MRSM Maths P1 2007

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Nama : . Kelas :

SULIT 1449/2

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1449/2 2007Hak Cipta Bahagian Pendidikan & Latihan (Menengah) MARA SULIT

MAKTAB RENDAH SAINS MARA

PEPERIKSAAN PERCUBAAN

SIJIL PELAJARAN MALAYSIA 2007

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN

INI SEHINGGA DIBERITAHU

1. Tuliskan nama dan kelas anda padaruang yang disediakan.

2. Kertas soalan ini adalah dalamdwibahasa.

3. Soalan dalam bahasa Inggerismendahului soalan dalam bahasa

Malaysia

4. Calon dibenarkan menjawabkeseluruhan atau sebahagian soalan

sama ada dalam bahasa Malaysia atau

bahasa Inggeris

5. Calon dikehendaki membaca maklumatdi halaman 2 atau halaman 3

Kertas soalan ini mengandungi 49 halaman bercetak dan 3 halaman tidak bercetak

1449/2

Matematik

Kertas 2

September

2007

2 jam

Bahagian SoalanMarkah

Penuh

Markah

Diperoleh

1 3

2 4

3 34 5

5 5

6 4

7 6

8 5

9 4

10 6

A

11 6

12 12

13 12

14 1215 12

B

16 12

Jumlah

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INFORMATION FOR CANDIDATES

1. This question paper consists of two sections : Section AandSection B. Answerallquestions inSection Aandfourquestions inSection B.

2.

Write your answer clearly in the spaces provided in the question paper.

3. Show your working. It may help you to get marks.4. If you wish to change your answer, neatly cross out the answer that you have done.

Then write down the new answer.

5. The diagrams in the questions provided are not drawn to scale unless stated.6. The mark allocated for each question and sub-part of a question is shown in brackets.7.

A list of formulae is provided on pages 4 to 7.

8. A booklet of four-figure mathematical tables is provided.9. You may use a non-programmable scientific calculator.10.This question paper must be handed in at the end of the examination.

Maths Tutor Mr Muruli

www.tutormuruli.blogspot.com

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

ones commonly used.

RELATIONS

1. nmnm aaa += 2. nmnm aaa = 3. mnnm aa =)(4.

=

ac

bd

bcadA

11

5.)(

)()(

Sn

AnAP =

6. )(1)( APAP = 7. Distance = 212212 )()( yyxx 8. Midpoint,

++=

2,

2),( 2121

yyxxyx

9. Average speed =takentime

travelleddistance

10.Mean =dataofnumber

dataofsum

11.Mean =sfrequencieofsum

frequency)mark(classofSum

12.Pythagoras Theorem, c2 = a2 + b213.

12

12

xx

yym

=

14.erceptint

erceptint

=

x

ym



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BENTUK DAN RUANG

1. Luas trapezium =2

1 hasiltambah dua sisi selari tinggi

2. Lilitan bulatan = d = 2j3. Luas bulatan = j24. Luas permukaan melengkung silinder = 2jt5. Luas permukaan sfera = 4j26. Isipadu prisma tegak = luas keratan rentas panjang7. Isipadu silinder = j2t8. Isipadu kon =

3

1j

2t

9. Isipadu sfera =3

4j

3

10.Isipadu piramid tegak =3

1 luas tapak tinggi

11.Hasil tambah sudut pedalaman poligon = (n 2) 180o12.

o360

pusatsudut

bulatanlilitan

lengkokpanjang=

13.o360

pusatsudut

bulatanluas

sektorluas=

14.Faktor skala, k=PA

AP

15. Luas imej = k2 luas objek



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Section A

[52 marks]

Answerall questions in this section.

1. Solve the equation for m2

+ m =3

8+m

[3 marks]

Answer :

2. Calculate the value ofx andy that satisfy both of the following equations:

x 2y = 1

x +3

y= 6

[4 marks]

Answer:

For

Examiners

Use



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3. On the graph provided, shade the region which satisfies the three inequalities;

x > 2 , y x3

2and 2443 + yx .

[3 marks]

Answer :

x

y

3x + 4y = 24

y = x3

2

0 1 2 3 4 5 6 7 8

6

5

4

3

2

1

For

xaminers

Use



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4. Table 1 shows the number of students from three schools who visited

a historical site on a particular day .

Number of studentsSchool

Male Female

A n 24B 18 7

C 10 10

TABLE 1

(a) A student is chosen at random from a group of male students. If the probability

that he is from school Cis 0.25, calculate the value ofn .

(b) Two students from school B are chosen at random. Calculate the probability

that they are of the same gender.

[ 5 marks ]

Answer: (a)

(b)

For

xaminers

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5. Diagram 1 shows straight lines AB , CD , MKand GL on a Cartesian plane. AB is

parallel to CD, GL is parallel tox-axis and straight line KMis parallel toy-axis.

Given the equation ofCD is y =2

1x 4,

G is a midpoint of a straight lineAB andMis x intercept of straight line CD.

Find ;

(a) they-intercept of straight line AB(b) the coordinate ofG(c) the coordinate ofK

[5 marks]

Answer :

(a)

(b)

(c)

xA(10 , 0)

C(0, 4)

G

B

K

D

y =2

1x4

M

L

0

y

DIAGRAM 1

For

Examiners

Use



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6. Diagram 2 shows a combined solid of a cuboid and a right pyramid. Given that

TV= 4.5 cm,EA = kcm and the total volume of the combined solid is 1020 cm3.

Calculate the height, in cm, of the combined solid from Tto the base ofABCD.

[ 4 marks ]

Answer:

For

xaminers

Use

DIAGRAM 2

T

C

G

12 cm

kcm

A B

D

E F

H

10 cm

V



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7. Diagram 3 shows an arc of a circle ABCD with centre O. The radius of the circleis10cm.

Using = 3.142, calculate the(a) perimeter, in cm, of the whole diagram,

(b) area, in cm2, of the whole diagram.

[6marks]

Answer:

(a)

(b)

For

Examiners

Use

60o

OC

D

A

B

DIAGRAM 3



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8. (a) Write the converse of the implication below:-

If the gradient of two straight lines are the same, then they are parallel.

(b) Determine whether the following statements are true or false:-

(i) 9 is an odd number and 9 is a prime number

(ii) 5 is a multiple of 10 or 10 is a multipe of 5.

(c) 5, 14, 29, 50, is a list of number pattern and can be written as

5 = 3(1) + 2

14 = 3(4) + 2

29 = 3(9) + 250 = 3(16) + 2

..

Make a general conclusion by induction regarding the list of number

pattern based on the information above.[5 marks]

Answer:

(a) __________________________________________________________________

__________________________________________________________________

(b)(i)________________________

(ii) ________________________

(c) __________________________________________________________________

__________________________________________________________________

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9. Diagram 4 shows a cuboid with a rectangular baseABCD . GivenHG =3

1JG .

DIAGRAM 4

Calculate the angle between the lineBHand the planeDCGJ.[ 4 marks ]

Answer :

A 12 cm B

D C

E F

J H G

8 cm

6 cm

For

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10. Diagram 5 shows the speed-time graph for the movement of a particle for a period

of t s.

Calculate

(a) the value oftif the total distance travelled by the particle for the whole journey

is 380 m.

(b) the acceleration of the particle, in ms-2

, at t= 5s.

(c) the average speed, in ms-1

, of the particle in the first 7s.

[ 6 marks ]

Jawapan :

(a)

(b)

(c)

Speed (ms-1

)

0 4 8 t Time (s)

DIAGRAM 5

40

30

For

Examiners

Use



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11. Given that

33

1 p

4

7is the inverse matrix ofM

n

4

6

7.

Find the values ofn andp.

Hence, using matrices, calculate the values ofx andy which satisfy both of the

following equations;

1063

774

=+

=+

yx

yx

[6 marks]

Answer :

For

Examiners

Use



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Section B

[48 marks]

Answerfourquestions from this section.

12. (a) Complete Table 1 in the answer space provided for the equation326 xxy += .

[2 marks]

(b) For this part of question, use the graph paper provided on page 29. You mayuse a flexible curve rule.

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 10 units on the

y-axis, draw the graph of 326 xxy += for 44 x .

[3 marks]

(c) Draw a suitable straight line on your graph to find values ofx which satisfiesthe equation xx 1293 =+ for 44 x . State the values ofx.

[5 marks]

(d) Shade the region defined by the inequalities y 6 + 2x x3, y < 30,1510 + xy and x 0.

[2 marks]

Answer :

(a)

TABLE 1

(b) Refer graph on page 29.

(c)

x = ...........................................

(d) Refer graph on page 29.

x -4 -3 -2 -1 0 1 2 3 4

y 62 10 5 6 7 2

For

Examiners

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Graph for Question 12



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13. Diagram 6 shows trapeziumsABCD ,LMNP ,RSNTandEFGHdrawn on a Cartesian

plane .

(a) Given that : Vis a reflection about the linex = 3 ,

Wis a translation

3

4

State the coordinates of the image of point Funder the following transformations :

(i) VW,

(ii) WV. [ 2 marks ]

(b) TrapeziumLMNP is the image of trapeziumABCD under the transformationXand

trapeziumRSNTis the image of trapeziumLMNP under the transformation Y.

(i) Describe , in full , transformationXand transformation Y.

(ii) Describe completely a single transformation which is equivalent to thecombined transformation YX.

[ 6 marks ]

(c) TrapeziumEFGH is the image of trapeziumABCD under an enlargement .(i) State the scale factor and centre of the enlargement ,

(ii) Given that the trapezium EFGH has an area of 50 cm2

, calculate the area of

trapeziumABCD .

[ 4 marks ]

For

Examiners

Use

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 x

5

4

3

2

1

8

7

6

9

10

y

E H

L P S R

D

C

F

G

M

A

DIAGRAM 6

B

N T

11



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Answer :

(a)( i)

( i i)

(b)( i)

( i i)

(c)( i)

( i i)

For

Examin

Use



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14. Data in Table 2 shows the score obtained by 45 students in a Mathematics quiz.

15 20 36 23 33 30 28 9 12

22 28 34 5 43 14 24 36 18

12 9 36 10 8 40 23 28 17

18 22 43 10 11 10 18 22 28

36 39 33 22 18 19 15 28 18

TABLE 2

(a) Using the data in table 1 and class interval of 5 marks, complete the table

in the answer space provided. [4 marks]

(b) Calculate the mean mark of the group.[3 marks]

(c) For this part of the question, use the graph paper provided on page 40.

Using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 1 student on they-axis. Draw a histrogram to respresent this data.

[3 marks]

(d) Using your histrogram or otherwise calculate the percentage of students whoscore less than 25 marks.

[2 marks]

For

Examiners

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Answers:

(a)

Score Frequency MidpointUpper

Boundaries

5-9 410-14 7

Total = 45

(b)

(c ) Refer to graph on page 40.

(d)

Fo

Examin

Use



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Graph for Question 14



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15. (a) Diagram 7 shows a solid consisting of a right prism and a half cylinder with

the diameter of 8 cm joined at a horizontal plane CDIH. FGHIJis a uniformcross-section of the prism.ABGFand CBGHare inclined planes. G andB are 3

cm horizontally from FandA respectively.

[ 4 marks ]

Draw to full scale the plan of the solid .

Answer:

For

xaminers

Use

A

BC

D

8cm

10cm

7cm

6cm

I

JG

F

E

H

DIAGRAM 7



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15. (b) Diagram 8 shows a right prism, a cuboid and a half hollow cylinder. The right

prism joined with a cuboid at a vertical planeEFJIand the cuboid joined witha half cylinder at a vertical plane ABGH. The height of the prism,

JF=IE=3 cm, the length ofKF= 3 cm and the length ofLK= 8 cm = diameter

of the cylinder. The cylinder is 2 cm higher than the cuboid and the cuboid is

5 cm high.

Draw to full scale , the elevation of the object on the vertical plane;

(i) parallel toLKas viewed fromX [ 4 marks]

(ii) parallel to KG as viewed from Y. [ 4 marks]

For

Examiners

Use

S T

OM N

2cm

P

BAR

DC

Q4cm

5cm

I J

GH

F

KL

3cm

8cm

2cm

E

3cm

X

Y

DIAGRAM 8



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Answer:

15. (b)(i), (b)(ii)

For

Examin

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16. P, Q andR are three points on the surface of the earth. PQ is a diameter of the earth

with P located at ( 50oS , 78

oE) whileR is 3500 nautical miles due north of P.

(a) Find

(i) the position ofQ [2 marks]

(ii) latitude ofR [2 marks]

(b) Calculate the shortest distance between Q andR. [3 marks]

(c) Wis due east ofR with a longitude of 130oE. An aeroplane took off from P andflew due north toR. It then changed its direction and flew due east until it reach

W. The whole journey took 15 hours and 41 minutes.

Calculate the average speed of the aeroplane.[5 marks]

Answer:

(a)(i)

(ii)

(b)

(c)

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END OF QUESTION PAPER

MRSM Maths P1 2007

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