solaf set 2 soalan k1 2011

8/4/2019 Solaf Set 2 Soalan k1 2011

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[Lihat halaman sebelah

3472/1 SULIT

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NAMA:.. NO. KAD PENGENALAN:..

SOLAF Set 2

NEGERI PERAK

SOLAF Set 2

3472/1ADDITIONAL MATHEMATICSKertas 1

Jun

2 jam Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Tuliskan nama dan nombor kad pengenalan andapada ruangan yang disediakan.

2. Kertas soalan ini adalah dalam dwibahasa.3. Soalan dalam bahasa Inggeris mendahului soalan

yang sepadan dalam bahasa Malaysia.

4. Calon dibenarkan menjawab keseluruhan atausebahagian soalan sama ada dalam bahasa Inggerisatau bahasa Malaysia.

5. Calon dikehendaki membaca maklumat di halamanbelakang kertas soalan ini.

SoalanMarkah

Penuh

Markah

Diperolehi

1 2

2 3

3 4

4 4

5 2

6 3

7 3

8 3

9 3

10 3

11 3

12 3

13 4

14 3

15 3

16 2

17 3

18 419 4

20 3

21 4

22 4

23 4

24 3

25 3

Jumlah 80

Kertas soalan ini mengandungi 22 halaman bercetak.


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

commonly used.

Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah

yang biasa digunakan.

ALGEBRA

1.2 4

2

b b acx

a

8.

loglog

log

ca

c

bb

a

2. m n m na a a 9. ( 1)nT a n d

3. m n m na a a 10. 2 ( 1)2

nn

S a n d

4. ( )m n mna a 11. 1nnT ar

5. log log loga a amn m n 12.( 1) (1 )

, 11 1

n n

na r a r

S rr r

6. log log loga a am

m nn

13. , 11

aS r

r

7. log logn

a am n m

CALCULUS

KALKULUS

1.d d d

,d d d

y v u y uv u v

x x x 4. Area under a curve

Luas di bawah lengkung

= db

ay x or (atau)

2.2

d dd d d,d

u vv uu y x xyv x v

= d

b

ax y

3.d d d

d d d

y y u

x u x 5. Volume of revolution

Isipadu kisaran

= 2 db

ay x or (atau)

= 2 db

ax y


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STATISTICS

STATISTIK

1.x

xN

7.i i

i

W II

W

2.fx

xf

8.!

( )!

nr

nP

n r

3.

2 22( ) x x x

xN N

9. !( )! !

nr

nC

n r r

4.

2 22( ) f x x fx

xf f

10. )()()()( BAPBPAPBAP

11. ( ) , 1n r n r rP X r C p q p q

5.

1

2

m

N F

m L Cf

12. Mean /Min , = np

13. npq

6. 1

0

100Q

I

Q

14.

XZ

GEOMETRY

GEOMETRI

1. Distance /Jarak 5. 2 2r x y

2 22 1 2 1( ) ( ) x x y y

2. Midpoint /Titik tengah 6.2 2

x i y jr

x y

1 2 1 2( , ) ,2 2

x x y yx y

3. A point dividing a segment of a line

Titik yang membahagi suatu tembereng garis

1 2 1 2, ,nx mx ny my

x ym n m n

4. Area of a triangle /Luas segi tiga= 312312133221

2

1yxyxyxyxyxyx


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TRIGONOMETRY

TRIGONOMETRI

1. Arc length, rs 8. sin )( BA = sinA cosB cosA sinB

Panjang lengkok, js sin )( BA = sinA kosB kosA sinB

2. Area of sector,21

2A r 9. cos )( BA = cosA cosB sinA sinB

Luas sektor, 21

2L j kos )( BA = kosA kosB sinA sinB

3. sin2A + cos

2A = 1 10. tan )( BA =

tan tan

1 tan tan

A B

A B

sin2A + kos

2A = 1

4. sec2A = 1 + tan

2A 11. tan 2A =

2

2tan

1 tan

A

A

sek2A = 1 + tan

2A

5. cosec2A = 1 + cot

2A 12.

C

c

B

b

A

a

sinsinsin

kosek2A = 1 + kot

2A

6. sin 2A = 2 sinA cosA 13. 2 2 2 2 cosa b c bc A

sin 2A = 2 sinA kosA 2 2 2 2 kosa b c bc A

7. cos 2A = cos2A sin2A 14. Area of a triangle /Luas segi tiga

= 2 cos2A 1 = ab

2

1sin C

= 1 2sin2A

kos 2A = kos2A sin

2A

= 2 kos2A 1

= 1 2sin2A


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BLANK PAGE

HALAMAN KOSONG


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For

Examiners

Use

Answer all questions.

Jawab semua soalan.

1 Diagram 1 shows the relation between set P and set Q.

Diagram 1

State

(a) the range of the relation,

(b) the type of the relation

[2 marks]

Answer:

(a)

(b)


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2 Given that2 3

( ) , 02

x f x k

k

and 1

5 3( ) , 0

x f x m

m

, where kand m are constants.

Find the values of kand ofm.

[3 marks]

Answer:

For

Examiners

Use

3 Given the function ( ) 4 3 f x x and2

( ) 5 1g x x x .

Find

(a) 1(7)f ,

(b) ( )gf x

[4 marks]

Answer:

(a)

(b)


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For

Examiners

Use4 If and are the roots of the equation

22 4 3 0x x , find the value of

(a)

(b)

(c)2 2

[4 marks]

Answer:(a)

(b)

(c)

5 Sketch the shape and position of the graph of the quadratic function 2( ) f x ax bx c when

0a and the roots are equal.[2 marks]

Answer:

x

f(x)


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6 Solve the inequality (2 1) 3x x .

[3 marks]

Answer:

For

Examiners

Use

7 Solve the equation1

3(2 ) 5(2 ) 8x x

. [3 marks]Answer:

8 Given that log 2a p and log 3a q , express log 36a in terms ofp and q.

[3 marks]

Answer:


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For

Examiners

Use

9 Solve the equation 3 3log ( 2) 3 log ( 4)x x .

[3 marks]

Answer:

10 Diagram 10 shows the straight line PQ which is perpendicular to the straight lineRQ

at the point Q.

The equation of the straight lineRQ isy = 2 3x .Find the coordinates ofQ.

[3 marks]

Answer:

P(0, 7)

Q

R

Ox

y

Diagram 10


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11 Diagram 11 shows a straight lineAC.

The pointB lies onACsuch thatAB :BC= 3 : 2.

Find the coordinates ofB.

[3 marks]

Answer:

12 A set of seven numbers has a mean of 8.

(a) Find(b)When a number p is added to this set, the new mean is 7.5.

Find the value ofp.

[3 marks]

Answer:

(a)

(b)

A(-3, 5)

B

Ox

y

C(7, 0)

Diagram 11


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For

Examiners

Use

13 Diagram 13 shows sector OAB with centre O and sectorAPQ with centreA.

Given that OB = 10 cm,AQ = 4 cm, PAQ = 1.2 radians and the length of arc

AB = 6 cm, calculate

(a) the value of , in radian,(b)the area, in 2cm ,of the shaded region.

[4 marks]

Answer:

(a)

(b)

14 The volume of water, Vcm3

, in a container is given by where h cm is the

height of the water in the container. Water is poured into the container at a rate of8 cm3

s-1

.

Find the rate of change of the height of water, in cm s-1

, at the instant when its height

is 3 cm.

[3 marks]

Answer:

P

O

A

B

Q

Diagram 13


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15 Two variables, x and y, are related by the equation2

12y

x .

Express, in terms ofp, the approximate change in y, when x changes from 3 to 3 +p,

where p is a small value.

[3 marks]

Answer:

For

Examiners

Use

16 The first three terms of a sequence are 4,p, 36.

Find the positive value ofp so that the sequence is

(a) an arithmetic progression,(b)a geometric progression.

[2 marks]

Answer:

(a)

(b)

17 The first three terms of a geometric progression are 64, 48, 36.

Find the sum to infinity of the geometric progression.

[3 marks]

Answer:


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For

Examiners

Use

18 The first three terms of an arithmetic progression are 3, 8, 13.

Find

(a) the common difference of the progression,(b)The sum of the first 12 terms after the 8th term.

[4 marks]

Answer:

(a)

(b)

19 The variables x and y are related by the equation 3 y kx , where k is a constant.

(a) Convert the equation 3 y kx to linear form.

(b) Diagram 19 shows the straight line obtained by plotting 10log y against 10log x .

Find the value of

(i) 10log k,

(ii) h.

[4 marks]

Answer:

(a)

(b)

(i) (ii)

(0, 2)(4, h)

Diagram 19


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20 The curve y =x2 18x + 12 has a maximum point atx =p, wherep is a constant.

Find the value ofp.

[3 marks]

Answer:

For

Examiners

Use

21 Given thatf(x) =)53(

12

x, evaluatef (-1) .

[4 marks]

Answer:


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For

Examiners

Use22 OABCis parallelogram such that OA = i +j and OC= - 4i + 3j .

Find

(a) OB ,(b)unit vector in the direction of OB .

[4 marks]Answer:

(a)

(b)

23 Diagram 23 shows a triangleABC. P is the mid point ofACand Q lies onBCsuch that

BQ : QC= 2 : 1 . Given that AB = 12x and AC = 6y, express each of the following

in terms ofx andy.

Diagram 23

(a) AQ

(b) PQ

[4 marks]

Answer:

(a)

(b)

A

C

PQ

B


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24 Given that sinA =3

kandA is an acute angle, find the values of the following in terms of k.

(a) cosecA

(b) cotA

[3 marks]

Answer:

(a)

(b)

For

Examiners

Use

25 Solve the equation 4 sin x cos xcos x = 0 for 0 x 360.

[3 marks]

Answer:

END OF QUESTION PAPER


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INFORMATION FOR CANDIDATES

MAKLUMAT UNTUK CALON

1. This question paper consists of25 questions.Kertas soalan ini mengandungi 25 soalan.

2. Answer all questions.Jawab semua soalan.

3. Write your answers in the spaces provided in the question paper.Tulis jawapan anda dalam ruangan yang disediakan dalam kertas soalan ini.

4. Show your working. It may help you to get marks.Tunjukkan langkah-langkah dalam kerja mengira anda. Ini boleh membantu anda untuk

mendapat markah.

5. If you wish to change your answer, cross out the work that you have done. Then write downthe new answer.

Sekiranya anda hendak menukar jawapan, batalkan dengan kemas jawapan yang telah dibuat.

Kemudian tulis jawapan yang baru.

6. The diagrams in the questions provided are not drawn to scale unless stated.Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

7. The marks allocated for each question are shown in brackets.Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan.

8. A list of formulae is provided on pages 2 to 4.Satu senarai rumus disediakan di halaman 2 hingga 4.

9. You may use a non-programmable scientific calculator.Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

10. Hand in this question paper to the invigilator at the end of the examination.Serahkan kertas soalan ini kepada pengawas peperiksaan pada akhir peperiksaan.

solaf set 2 soalan k1 2011

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