram 11 shows the graph of y = sin x .

Find t

A

B

C

D

27 In Diag

Calcu

A 2

B 4

C 4

D 6

1

(m, 50 )

O

y

x

MOZ@C

8 H

he

1

2

2

3

ra

lat

6

1

8

3

ak Cipta Sektor SBP [Lihat sebelahSULIT

13

value of m.

90°

10°

40°

00°

m 12, PQ and RS are two vertical poles on a horizontal plane.

e the angle of depression of vertex R from vertex P.

34

59

01

26

1

DIAGRAM 11

P

Q

R

S

20 m

45 m

50 m

DIAGRAM 12


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14

29. Diagram 14 shows a cuboid with a horizontal base PQRS.

Name the angle between the line NM and the plane PQM.

A NQP

B NQM

C NMP

D NMQ

28 Diagram 13 shows a steel frame LKPMN placed on a horizontal plane.

KL and PMN are vertical while KM is horizontal.

The angle of elevation of point M from point L is 68.

Calculate the height, in m, of PN .

A 9

B 11

C 13·42

D 25·8

P S

Q

M

K

R

N

L

DIAGRAM 14

P

N

M

L

K

8 m

10 m

DIAGRAM 13

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1449/1 2008 Hak Cip

30. Diagram 15 shows a pyramid with rectangular base TUVW.

Vertex S is vertically above W. Name the angle between the plane STU and the

base TUVW.

A USW

B TSW

C SUW

D STW

31 Diagram 16 shows a regular pentagon PQRST. PRU and VWU are straight lines.

PRU is parallel to TS.

Calculate the

A 69

B 87

C 94

D 112

S

TW

VU

DIAGRAM 15

Q

MOZ@C

ta Sektor SBP [Lihat sebelahSULIT

15

DIAGRAM 16

value of x + y .

PR

ST V

U

xy

2257

W

»

»


SULIT

1449/1 2008 Hak Cipta Sektor SBP 16

32 In Diagram 17, JKLM is a parallelogram. VW is parallel to JK.

DIAGRAM 17

Calculate the value of p + q .

A 175

B 140

C 135

D 100

33 Diagram 18 shows five pentagons drawn on square grids.

DIAGRAM 18

Which of the pentagons A, B, C or D, is an image of pentag

K

A

B

C

D

J K

LM

VW

150

q

p

80

»

»

»

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70

[Lihat sebelahSULIT

on K under a rotation?

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17

34 Diagram 19 shows two quadrilaterals, L and M, drawn on square grids.

DIAGRAM 19

M is the image of L under an enlargement.

Which of the point, A, B, C, or D, is the centre of the enlargement?

35. Choose a suitable linear equation in one unknown for the following statement.

A 3(x + 7 ) = 34

B 3 + x + 7 = 34

C 3 + 7x = 34

D 3x + 7 = 34

36. Given thatqr

rp

4 , express q in terms of p and r.

A

2

4

1

r

p

rq

B 24

1prrq

C

r

p

rq

2

1

D prrq 2

1

A

B

C D

M

L

When a number is multiplied by 3 and increased by 7, the result is 34.

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1449/1 2008 Hak Cip

37.

2

2

5

32

1

25

57

=

A7

1

B7

5

C 7

D 35

38. Simplify3

82

32)(

n

nm .

A nm3

B 53nm

C nm 4

3

D54

3

nm

39 Solve the inequalities 8 – 3x x + 16 and 5 – 2x > x – 10.

A

B

C

D

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2

2

2

5

6

6

ta Sektor SBP [Lihat sebelahSULIT

18

2 5


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19

40. Given that x is an integer, find all the values of x that satisfy both of the

inequalities2

4x

≤ 5 and x32 > 3 .

A 1,0,1

B 2,1,0,1

C 1,0,1,2

D 2,1,0,1,2

END OF QUESTION PAPER

MOZ@C


QUESTION ANSWER QUESTION ANSWER

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

MOZ@C


1449/2 Form Four1

NAMA : ___________________________________

TINGKATAN : _____________________________

MOZ@C

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


BAHAGIAN SEKOLAHKEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/2TINGKATAN EMPATMATHEMATICSKertas 2Oktober2½ jam Dua jam tiga puluh minit

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian SoalanMarkahPenuh

MarkahDiperoleh

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 halaman

2 & 3.

5. Anda dibenarkan menggunakan kalkulatorsaintifik yang tidak boleh diprogram.

3 4

4 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

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



1449/2 Form Four

1449/2 Form FourMaths / F4 / P2 /2008

2


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

xx

yym

3 (am )n = am n 14

intercept

intercept

x

ym

4

ac

bd

bcadA

11

5

)(

)()(

Sn

AnAP

6 )(1)'( APAP

7 Distance = 212

212 )()( yyxx

8Midpoint,

2,

2),( 2121 yyxx

yx

9

takentime

travelleddistancespeedAverage

10

dataofnumber

dataofsumMean

11

sfrequencieofsum

frequency)marks(classofsumMean

MOZ@C


1449/2 Form Four


3

SHAPES AND SPACE

1heightsidesparallelofsum

2

1trapeziumofArea

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

3

1

9Volume of sphere 3

3

4r

10Volume of right pyramid heightareabase

3

1

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

12o360



lengtharc

13o360


circleofarea

sectorofarea

14

PA

PA'k ,factorScale

15 Area of image = k2 area of object

MOZ@C


1449/2 Form Four


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

KM

L

KM

MOZ@C


1449/2 Form Four


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]

Answer:

For

Examiner’s

Use

E

G

D

M

S

F

N

5 cm

16 cm6 cm

MOZ@C


1449/2 Form Four


6

For

Examiner’s

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]

Answer:

J

K L

H

G

N

M

6 cm

5 cm

12 cm

MOZ@C


1449/2 Form Four


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 using7

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

[4 marks]

Answer:

For

Examiner’s

Use

7 cm

12 cm

DIAGRAM 3

MOZ@C


1449/2 Form Four


8

For

Examiner’s

Use

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

[4 marks]

Answer:

5 Using factorisation, solve the quadratic equation pp

5

23 2

.

[4 marks]

Answer:

MOZ@C


1449/2 Form Four


9

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

linear equations:

1223

166

nm

nm

[4 marks]

Answer:

For

Examiner’s

Use

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

linear equations:

273

644

3

hk

hk

[4 marks]

Answer:

MOZ@C


1449/2 Form Four

1449/2Maths / F4 / P2 /2008

10

For

Examiner’s

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

It is given that POQ = 60.

By using =7

22, calculate

(a) the perimeter, in cm, of

(b) the area, in cm2, of the

Answer:

(a)

(b)

T

Q 14 cm

7 cm

R

S

O

P

MOZ@C

SMS MUZ
Form Four
the whole diagram,

shaded region.

[ 6 marks ]

DIAGRAM 4

AFFAR SYAH , MELAKA

1449/2 Form Four


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]

Answer:

(a) Implication 1:………………………………………………………

Implication 2:………………………………………………………

(b) ………………………………………………………………………

……………………………………………………………………...

(c) ………………………………………………………………………...

For

Examiner’s

Use

MOZ@C


1449/2 Form Four


12

For

Examiner’s

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]

Answer:

(a)

(b)

x

R ( 4 ,12)

DIAGRAM 5

y

P ( 3 , 6 )

O

Q

MOZ@C


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

(b) the equation of the straight

Answer:

(a)

(b)

For

Examiner’s

Use

x

K

R

S

DIA

y

P

Q (3,

MOZ@C

SMS MUZAF

O 3

line PQ,

line RS.

GRAM 6

3)

FAR SYA

[Turn over

[5 marks]

L

H , MELAKA

1449/2 Form Four

1449/Maths

14

For

Examiner’s

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]

Answer:

(i)

(ii)

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2/ F4 / P2 /

P

Q

R

Form Four2008

P

Q

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 lin

Answer:

(i)

(ii)

For

Examiner’s

Uses

y

R

N ( 4,9 )

O

DIAGRAM 7

MOZ@C

SMS MUZAFFAR

[Turn over

,

e RN .

[5 marks]

x

Q (3, 4)

SYAH , MELAKA

1449/2 Form Four


16

For

Examiner’s

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]

Answer:

E

P

G

H

Q

R

F

V

U

S

W8 cm12 cm

5 cm

MOZ@C


1449/2 Form Four


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]

Answer:

(i)(a) _________________________________

(b) _________________________________

(ii) ______________________________________________________

(iii) Premise 1 :______________________________________________

(iv) (a) 6 3

(b) 8 24

For

Examiner’s

Uses

MOZ@C


1449/2 Form Four


18

For

Examiner’s

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.

Using7

22 , calculate

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

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

. [6 marks]

Answer:

(i)

(ii)

60°

R

S

T

L

K

O

MOZ@C


1449/2 Form Four


19

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

6

52

.

[4 marks]

Answer:

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

equations:

144

102

13

ed

ed

[4 marks]

Answer:

For

Examiner’s

Uses

MOZ@C


1449/2 Form Four


20

For

Examiner’s

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 =7

22)

[4 marks]

Answer:

2 cm

2 cm

8 cm

7 cm

DIAGRAM 10

MOZ@C


1449/2 Form Four


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

Examiner’s

Use

MOZ@C


1449/2 Form Four


22

For

Examiner’s

Use

Answer:

(a)

Age (years) Midpoint Frequency

11 – 15

TABLE 1

(b) i)

ii)

(c) Refer graph on page 23.

MOZ@C


1449/2 Form Four


23MOZ@C


1449/2 Form Four


24

For

Examiner’s

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

the answer space.

[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]

MOZ@C


1449/2 Form Four


25

Answer:

a)

Marks Frequency Cumulative Frequency Upper Boundary

61 – 65

TABLE 2

b) Refer graph on page 26

c)

For

Examiner’s

Use

MOZ@C


1449/2 Form Four


26MOZ@C


1449/2 Form Four


27


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.

4. Show your working. It may help you to get marks.

5. If you wish to change your answer, cross out the answer that you have done. Thenwrite down the new answer.


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


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


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

MOZ@C


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

312

2

7

2

7

7

22

2

1

62

7

2

7

7

22

3

1

2

1

5.269/2

1269

62

7

2

7

7

22

3

1

2

112

2

7

2

7

7

22

2

1

K1

K1

K1

N1 4

L

K

M

L

KM

MOZ@C



4

1,6

1

0116

0156 2

x

xx

xx K1K1

N1,N1 4

5

3

1,2

0132

0253 2

p

pp

pp K1K1

N1,N1 4

6

2,3

6020

48183

mn

n

nm K1K1

N1, N1 4

7

8,3

5117

24163

kh

h

hk K1K1

N1, N1 4

8 a) 77

222

360

6021

7

222

360

450

0

0

0

OR

83.65/6

565

777

222

360

601421

7

222

360

4521

0

0

0

0

b) 22 77

22

360

6021

7

22

360

45

OR

42.174@12

5174

772

17

7

22

360

6021

7

22

360

45 22

0

0

K1

K1

N1

K1

K1

N1 6

MOZ@C



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

Implication 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) 304

012

ORPQ mm

153

15336

xy

cORc

b) 15y

K1

K1N1

N1 4

11 a)2

1

33

03

PQm

62

1

6)0(2

16

2

1

xy

cORc

mm RSPQ

K1, N1

K1

K1

N1 5

MOZ@C


Section B[48 marks]


12 a)i

ii.

b)i.

ii.

c)

MOZ@C

P1P Q

R

3

4m

83

4

)9(3

44

xy

c

83

40 x

6x

VWU

Tan12

5

'3722/62.22

P2

K1

K1

N1

K1

N1

P1

K2

N1 12

PQ

R



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

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

b) >

(b) i) 147

222

360

600

0

OR 77

222

360

300

0

147

222

360

600

0

+ 77

222

360

300

0

+14+7+7

3

146 OR 46.34

ii) 14147

22

360

600

0

OR 777

22

360

300

14147

22

360

600

0

+ 777

22

360

300

= 89.83 2cm or6

589

P1P1

P1P1P1P1

K1

K1

N1

K1

K1

N112

14

5,1

051

056)( 2

m

mm

mma

2

3

62

206)(

e

d

d

edb

cm

cmw

wc

6292298

292727

22

2

187

87)(

22

K1N1N1,N1

K1K1N1N1

K1

K1, K1

N112

MOZ@C



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)

5.25

50

1275

50

)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 x

and 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

MOZ@C



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

MOZ@C


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.

MOZ@C


655605 705 755 805 855 905

0

5

10

15

20

25

30

35

40



95.5

CumulativeFrequency

UpperBoundary

MOZ@C


SULIT 1449/11449/1MatematikKertas1PeraturanPemarkahanOktober2008

SEKTOR SB

KEMENTE

PERPEPERIKSA

EKOLAH BERASRAMA PENUHAHAGIAN SEKOLAHRIAN PELAJARAN MALAYSIA

ATURAN PEMARKAHANAN AKHIR TAHUN TAHUN 2008

TINGKATAN 4

MATEMATIK

KERTAS 1 & 2

1449/1/2

QUESTION ANSWER QUESTION ANSWER

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 SEKOLAHKEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/2TINGKATAN EMPATMATHEMATICSKertas 2Oktober2½ jam Dua jam tiga puluh minit

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian SoalanMarkahPenuh

MarkahDiperoleh

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 halaman

2 & 3.

5. Anda dibenarkan menggunakan kalkulatorsaintifik yang tidak boleh diprogram.

3 4

4 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

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


1449/2 Form Four


2


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

xx

yym

3 (am )n = am n 14

intercept

intercept

x

ym

4

ac

bd

bcadA

11

5

)(

)()(

Sn

AnAP

6 )(1)'( APAP

7 Distance = 212

212 )()( yyxx

8Midpoint,

2,

2),( 2121 yyxx

yx

9

takentime

travelleddistancespeedAverage

10

dataofnumber

dataofsumMean

11

sfrequencieofsum

frequency)marks(classofsumMean

1449/2 Form Four


3

SHAPES AND SPACE

1heightsidesparallelofsum

2

1trapeziumofArea

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

3

1

9Volume of sphere 3

3

4r

10Volume of right pyramid heightareabase

3

1

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

12o360



lengtharc

13o360


circleofarea

sectorofarea

14

PA

PA'k ,factorScale

15 Area of image = k2 area of object

1449/2 Form Four


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

KM

L

KM

1449/2 Form Four


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]

Answer:

For

Examiner’s

Use

E

G

D

M

S

F

N

5 cm

16 cm6 cm

1449/2 Form Four


6

For

Examiner’s

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]

Answer:

J

K L

H

G

N

M

6 cm

5 cm

12 cm

1449/2 Form Four


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 using7

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

[4 marks]

Answer:

For

Examiner’s

Use

7 cm

12 cm

DIAGRAM 3

1449/2 Form Four


8

For

Examiner’s

Use

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

[4 marks]

Answer:

5 Using factorisation, solve the quadratic equation pp

5

23 2

.

[4 marks]

Answer:

1449/2 Form Four


9

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

linear equations:

1223

166

nm

nm

[4 marks]

Answer:

For

Examiner’s

Use

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

linear equations:

273

644

3

hk

hk

[4 marks]

Answer:

1449/2 Form Four

1449/2Maths / F4 / P2 /2008

10

For

Examiner’s

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

It is given that POQ = 60.

By using =7

22, calculate

(a) the perimeter, in cm, of

(b) the area, in cm2, of the s

Answer:

(a)

(b)

T

Q 14 cm

7 cm

R

S

O

P

Form Four

the whole diagram,

haded region.

[ 6 marks ]

DIAGRAM 4

1449/2 Form Four


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]

Answer:

(a) Implication 1:………………………………………………………

Implication 2:………………………………………………………

(b) ………………………………………………………………………

……………………………………………………………………...

(c) ………………………………………………………………………...

For

Examiner’s

Use

1449/2 Form Four


12

For

Examiner’s

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]

Answer:

(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

(b) the equation of the straight

Answer:

(a)

(b)

For

Examiner’s

Use

x

K

R

S

DIA

y

P

Q (3,

O 3

line PQ,

line RS.

GRAM 6

3)

[Turn over

[5 marks]

L

1449/2 Form Four

1449/Maths

14

For

Examiner’s

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]

Answer:

(i)

(ii)

2/ F4 / P2 /

P

Q

R

Form Four2008

P

Q

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 lin

Answer:

(i)

(ii)

For

Examiner’s

Uses

y

R

N ( 4,9 )

O

DIAGRAM 7

[Turn over

,

e RN .

[5 marks]

x

Q (3, 4)

1449/2 Form Four


16

For

Examiner’s

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]

Answer:

E

P

G

H

Q

R

F

V

U

S

W8 cm12 cm

5 cm

1449/2 Form Four


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]

Answer:

(i)(a) _________________________________

(b) _________________________________

(ii) ______________________________________________________

(iii) Premise 1 :______________________________________________

(iv) (a) 6 3

(b) 8 24

For

Examiner’s

Uses

1449/2 Form Four


18

For

Examiner’s

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.

Using7

22 , calculate

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

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

. [6 marks]

Answer:

(i)

(ii)

60°

R

S

T

L

K

O

1449/2 Form Four


19

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

6

52

.

[4 marks]

Answer:

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

equations:

144

102

13

ed

ed

[4 marks]

Answer:

For

Examiner’s

Uses

1449/2 Form Four


20

For

Examiner’s

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 =7

22)

[4 marks]

Answer:

2 cm

2 cm

8 cm

7 cm

DIAGRAM 10

1449/2 Form Four


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

Examiner’s

Use

1449/2 Form Four


22

For

Examiner’s

Use

Answer:

(a)

Age (years) Midpoint Frequency

11 – 15

TABLE 1

(b) i)

ii)

(c) Refer graph on page 23.

1449/2 Form Four


23

1449/2 Form Four


24

For

Examiner’s

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

the answer space.

[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


25

Answer:

a)

Marks Frequency Cumulative Frequency Upper Boundary

61 – 65

TABLE 2

b) Refer graph on page 26

c)

For

Examiner’s

Use

1449/2 Form Four


26

1449/2 Form Four


27


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.

4. Show your working. It may help you to get marks.

5. If you wish to change your answer, cross out the answer that you have done. Thenwrite down the new answer.


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


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


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

Mathematics Form 4 Final year 2008Section A

[ 52 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

312

2

7

2

7

7

22

2

1

62

7

2

7

7

22

3

1

2

1

5.269/2

1269

62

7

2

7

7

22

3

1

2

112

2

7

2

7

7

22

2

1

K1

K1

K1

N1 4

L

K

M

L

KM


4

1,6

1

0116

0156 2

x

xx

xx K1K1

N1,N1 4

5

3

1,2

0132

0253 2

p

pp

pp K1K1

N1,N1 4

6

2,3

6020

48183

mn

n

nm K1K1

N1, N1 4

7

8,3

5117

24163

kh

h

hk K1K1

N1, N1 4

8 a) 77

222

360

6021

7

222

360

450

0

0

0

OR

83.65/6

565

777

222

360

601421

7

222

360

4521

0

0

0

0

b) 22 77

22

360

6021

7

22

360

45

OR

42.174@12

5174

772

17

7

22

360

6021

7

22

360

45 22

0

0

K1

K1

N1

K1

K1

N1 6


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

Implication 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) 304

012

ORPQ mm

153

15336

xy

cORc

b) 15y

K1

K1N1

N1 4

11 a)2

1

33

03

PQm

62

1

6)0(2

16

2

1

xy

cORc

mm RSPQ

K1, N1

K1

K1

N1 5

Section B[48 marks]


12 a)i

ii.

b)i.

ii.

c)

P1P Q

R

3

4m

83

4

)9(3

44

xy

c

83

40 x

6x

VWU

Tan12

5

'3722/62.22

P2

K1

K1

N1

K1

N1

P1

K2

N1 12

PQ

R


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

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

b) >

(b) i) 147

222

360

600

0

OR 77

222

360

300

0

147

222

360

600

0

+ 77

222

360

300

0

+14+7+7

3

146 OR 46.34

ii) 14147

22

360

600

0

OR 777

22

360

300

14147

22

360

600

0

+ 777

22

360

300

= 89.83 2cm or6

589

P1P1

P1P1P1P1

K1

K1

N1

K1

K1

N112

14

5,1

051

056)( 2

m

mm

mma

2

3

62

206)(

e

d

d

edb

cm

cmw

wc

6292298

292727

22

2

187

87)(

22

K1N1N1,N1

K1K1N1N1

K1

K1, K1

N112


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)

5.25

50

1275

50

)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 x

and 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


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


38

43

Frequency

Mid-point


655605 705 755 805 855 905

0

5

10

15

20

25

30

35

40



95.5

CumulativeFrequency

UpperBoundary

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