Solaf Set 2 Soalan k2 2011

8/4/2019 Solaf Set 2 Soalan k2 2011

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SOLAF

SET 2

NEGERI PERAK

SET 2 3472/2ADDITIONAL MATHEMATICS

Kertas 2

22

1jam Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

MAKLUMAT UNTUK CALON

1. Kertas soalan ini adalah dalam dwibahasa.

2. Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam bahasa Malaysia.

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

4. Calon dikehendaki menceraikan halaman 13 dan ikat bersama-sama dengan kertas jawapan,

sebagai muka hadapan.

Kertas soalan ini mengandungi 14 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 logna 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 d

d d d,d

u vv u

u y x xyv x v

= dba x 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 d

b

a

x 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

IQ

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

= 3123121332212

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. sec2

A = 1 + tan2

A 11. tan 2A = 22tan

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 sin

2A 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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Section A

[40 marks]

Answer all questions from this section.

Jawab semua soalan dalam bahagian ini.

1 Solve the following simultaneous equations:

2

2 6

8

x y

x xy

[5 marks]

2 Diagram 2 below shows a rectangleABCD and a triangleABE.

Diagram 2

The height of the triangle is 4 cm.

(a)show that the shaded region can be represented by 3x22x(b)[3 marks](b) given the area of the shaded region is 265 cm ,

find thevalue ofx, [2 marks]

(c) determine the perimeter of the rectangleABCD. [2 marks]

3 Table 3 below shows the length in cm for a sample of 250 sugar cane harvested by the Gula Manis

Plantation.

Table 3

(a) Calculate the mean length of the sugar cane, [3 marks]

(b) Draw an ogive to show the distribution of the length of the sugar cane, [2 marks](c) From the ogive, find the percentage of sugar cane which is longer than 240 cm. [2 marks]


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4 Diagram 4 shows three consecutive squares arranged in ascending order.

(x + 4) cm

(x + 2) cm

x cm

x cm (x + 2) cm (x + 4) cm

Diagram 4

(a)Show that perimeter of the squares from an arithmetic progression.Hence, state the value of common difference. [2 marks]

(b)Given that x = 8 cm, find(i) the sum of the perimeter of the first 16 squares,(ii) the first square that has the perimeter of more than 210 cm.

[5 marks]

5. The diagram shows a curve such that 62 xdx

dy. The minimum point of the curve is A(3,1). AB

is a straight line passing through A and B where B is the point of intersection between the curveandy-axis.

(a) Find the equation of the curve. [3 marks]

(b) Calculate the area of the shaded region. [4 marks]

x

y

O

A

B


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6 (a) Prove the identity (cos 2+ 1) tan = sin 2 . [3 marks]

(b) (i) Sketch the graph ofy = 3 + x2sin for 0 2 .

(ii) Hence, using the same axes, sketch a suitable straight line graph to find the number

of solutions for the equation 0.5 = x2sin for 0 2 .

State the number of solutions.

[4 marks]

Section B

[40 marks]

Answer any four questions from this section.

Jawab mana-mana empat soalan daripada bahagian ini.

7 Solutions to this question by scale drawing will not be accepted.In Diagram 7, the straight lineBChas an equation of 3y +x + 6 = 0 and is perpendicular to straight

lineAB at pointB.

(a) Find

i) the equation of the straight lineAB

ii) the coordinates ofB. [5 marks]

(b) The straight lineAB is extended to a pointD such thatAB :BD = 2 : 3.

Find the coordinates ofD. [2 marks]

(c) A point P moves such that its distance from pointA is always 5 units.

Find the equation of the locus ofP. [3 marks]

A(-6, 5)

B

C

3y + x + 6 = 0

x

y

O

Diagram 7


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8 Diagram 8 shows a sectorAOB of a circle , centre O. The point P lies on OA , the point Q

lies on OB and PQ is perpendicular to OB. The length ofOP is 9 cm and AOB = .6

rad

It is given that OP: OA= 3 : 5 .

( Using = 3.142 )

Calculate

(a) the length, in cm, ofPA, [ 1 mark]

(b)the perimeter, in cm, of the shaded region, [ 5 marks ](c) the area, in cm2, of the shaded region. [ 4 marks ]

9 Use graph paper to answer this question.Table 9 shows the values of two variables ,x andy obtained from an experiment. Variablesx andy

are related by the equation 22 ,n

y rx xr

where rand n are constants.

x 2 3 4 5 6 7

y 8 13.2 20 27.5 36.6 45.5

(a) Ploty

xagainst x , using a scale of 2 cm to 1 unit on both axes.

Hence, draw the line of best fit. [5 marks]

(b) Use your graph in (a), to find the value of

(i). n,

(ii). r,

(iii). y whenx = 1.5. [5 marks]

Table 9

O

P

A

BQ

rad6

Diagram 8


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R

10 Diagram 10 shows the straight liney = 3x intersecting the curvey = 4 x2

at point P.

Find

(a) the coordinates ofP, [3 marks](b)the area of regionR which is bounded by the liney = 3x, the curve

y = 4 x2

and thex-axis. [4 marks]

(c) the volume generated by region bounded by the curve, straight liney = 4,x-axis, andy-axis is revolved 360

oabout they-axis. [3 marks]

11 Diagram 11 below shows triangle OAB. The straight lineAP intersects the straight line OQ atR. It

is given that OP = 3

1

OB,AQ = 4

1

AB,

x and

y

A

R

O P B

(a) Express in terms ofx and/ory:

(i) AP

(ii) OQ [4 marks]

(b) (i) Given that ,APhAR state AR in terms of h, x andy.

(ii) Given that ,OQkRQ state RQ in terms of k, x andy. [2 marks]

(c) Using AR and RQ from (b), find the value of h and of k. [4 marks]

Q

Diagram 11

x

y

P

y = 3x

Diagram 10

O

y = 4x2


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Section C

[20 marks]

Answer two questions from this section.

Jawab dua soalan daripada bahagian ini.

12 Diagram 12 shows triangle PQR such that S lies on QR and Tlies on QP.

S

Q R

60

T

P

Diagram 12

It is given that SQ =13 cm, QT=10 cm , SR = 17 cm, TP = 18 cm and QRP = 60.(a) Find

(i) QPR, [2 marks](ii) the length, in cm, of ST. [3 marks]

(b)Find the area, in cm2, of the quadrilateral SRPT. [3 marks](c)A point P lies on PQ such that PR=PR. Find the length, in cm, ofPQ. [2 marks]

13 Diagram 13 shows quadrilateralABCD.

B C

9 cm

40

A 8 cm D

Diagram 13

Given thatBC andAD are parallel. The area of triangleACD is 30.18 cm2.

Find,

(a) CDA [2 marks](b) the length, in cm, ofAC [2 marks](c) ABC [3 marks](d) the area, in cm2, of the triangleABC [3 marks]


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14 A cake was made by using 4 special ingredients,A, B, CandD. Table 14 shows the prices

in years 2009 and 2010, the price indices for year 2010 based on the year 2009 and the

number of parts of the ingredients used in making the cake.

Table 14

(a)Find the values ofx,y andz. [4 marks](b)Calculate

(i) the composite index for the production cost of a cake in year 2010 based on the year2009. [2 marks]

(ii) the price of the cake in the year 2010 if its price in the year 2009 is RM40.[2 marks]

(c) The cost of all the ingredients increased by 25% from the year 2010 to the year 2011.

Calculate the composite index for the year 2011 based on the year 2009. [2 marks]

15 The Table 15 shows the price index and weightage of four types of items for the year 2009

based on the year 2007.

Item Price index Weightage

A 115 k

B 110 5C 150 2

D 130 1

Table 15

(a)Given the price of itemA in the year 2009 is RM 2.30, find the price of itemA in the year2007. [2 marks]

(b)Given the price of item Cin the year 2007 is RM 3.20, find the price of item Cin the year2009. [2 marks]

(c)Given the composite index in the year 2009 based on the year 2007 is 120, calculate thevalue of k. [3 marks]

(d)The price index of itemD increase by 10% from the year 2009 to year 2010, where elsethe price indices of all the other items remain unchanged. Calculate the composite index for

the year 2010 based on the year 2007. [3 marks]

END OF QUESTION PAPERKERTAS SOALAN TAMAT

Ingredients Price per unit (RM) Price index Number of parts

2009 2010

A 2.50 3.00 x 2

B y 8.00 160 3

C 4.00 5.00 125 4

D 4.00 z 140 1


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NAMA :

ANGKA GILIRAN

INFORMATION FOR CANDIDATES

Arahan Kepada Calon

1. Tuliskan nama dan angka giliran anda pada ruang yang disediakan.2. Tandakan untuk soalan yang dijawab.3. Ceraikan helaian ini dan ikatkan bersama-sama dengan kertas jawapan sebagai muka

hadapan.

Kod Pemeriksa

Bahagian Soalan Soalan

Dijawab

Markah

Penuh

Markah Diperoleh

(Untuk Kegunaan Pemeriksa)

A

1 5

2 7

3 7

4 7

5 7

6 7

B

7 10

8 10

9 10

10 10

11 10

C

12 10

13 1014 10

15 10

Jumlah


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MAKLUMAT UNTUK CALON

1. This question paper consists of three sections: Section A, Section B and Section C.Kertas soalan ini mengandungi tiga bahagian: Bahagian A, Bahagian B danBahagian C.

2. Answer all questions in Section A, any four questions from Section B and any two questionsfrom Section C.

Jawab semua soalan dalam Bahagian A, mana-mana empat soalan daripada Bahagian B dan

mana-mana dua soalan daripada Bahagian C.

3. Write your answers on your answer sheet.Jawapan anda hendaklah ditulis di atas kertas jawapan anda.

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

membantu anda untuk mendapatkan markah.

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

.

6. The marks allocated for each question and sub-part of a question are shown in brackets.Markah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkandalam kurungan.

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

8. You may use a non-programmable scientific calculator or a booklet of four-figure mathematicaltables.

Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram

atau buku sifir matematik empat angka .

Solaf Set 2 Soalan k2 2011

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Transcript of Solaf Set 2 Soalan k2 2011