SPM Trial 2010 AddMath Q&A (Melaka)

8/8/2019 SPM Trial 2010 AddMath Q&A (Melaka)

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PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

DENGAN KERJASAMA

JABATAN PELAJARAN MELAKA

PEPERIKSAAN PERCUBAAN

SIJIL PELAJARAN MALAYSIA 2010

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

Kertas soalan ini mengandungi 18 halaman bercetak

Nama : ....

Tingkatan: ..3472/1

Matematik Tambahan

Kertas 1

Sept 2010

2 jam

1. This question paper consists of25 questionsKertas soalan ini mengandungi 25 soalan.

2. Answer all questions.Jawabsemua soalan.

3. Give only one answer for each questionBagi setiap soalan berikan SATU jawapan sahaja.

4. Write the answers clearly in the space provided in the question paper. Jawapan hendaklah ditulis pada ruang yang disediakan dalam kertas soalan.

5. 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.

6. If you wish to change your answer, cross out the work that

you have done. Then write down the new answer.Sekiranya anda hendak menukar jawapan, batalkan kerja mengira yang telah

dibuat. Kemudian tulis jawapan yang baru.

7 The diagram in the questions provided are not drawn to scale unless

stated.Rajah yang mengiringi soalan ini tidak dilukiskan mengikut skala kecuali dinyatakan.

8. The marks allocated for each question and sub-part of a question are

shown in brackets.Markah yang diperuntukkan bagi setiap soalan atau ceraian soalan ditunjukkan

dalam kurungan.

9.A list of formulae is provided on page 2 to 3Satu senarai rumus disediakan di halaman 2 hingga 3

10. You may use a non-programmable scientific calculator.Anda dibenarkan menggunakan kalkulator saintifik yang tidak bolehdiprogram.

11.This question paper must be handed in at the end of the examination. Kertas soalan ini hendaklah diserahkan pada akhir peperiksaan .

Kod

Pemeriksa

SoalanMarkah

Penuh

Markah

Diperoleh

1 2

2 2

3 4

4 3

5 3

6 3

7 3

8 4

9 310 4

11 4

12 4

13 3

14 3

15 4

16 3

17 4

18 3

19 3

20 3

21 322 3

23 3

24 3

25 3

Jumlah80

MATEMATIK TAMBAHAN

Kertas 1

Dua Jam

www.papercollection.batukawa.info


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2

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

used.Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan. . Simbol-simbol yang diberi adalah yang biasa

digunakan.

ALGEBRA

12 4

2

b b acx

a r

2 am u an = a m + n

3 am y an = a m - n

4 (am) n = a

nm

5 logamn = log am + logan

6 logan

m= log am - logan

7 log amn = n log am

8 logab =ab

c

c

loglog

9 Tn = a + (n -1)d

10 Sn = ])1(2[2

dnan

11 Tn = arn-1

12 Sn =r

ra

r

ra nn

1

)1(

1

)1(, (rz 1)

13r

aS

f 1, r


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SULIT 2STATISTICS

1 Arc length, s = rT

( Panjang lengkok) s = j T

2 Area of sector ,L = 21

2rT

( Luas sektor L = T22

1j )

3 sin2A + cos

2A = 1

4 sec2A = 1 + tan

2A

5 cosec2A = 1 + cot2A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A sin

2A

= 2 cos2A - 1

= 1 - 2 sin2A

8 tan 2A =A

A2tan1

tan2

TRIGONOMETRY

9 sin (ArB) = sinA cosB r cosA sinB

10 cos (ArB) = cosA cosB # sinA sinB

11 tan (ArB) =BtanAtan

BtanAtan

#1

r

12C

c

B

b

A

a

sinsinsin

13 a2

= b2

+ c2

- 2bc cosA

14 Area of triangle = Cabsin

2

1

( Luas Segitiga )

1 x =N

x

2 x =

f

fx

3 V =N

xx 2)(=

2_2

xN

x

4 V =

f

xxf 2)(=

22

xf

fx

5 m = Cf

FN

Lm

2

1

6 1

0

100Q

IQ

u

71

11

w

IwI

8)!(

!

rn

nP

r

n

9!)!(

!

rrn

nC

r

n

10 P(AB) = P(A)+P(B)- P(AB)

11 P (X= r) = rnrr

n qpC , p + q = 1

12 Mean = np

13 npqV

14 z =V

Px

3



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SULIT 4

Answer all questions.

Jawab semua soalan

1 Diagram 1 shows the relation between two sets of number .Rajah 1 menunjukkan satu hubungan diantara dua set nombor.

Diagram 1Rajah 1

Based on the above information, the relation between P and Q is defined by the set

of ordered pairs { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}.Berdasarkan maklumat diatas hubungan antara P dan Q ditarifkan sebagai set pasangantertib { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}.

State,

Nyatakan,(a) the image of 2.

imej bagi 2

(b) the object of 0.imej bagi 0

[2 marks][ 2 markah ]

Answer/Jawapan: (a) ..

(b) ...

2 Given the function g :x x2

+1 , find the values of g-1

(10)Di beri g :x x

2+1 . Cari nilai nilai bagi g

-1(10)

[ 2 marks ][ 2 markah ]

Answer/Jawapan: ......2

2

For

examiners

use only

P ={ -3, -2, -1, 0, 1, 2 }

Q ={ -1, 0, 1, 2, 3 }

2

1



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3 The functionfis defined by f:x okx2 +p and the function g is defined by g:xo1 + 2x.Given the composite function fg :xox2 + x + 6, find the values of kandp.Fungsifditakrifkan sebagaif: x okx

2+ p dan fungsi g ditarifkan sebagai g: x o1+ 2x

Diberi fungsi gubahanfg : x ox2

+ x + 6, cari nilai k dan nilaip[4 marks]

[ 4 markah]

Answer/ Jawapan : k = ....p =

4 Given thatp

1is one of the roots of the quadratic equation px

2 + 7x 2p = 0, find the values ofp.

Diberi bahawap

1ialah salah satu punca bagi persamaan kuadratikpx

2 + 7x 2p = 0, cari nilai-nilai

bagip


Answer /Jawapan: ....

For

examiners

use only

4

3

4



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SULIT 6

( 4, q )

5 Diagram 5 shows the graph of a quadratic functionf(x) = 3(x +p)2 + 2, wherep

is a constant. The curve y =f(x) has the minimum point (4, q), where q is a constant.Rajah 5 menunjukkan graf fungsi kuadratikf(x) = 3(x +p)

2 + 2 , dimana p ialah pemalar

Lengkung y =f(x) mempunyai titik minimum (4, q), dimana q ialah satu pemalar.

State,Nyatakan,

(a) the value ofp, nilai p

(b) the value ofq, nilai q

(c) the equation of the axis of symmetry.persamaan paksi semetri

[ 3 marks ][ 3 markah]

Answer: (a) ........................

(b) ........................

(c)..................................

For

examiners

use only

5

Diagram 5Rajah 5



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6 Find the range of values ofx for which 27)6( dxx .

Cari julat nilai- nilai x dimana 27)6( dxx

[3 marks][ 3 markah]

Answer/Jawapan: ................................

7 Solve the equation 02781 321 xx .

Selesaikan persamaan 02781 321 xx [ 3 marks ]

[ 3 markah]

Answer /Jawapan: x = ...

8 Given log7 2 = h and log7 5 = k. Express log7 2.8 in terms of h and k.Diberi log7 2 = h dan log7 5 = k. Ungkapkan log7 2.8 dalam sebutan h dan k.

[ 4 marks ]

[ 4 markah ]

Answer /Jawapan : = .................................

For

examiner

use only

8

6

3

7



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9 Solve 1)1(log)4(log 33 xx

Selesaikan 1)1(log)4(log 33 xx


Answer/Jawapan: ..........

10 The first three terms of an arithmetic progression are 6, t 2, 14,....Tiga sebutan pertama satu janjang arithmatik ialah 6, t 2, 14,....

find,

cari,(a) the value of t,nilai t

(b) the sum of the first ten term .hasil tambah sepuluh sebutan pertama


Answer /Jawapan: (a)......

(b) .............

11 The sum of the first n terms of the geometric progression, 64, 32, 16, .. is 126.Hasil tambah n sebutan pertama suatu janjang geometri, 64, 32, 16, .. ialah 126

Find,Cari,

(a) the value ofn,

nilai n(b) the sum to infinity of the geometric progression.

hasiltambah ketakterhingaan janjang geometri ini,


Answer/Jawapan: (a) n = .

(b).

4

10

For

examiners

use only

3

9

4

11



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9


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12 x andy are related by the equationm

x nyx

, where m and n are constants.

A straight line is obtained by plottingxy againstx2, as shown in Diagram 12 .

x dany dihubungkan oleh persamaanm

x nyx

, dimana m dan n ialah pemalar.

Satu garislurus diperolehi dengan memplotkan xy melawan x2, sebagaimana ditunjukkan

dalam Rajah 12

Calculate the value ofm and ofn.Kira nilai m dan nilai n


Answer/Jawapan: m=

n =.....

4

12

For

examiner

use only

xy

x (12, 2 )

x ( 6, 0) x

2

Diagram 12Rajah 12



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13 Given that the point P 3,2 divides the line segment that joining ),4( tA and )8,(rB inthe ratio AP : PB = 1 : 4. Find the value ofrand of t.

Diberi bahawa titik P 3,2 membahagi segmen garis yang menghubungkan),4( tA dan )8,(rB dalam nisbah AP : PB = 1 : 4. Cari nilai r dan nilai t.

[3 marks][3 markah]

Answer/Jawapan: ..

14 Given that 2 2a i j

, 2 3b i j

and 2c a b

.

Diberi bahawa 2 2a i j

, 2 3b i j

dan 2c a b

.

Find,Cari,

(a) c

(b) unit vector in the direction ofc

.

vektor unit dalam arah c

[3 marks][3 markah]

Answer: (a)

(b) ...

For

examiners

use only

13

14



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15 Diagram 15 shows a triangle POQRajah 15 menunjukkan segitiga POQ

Diagram 15Rajah 15.

Given that OPo

= p and OQo

= q .PointX is lies on OP where OX:XP = 2 : 1 and point Y

is lies on OQ where OY: YQ = 3 : 1 . Straight line QXand line PYintersect at point C.

Diberi OPo = p dan OQo = q . TitikX terletak pada OP di mana OX:XP = 2 : 1 dan titikYadalah

titik pada OQ di mana OY: YQ = 3 : 1 . Garis lurus QXdan garis lurus PY bersilang pada titikC.

Express in terms of p and q

Ungkapkan dalam sebutan p dan q

(a) PYo

(b) QXo

[ 4 marks]

[4 markah]

Answer/Jawapan: (a) ..............................................

(b) ..............................................

O PX

C

Y

Q

4

15

For

examiner

use only



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SULIT 12

16 Given that T is an acute angle andq

pTsin , find in terms of p and /orq

Diberi bahawa T ialah sudut tirus danq

pTsin , cari dalam sebutanp dan/atau q

a) cos T kosT

b) tan ( 180 - T)

[3 marks][ 3 markah ]

Answer /Jawapan (a) .......................................

(b) .......................................

17 Solve 3cos 2T + 4 cos T +1 = 0 for

00

3600dd

T Selesaikan 3cos 2T + 4 cos T +1 = 0 untuk 00 3600 ddT

[4 marks][4 markah]

Answer/Jawapan: ...........

4

17

For

examiners

use only

3

16



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13


SULIT

A

C

R

S

OB 1.6 S

8 cm

18 Diagram 18 shows a circleABC with centre O, of radius 8 cm. SR is an arc ofa circle with centerO. The reflex angleAOCis 1.6S radian.

Rajah 18 menunjukkan satu bulatanABC dengan pusat O dan berjejari 8 cm, SR ialah

lengkuk sebuah bulatan berpusat di O . Sudut reflekAOC ialah 1.6S radian.

Given thatA and C are midpoints ofOS and OR respectively, find the area of shadedregion, in terms ofS .Diberi bahawa A dan C ialah titik tengah kepada OS dan OR , cari luas kawasan berlorek

dalam sebutan S

[ 3 marks][ 3 markah ]

Answer / Jawapan : . cm2

19 The radius of circle decreases at the rate of 10.5cms . Find the rate of change of the

area of a circle when the radius is 4 cm. .[ Given the area of a circle is A = r2

]Jejari sebuah bulatan berkurang dengan kadar 0.5 cms-1.Cari kadar perubahan luas

bulatan apabila jejarinya ialah 4 cm, [ Diberi luas bulatan A = r2]

[ 3 marks]

[ 3 markah]

Answer/Jawapan:

For

examiner

use only

19

3

18

Diagram 18

Rajah 18



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20 Given that5

1

( ) 5g x dx , find the value of m if5

1

[ 2 ( )] 3mx g x dx m

Diberi bahawa

5

1

( ) 5g x dx , cari nilai m jika5

1

[ 2 ( )] 3mx g x dx m


Answer / Jawapan :................................................

21 A set of numbers 1 2 3 4, , , ,..., nx x x x x has a median of 5 and a standard deviation of 2.

Find the median and the variance for the set of numbers

1 2 36 1,6 1,6 1,.......,6 1nx x x x .

Satu set nombor1 2 3 4, , , ,..., nx x x x x mempunyai median 5 dan sisihan piawai 2.

Cari median dan variance bagi set nombor 1 2 36 1,6 1,6 1,.......,6 1nx x x x

.


Answer/Jawapan : median = ..

variance =...

For

examiners

use only

20

21



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22 A box contains 6 black balls andp white balls. If a ball is taken out randomly from the

box, the probability of getting a white ball is7

4. Find the value ofp.

Sebuah kotak mengandungi 6 biji bola hitam danp biji bola putih . Jika sebiji bola diambil

secara rawak dari kotak itu kebarangkalian mendapat sebiji bola putih ialah7

4. Cari nilai p.

[ 3 marks ][3 markah]

Answer/Jawapan: ............

23 An expedition team consisting of 10 members to be chosen from a group of 4 teachersand 12 students.Satu kumpulan ekspedisi mengandungi 10 ahli yang akan dipilih daripada kumpulan 4orang guru dan 12 orang pelajar.

(a) Calculate the number of teams that can be formed.Kira bilangan kumpulan yang boleh dibentuk .

(b) If the team must consist of at least 2 teachers, calculate the numbers of teams thatcould be formed.Jika kumpulan ekspedisi itu mesti mengandungi sekurang-kurangnya 2 orang guru kira

bilangan kumpulan yang boleh dibentuk.


Answer/ Jawapan: (a) .......

(b) ..................................

For

examiners

use only

3

23

22



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25 Diagram 25 shows a standard normal distribution graph.Rajah 25 menunjukkan graf taburan normal piawai

The probability represented by the area of the shaded region is 0.803.Kebarangkalian yang diwakili oleh kawasan berlorek ialah 0.803

(a) Find the value of P( Z > k)Cari nilai P( Z > k)

(b) X is a continuous random variable which is normally distributed with a mean of

P and a standard deviation of 2. If the value ofXis 85 when the Z-score is k,

find the value of P.

Xialah pembolehubah rawak selanjar yang bertabur secara normal piawai dengan min

P dan sisihan piawai 2. Jika nilaiXialah 85 bila skor- Z ialah k, cari nilai P .


Answer: (a)

(b) .

END OF THE QUESTION PAPER

KERTAS SOALAN TAMAT

3

25

For

examiners

use only

-k k z

f(z))

0.803

Diagram 25

Rajah 25



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3472/2 SULIT

3472/2

Matematik

Tambahan

Kertas 2

Sept

2010

2 jam



DENGAN KERJASAMA




MATEMATIK TAMBAHAN

Kertas 2

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. This question paper consists of three sections : Section A, Section BandSection CKertas soalan ini mengandungi tiga bahagian : Bahagian A, Bahagian B dan Bahagian C.

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

questions from Section C.Jawab semua soalan dalam Bahagian A, empat soalan daripada Bahagian B, dan dua soalan

daripada Bahagian C.

3. Give only one answer/solution to each question.

Bagi setiap soalan, berikan satu jawapan / penyelesaian sahaja.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

bracketsMarkah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan dalam kurungan.

7. A list of formulae is provided on pages 2 and 3.Satu senarai rumus disediakan di halaman 2 dan 3.

8. A booklet of four-figure mathematical tables is provided.Buku sifir matematik empat angka boleh digunakan.

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

Kertas soalan ini mengandungi 17 halaman bercetak



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2

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

the ones commonly used.Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan. . Simbol-simbol yang diberi adalah yang

biasa digunakan.

ALGEBRA

1

2

42

b b acxa

r

2 am u an = a m + n

3 am y an = a m - n

4 (am)

n= a

nm

5 loga mn = log am + loga n

6 logan

m= log am - loga n

7 log a mn = n log a m

8 logab = a

b

c

c

log

log

9 Tn = a + (n-1)d

10 Sn = ])1(2[2

dnan

11 Tn = arn-1

12 Sn =r

ra

r

ra nn

1

)1(

1

)1(, (rz 1)

13

r

aS

f1

, r


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3

STATISTICS ( STATISTIK)

1 Arc length , s = rT

(Panjang lengkok, s = jT)

2 Area of sector ,A =21

2rT

(Luas sektor , L =21

2j T )

3 sin2A + cos

2A = 1

4 sek2A = 1 + tan2A

5 cosec2A = 1 + cot2A

6 sin2A = 2 sinAcosA

7 cos 2A = cos2A sin2A= 2 cos2A-1= 1- 2 sin

2A

8 tan2A =A

A2

tan1

tan2

TRIGONOMETRY

9 sin (ArB) = sinAcosB r cosAsinB

(sin (ArB) = sinAkosB r kosAsinB)

10 cos (ArB) = cosAcosB # sinAsinB(kos (ArB) = kos AkosB # sinAsinB )

11 tan (ArB) =BA

BA

tantan1

tantan

#

r

12C

c

B

b

A

a

sinsinsin

13 a2

= b2

+c2

- 2bc cosA

( a2 = b2 +c2 - 2bckosA )

14 Area of triangle ( Luas segitiga) = Cabsin2

1

1 x =N

x

2 x = f

fx

3 V =N

xx 2)(=

2_2

xN

x

4 V =

f

xxf2

)(=

22

xf

fx

5 m = Cf

FN

Lm

2

1

6 1

0

100Q

IQ

u

71

11

w

IwI

8 )!(

!

rn

n

Prn

9!)!(

!

rrn

nC

r

n

10 P(AB)=P(A)+P(B)-P(AB)

11 P(X=r) = rnrr

n qpC , p + q = 1

12 Mean, = np

13 npqV

14 z =V

Px



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Section A

[40 marks]

[ 40 markah]Answerall questions in this section .

Jawabsemua soalan dalam bahagian ini.

1 Solve the following simultaneous equations:

Selesaikan persamaan serentak berikut

284 2 nmmnm[5 marks]

[5 markah]

2 Solution by scale drawing will not be acceptedPenyelesaian secara lukisan berskala tidak diterima.

Diagram 2 shows the rhombusABCD with vertexA( -1, 5). The vertexB lies on thex-axis.Rajah 2 menunjukkan sebuah rombusABCD dengan bucuA( -1, 5). BucuB terletak pada paksi x

0

y

x

E

D

C

B

A(-1,5)

Diagram 2Rajah 2

The equation of the straight lineBD is x + 2y = 4. The diagonalsACandBD intersect at pointE.Persamaan bagi garislurusBD ialah x + 2y = 4. Garis pepenjuruACdanBD bersilang pada titikE.

FindCari

(a) the equation of the straight lineAC [3 marks]persamaan bagi garislurusAC [3 markah]

(b) the coordinates of the pointE [2 marks]koordinat bagi titikE [2 markah]

(c) the coordinates of the point C [2 marks]koordinat bagi titikC [2 markah]

4



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5

3 (a) Sketch the graph of y = 3sin 2x + 1 for S2

30 ddx [4 marks]

Lakarkan graf y = 3sin 2x + 1 bagi S2

30 ddx [4 markah]

(b) Hence, using the same axes, sketch a suitable straight line to find the numberof solutions for the equation xx 22sin3 S for S

2

30 ddx . State the number of solutions

[3 marks]Seterusnya, gunakan paksi yang sama, lakarkan garislurus yang sesuai untuk mencari bilangan

penyelesaian persamaan xx 22sin3 S bagi S2

30 ddx .

Nyatakan bilangan penyelesaian. markah]

4 The gradient function of a curve is kx2

x, where k is a constant. The equation of the normal tothe curve at point (1, - 2) is 5y +x = 7.Fungsi kecerunan bagi suatu lengkung ialah kx2 x, di mana k ialah pemalar. Persamaan garis normal

kepada lengkung di titik (1, - 2) ialah 5y +x = 7.

Find

Cari

(a) the value ofk, [4 marks]nilai k, [4 markah]

(b) the equation of the curve, [3marks] persamaan lengkung itu, markah]



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6

5 Table 5 shows the frequency distribution of the ages of a group of villagers in a village.Jadual 5 menunjukkan taburan kekerapan umur bagi sekumpulan penghuni di sebuah kampung.

Table 5Jadual 5

(a) (i) Without drawing an ogive, calculate the third quartile [3 marks]

Tanpa melukis ogif, hitungkan kuartil ketiga [3 markah]

(ii) Calculate the standard deviation of the distribution [3 marks]Hitungkan sisihan piawai bagi taburan itu. [3 markah]

(b) If two villagers with the ages of 20 and 40 years old respectively were shifted out from the

village, find the new variance. [2 marks]Sekiranya dua orang penghuni kampung itu yang berumur 20 dan 40 tahun masing-masing telah

berpindah keluar dari kampung itu, cari varians yang baru.

[2 markah]

Age/Umur

(year/tahun)

Number of villagers/

bilangan penghuni kampung1 - 10 25

11 - 20 32

21 - 30 28

31 - 40 9

41 - 50 6



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7

6 Diagram 6 shows the waves formed when a stone is thrown into the water. Each wave has theshape of a circle and is rcm away from the one before it.Rajah 6 menunjukkan gelombang yang terbentuk apabila seketul batu telah dibaling ke dalam air. Setiap

gelombang berbentuk bulatan dengan jaraknya rcm jauh daripada bulatan sebelumya.

Diagram 2Rajah 2

r cmr cmr cm

(a) show that the circumferences of the waves form an arithmetic progression and find the common

difference. [3 marks]Tunjukkan bahawa lilitan bulatan gelombang itu membentuk satu janjang aritmatik dan carikan beza

sepunya. [3 markah]

(b) If the radius of the smallest wave is 4 cm, find the radius of the tenth wave . Hence, find its

circumference in terms of S . [3marks]Sekiranya jejari bagi gelombang terkecil ialah 4 cm, hitungkan jejari bagi gelombang yang kesepuluh.

Seterusnya, cari lilitan bulatan gelombang kesepuluh dalam sebutan S . [3 markah]

Diagram 6

Rajah 6



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8

Section B

[40 marks]

[ 40 markah]

Answerfour questions from this section.Jawab empat soalan dalam bahagian ini

7 Table 7 shows the values of two variables,x andy, obtained from an experiment. The

variables are related by the equation pyx k 5 , where kandp are constants.Jadual 7 menunjukkan nilai-nilai bagi dua pembolehubah,x dany, yang diperoleh dari suatu

eksperimen. Pembolehubah-pembolehubah itu dihubungkan oleh persamaan pyx k 5 ,di mana kdanp adalah pemalar.

x 1.4 1.9 2.5 3.2 4.1 5.5

y 3.3 5.3 7.9 12 15.8 26.3

Table 7

Jadual 7

(a) Based on Table 7, construct a table for the values of log10y and log10x

[2 marks]Berdasarkan Jadual 7, bina satu jadual bagi nilai-nilai log10y and log10x

[ 2 markah]

(b) Plot log10y against log10x by using a scale of 2 cm to 0.1 unit on the log10x- axis and 2 cm to

0.2 unit on the log10y- axis. Hence, draw the line of best fit.[3 marks]

Dengan menggunakan skala 2 cm kepada 0.1 unit pada paksi- log10

x and 2 cm kepada 0.2 unit pada

paksi-log10y, plot log10y lawan log10x dan seterusnya lukiskan garis penyuaian terbaik.

[3 markah]

(c) Use your graph in (a) to find the value ofGunakan graf anda di (a) untuk cari nilai

(i) k

(ii) p[5 marks]

[5 markah]



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8 Diagram 8 shows ODC, OEA,BDEandACB are straight lines.Rajah 8 menunjukkan ODC, OEA, BDEdanACB ialah garis-garis lurus.

E

D

C

B

AO

Diagram 8Rajah 8

It is given that xOA 6 , yOB 3 , OE: OA = 1 : 3, andDE= 3BD.

Diberi bahawa xOA 6 , yOB 3 , OE : OA = 1 : 3, danDE= 3BD.

(a) Express in terms ofx and y

Ungkapkan dalam sebutan x dan y

(i) AB

(ii) OD

[3 marks] [3 markah]

(b) If ODmOC and BAnBC , where m and n are constants. Find the value ofm and n.

[5 marks]

Jika ODmOC and BAnBC , di mana m dan n ialah pemalar. Cari nilai bagi m dan n.[5 markah]

(c) Given that 4x unit and the area of the triangle OBEis 20 unit2. Find the perpendicular

distance fromB to OA

[2 marks]

Diberi bahawa 4x unit dan luas segitiga OBEialah 20 unit2. Kirakan jarak serenjang dariB ke OA.

[2 markah]



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10

9 Diagram 9 shows OQRS is a sector of a circle with centre O. SOP is a straight line and OPQ is a

right angle tringle.Rajah 9 menunjukkan OQRS ialah sebuah sektor bulatan yang berpusat di O. SOP ialah garislurus dan

OPQ ialah sebuah segitiga bersudut tegak.

Given that OP = 12 cm, q 30OPQ and the length of the arc QR is cm2

S.

Diberi OP = 12 cm, q 30OPQ dan panjang lengkok QR ialah cm2

S.

Find,Cari,

(a) the length, in cm, of OQ [2 marks] panjang , dalam cm, bagi OQ [2markah]

(b) QOR , in radians, [2 marks]

QOR , dalam radian, [2 markah]

(c) the area, in cm2, of the sectorROS, [3 marks]

luas, dalam cm2, bagi sektorROS, [3 markah]

(d) the perimeter, in cm, of the shaded region. [3 marks] perimeter, dalam cm, bagi rantau berlorek. [3markah]

Diagram 9Rajah 9



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11

10 Diagram 10 shows the straight liney = -x + k touching the curvey = 3x x2

at pointA.Rajah 10 menunjukkan garislurusy = - x + k menyentuh lengkungy = 3x x2pada titikA.

Diagram 10Rajah 10

Find,Cari,

(a) the value ofk [2 marks]nilai k [2 markah]

(b) the coordinates of pointA [2 marks]titik koordinatA [2 markah]

(c) the area of the shaded region [3 marks]luas rantau berlorek [3 markah]

(d) the volume generated,in terms ofS , when the region bounded by the curvey = 3x x2

and thex-axis

is revolved through 360 about thex-axis. [3 marks]isipadu janaan apabila rantau yang dibatasi oleh lengkungy = 3x x2 dan paksi -x dikisarkan melalui 360

pada paksi -x. [3 markah]



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12

11 (a) In a survey carried out in a school, it is found that 3 out of 5 students have computer at home. If10 students from that school are chosen at random, calculate the probability thatDalam suatu soalselidik yang telah dijalankan di sebuah sekolah, didapati 3 daripada 5 orang pelajar

mempunyai komputer di rumah. Sekiranya 10 orang pelajar dipilih secara rawak, hitung kebarangkalian

(i) exactly 7 students have computer at home

tepat 7 orang pelajar mempunyai komputer di rumah(ii) at least 2 students have computer at home

sekurang-kurangnya 2 orang pelajar mempunyai komputer di rumah

[ 5 marks] [5 markah]

(b) The mass of a packet of cake produced by a factory is normally distributed with the mean of

350g and a variance of 25g2.

Jisim bagi sebungkus kek yang dihasilkan oleh sebuah kilang bertaburan normal, dengan minnya ialah

350g dan varians 25g2.

Find,

Cari,(i) the probability that the mass of a packet of cake chosen at random will be less than 345g,

kebarangkalian sebungkus kek yang dipilih secara rawak mempunyai jisim kurang daripada

345g,

(ii) the number of the packet of cakes whose masses exceed 342g if the factory produced

1500 packets of cake daily.Bilangan bungkus kek yang berjisim lebih daripada 342g yang dapat dihasilkan oleh kilang itu

jika ia menghasilkan 1500 bungkus kek sehari.

[5 marks] [5 markah]



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13

Section C

[20 marks]

[ 20 markah]

Answertwo questions from this section.

Jawabdua soalan dalam bahagian ini

12 A product is make up of four components,A,B, CandD .Table 12 shows the prices of the four

components in the year 2004 and 2005 as well as their respective weightages.Suatu keluaran dihasilkan daripada gabungan empat komponen iaituA,B, CdanD. Jadual 12 menunjukkan

harga setiap komponen pada tahun 2004 dan 2005 serta pemberat masing-masing.

Componentkomponen

Price/harga(RM) Price index for the year 2005based on the year 2004

Index harga tahun 2005

berasaskan tahun 2004

WeightagepemberatYear/tahun

2004

Year/tahun

2005

A 90 x 150 2

B 60 90 150 m

C y 100 125 4

D 30 42 z 8

Table 12Jadual 12

(a) Calculate the values ofx,y danz [3 marks]Hitungkan nilai bagix,y, danz [3 markah]

(b) Given that the composite index of the product in the year 2005 based on the year 2004 was 141,

find the value ofm. [3 marks]

Diberi indeks gubahan bagi keluaran itu pada tahun 2005 berasaskan tahun 2004 ialah 141, Cari nilai m.[3 markah]

(c) If the product is sold for RM350 a unit in the year 2004. Calculate the selling price of the

product in the year 2005 in order to maintain the same profit. [2 marks]Sekiranya keluaran itu dijual dengan harga RM350 pada tahun 2004. Hitungkan harganya pada tahun 2005

jika keuntungan yang sama dikekalkan. [markah]

(d) If the prices of all components of the product was increased by 50% from the year 2004 to theyear 2006, find the composite index of the product in the year 2006 based on the year 2005.

[2 marks]

Sekiranya harga bagi semua komponen keluaran itu meningkat sebanyak 50% dari tahun 2004 ke tahun2006, cari indeks gubahan bagi keluaran itu pada tahun 2006 berasaskan tahun 2005.

[2 markah]



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14

13 Diagram 13 shows a pyramid with a triangular base. The peakVis vertically above P.Rajah 13 menunjukkan sebuah piramid dengan tapak berbentuk segitiga. PuncakVterletak tegak di atas P.

V

6 cm

8 cm

11 cm

Q

R

P

Diagram 13Rajah 13

Given that PR = 8 cm, PV= 6 cm, VQ = 11 cm and q 40PQR ,

Diberi PR = 8 cm, PV= 6 cm, VQ = 11 cm dan q 40PQR ,

Find,Cari,

(a) the length, in cm, ofPQ; correct to 2 decimal places [2 marks] panjang PQ, dalam cm; betul kepada 2 tempat perpuluhan [2markah]

(b) the length, in cm, ofQR [4 marks]panjang QR, dalam cm [4 markah]

(c) the area, in cm2, of the inclined plane QVR [4 marks]

luas , dalam cm2 bagi permukaan condong QVR [4 markah]



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15

14 Use graph paper to answer this question.Gunakan kertas graf untuk menjawab soalan ini.

On a particular ferry trip to Langkawi, the passengers in the ferry comprisex adults andy

children, with each adult paying a fare of RM40 and each children paying a fare of RM30. Thisparticular ferry trip is based on the following constraints.

Pada suatu perjalanan feri pergi ke Langkawi, penumpang feri itu mengandungix orang dewasa danyorang kanak-kanak di mana setiap dewasa dan kanak-kanak perlu membayar tambang RM40 dan RM30

masing-masing. Perjalanan feri itu perlu mematuhi syarat-syarat berikut.

1 : The ferry can accommodate up to 40 passengers onlyFeri itu boleh muat sebanyak 40 orang penumpang sahaja.

11 : The amount collected from the passengers fares must at least RM360, in

order for the ferry company to make profit.Jumlah tambang yang dikutip daripada penumpang mesti sekurang-kurangnya

RM360 supaya syarikat feri itu boleh memperoleh keuntungan daripada perjalanan

itu.

III : The number of adult passengers is not more than twice the number of childrenBilangan penumpang dewasa tidak lebih daripada dua kali ganda bilangan penumpangkanak-kanak.

(a) Write three inequalities, other than 0tx and 0ty , which satisfy the above constraints.

[3 marks]Tulis tiga ketaksamaan, selain daripada 0tx dan 0ty , yang mematuhi syarat- syarat di atas.

[3 markah]

(b) Using a scale of 2 cm to 5 passengers on both axes, construct and shade the region R, which

satisfies all the above constraints. [3 marks]Dengan menggunakan skala 2 cm kepada 5 orang penumpang bagi kedua-dua paksi, bina dan lorekkan

rantau R yang mematuhi semua syarat-syarat di atas. [3 markah]

(c) By using your graph from (b), findDengan menggunakan graf anda dari (b), cari

(i) the minimum number of passengers on this ferry trip if there are five adult passengers

only.bilangan minima penumpang dalam perjalanan feri ini jika hanya ada lima orang penumpang

dewasa sahaja.

(ii) the maximum amount collected from the fares of the passengers.amaun maksima tambang penumpang

[4 marks][4 markah]



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16

15 A particle moves along a straight line and passes through a fixed point O. Its velocity, V ms-1

,is given by v = t

2- 9t+ 18, where t is the time in second after passing through O.

[Assume motion to the right is positive]Suatu zarah bergerak sepanjang garislurus dan melalui titik tetap O. Diberi halaju zarah itu, Vms-1, ialah

v = t2 - 9t+ 18, Di mana t ialah masa dalam saat selepas zarah itu melalui titikO.

[Anggap gerakkan ke kanan sebagai positif]

Find,Cari,

(a) the initial velocity, in ms-1

, of the particle. [1 mark]halaju awal, dalam ms-1, bagi zarah itu [1markah]

(b) the maximum velocity , in ms-1

, of the particle. [3 marks]halaju maksima, dalam ms-1, bagi zarah itu [3markah]

(c) the range of values of t when the particle moves to the left [2 marks]Julat nilai t apabila zarah itu bergerak ke arah kiri [2 markah]

(d) the total distance, in m, travelled by the particle in the first 5 seconds [4 marks]Jumlah jarak, dalam m, yang dilalui oleh zarah itu dalam 5 saat pertama [4 markah]

END OF QUESTION PAPER

KERTAS SOALAN TAMAT



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36/106

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3472/1

Additional

Mathematics

Paper 1

Sept

2010



DENGAN KERJASAMA




ADDITIONAL MATHEMATICS

Paper 1

MARKING SCHEME

This marking scheme consists of 5 printed pages



37/106

PAPER1

QUESTION

NUMBERSWORKING MARKS

FULL

MARKS

1

(a) 3

(b) 1

1

1

2

2

3,3

x2+1=10or 11 xg

2

B1 2

3

4

23

4

1 pandk

4

23

4

1 pork

614 pkork

pxk 2)21(

4

B3

B2

B1

4

4

2 , -2

028

pp

02)

1

(7)

1

(

2 pppp

3

B2

B1

3

5

a) -4

b) 2

c) x = 4

1

1

1

3

6

3 9x d d

2

( 9)( 3) 0

6 27 0

x x

x x

d

d

3

B2

B13

7

2

13x

4 4 6 9x x

033 )32(3)1(4 xx

3

B2

B1

3

3 9or or -3 and 9



38/106

QUESTION


FULL

MARKS

8

7 7 7

7 7

7

1

log 2 log 7 log 5

log 2 log 7

28

log 10

h k

4

B3

B2

B1

4

9

1

4log

31

4

3

3x

x

x

x

x

3

B2

B13

10

a)t=12

t8=16t

b)240

10

[(2(6) 9(4)]2

2

B1

2

B1

4

11

a) n=6

5.01

)5.01(64

126

n

b) 128fs

5.01

64

fs

2

B1

2

B1

4

12

m = -6 and n = 3

m = -6 or n = 3

n

m

n 6

0 and n

m

n 12

2

n

m

n

60 or

n

m

n

122

4

B3

B2

B1

4

13

r=6and7

4t

3

3



39/106

QUESTION


FULL

MARKS

4

7t orr=6

5

)4(42

r or

5

843

t

B2

B1

14 (a) 10

6 8i j

b) )43(5

1ji

2

B1

1

3

15(a) PY

o= p +

3

4q

PY

o= OQPO

o

o

4

3

(b) QXo

=q+2

3p

QXo

= OPQOo

o

3

2

2

B1

2

B1

4

16a)

q

pq 22

b) 22 pq

p

22 pq

p

1

2

B1

3

17 70.53 ,180 , 289.47$ $ $

B3: 70.53 ,180$ $

B2:(3cosT 1)(cosT +1)=0

B1:2cos2T 1

4

B3

B2

B1

4



40/106

QUESTION


FULL

MARKS

18

2 2

38.4

1 116 0.4 8 0.4

2 2

S

S Su u u u

2 21 116 0.4 8 0.42 2

orS Su u u u

3

B2

B1

3

19

4

2 (4)( 0.5)

2dA

rdr

S

S

S

3

B2

B1

3

2023

B2:

2 25 1[ ] 10 3

2 2m m

B1:

5 52

1 1

2 ( )2

mxor mx dx g x dx

3

B2

B1

3

21

2

2

31 var 144

6(5) 1 6 (4)

6(5) 1 6 (4)

median and iance

and

or

3

B2

B1

3

22

pp

p

p

p

6

7

4

6

8

3

B2

B1

3

23 (a) 8008

(b) 7062

B1:4 12 4 12 4 12

2 8 3 7 4 6C C C C C C Or

4 12 4 12

1 9 0 108008 C C C C

3

2

B1

3

or12.57



41/106

QUESTION


FULL

MARKS

24 (a) 20

B1: )4.0)(6.0(N =5

24

(b) 12

2

B1

1 3

25 (a) 0.0985

(b) 82.42

B1:85

1.292

orP

1

2

B1

3



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Additional

Mathematics

Paper 2Sept

2010



DENGAN KERJASAMA





Paper 2

MARKING SCHEME

This marking scheme consists of 13 printed pages



43/106

Question Mark Scheme of Paper 2 Trial SPM 2010 Melaka Sub

Marks

Total

Marks

1.n= -6 4m or n = m2 +m-2 or

4

6 nm

m2+m+6+4m=2 or 4m+m2+m-2+8=2 or 2)4

6(2)4

6( nnn

(m+4)(m+1)=0 or (n-10)(n+2)=0 or use formula/completing the square

m= -4, -1 or n=10, -2

n=10, -2 or m= -4, -1

P1

K1

K1

N1

N1

5

2.(a)

(b)

(c)

m2 = 2

y -5= 2(x+1) or equivalent

y = 2x +7

Solve simultaneous equations: 22

172 xx

E( -2, 3)

)3,2()2

5,2

)1((

yx

C( -3, 1)

K1

K1

N1

K1

N1

K1

N1

7

3.(a)

(b)

Shape of sin x

Graph of sin x shifted up 1 unit

Miximum = 4, minimum = -2

1 cycles in S

2

30 ddx

12

xyS

or equivalent

Sketch the straight line involves x and y

Number of solutions = 4

P1

P1

P1

P1

N1

K1

N1

7

4.(a) Gradient of tangent = 5

kx2-x = 5

substitute x = 1 to kx2-x = 5

K1

K1

K1

xSx

4x

1

-2

02

S

2

3S

3

y



44/106

(b)

k = 6

cxx

y 23

6 23

c2

)1(

3

)1(62

23

2

7

22

23

xxy or equivalent

N1

K1

K1

N1 7

5.(a)(i)

(ii)

(b)

L = 20.5 F = 57 fQ3 = 28

1028

57)100(4

3

5.203

Q

= 26.93

100

)5.45(6)5.35(9)5.25(28)5.15(32)5.5(25 x

=19.4

222222

4.19100

)5.45(6)5.35(9)5.25(28)5.15(32)5.5(25

V

= 11.30

222

2

98

20401940

98

204050415

V

= 126.02

P1

K1

N1

K1

K1

N1

K1

N1

8

6. (a)

(b)

d = 2r or 2r, 4r, 6r

d = 4r - 2r = 6r - 4r

2r = 2r

T10 = 4 + 9(4) or T10 = 2r + 9 (2r )= 40 = 20 (r)

Circumference = 2(40) = 20 (4)

= 80 = 80

P1

K1

N1

K1

N1

N1

6

7.(a)

(b)

(c)

(i)

(ii)

log10x 0.15 0.28 0.40 0.51 0.61 0.74

log10y 0.52 0.72 0.90 1.08 1.20 1.42

Refer to the appendix

One point correctly plotted with uniform scales

6 points correctly plotted with uniform scales

Line of best fit

xkpy 101010 log5loglog

-5k=1.52

35.025.0 lk

log10p = 0.29

N1

N1

K1

N1

N1

P1

K1

N1

K1

N1



45/106

0.29.1 lp 10

8(a)(i)

(ii)

(b)

(c)

OBAOAB or equivalent

yx 36

xyOD 2

1

4

9

)2

1

4

9( xymOC

)36( yxnBC

)36()2

1

4

9(3 yxnxymy

5

6m

10

1n

x 8 x h = 20

h = 5

K1

N1

N1

P1

P1

K1

N1

N1

K1

N1

10

9(a)

(b)

(c)

(d)

1230sin

OQq or equivalent

OQ = 6

TS

62

QOR rad12

ST // 0.2618 rad

radradROS 833.1/127/1051560180 Sqqqq

Area of sector ROS = ROSuu 262

1

=32.99 or 10.5

Perimeter of shaded region = )5.52sin6(2)12

7(6 qS

=20.52

K1

N1

K1

N1

P1

K1

N1

K1K1

N1

10

10(a)

(b)

(c)

Use b2 4ac = 0

(-4)2 4(1)k =0

k = 4

Solve equation : (x 2)(x 2) = 0

A(2, 2)3

2

32

32

3

xx

3

2

2

)2(3

3

3

2

)3(3 3232

K1

N1

K1

N1

K1

K1

N1



46/106

(d)

=6

7

3

0

543

54

6

3

9

xxxS

= 05

34)3(6

3)3(9

543

S

= 8.1

K1

K1

N1

10

11(a)(i)

(ii)

(b)(i)

(ii)

377

10 )4.0()6.0(C

= 0.215

1 P(x=0) P(x=1) or P(x=2)+P(x=3)+P(x+4)+ .+P(x=10)

= 91110100

010 )4.0()6.0()4.0()6.0(1 CC

= 0.9983

)5

350345(

zP

= 0.1587 // 0.15866

P(x >342) = 1 P(z > 1.6) or other valid method

Number of cakes = 0.9452 x 1500

= 1417 // 1418

K1

N1

P1

K1

N1

K1

N1

K1

K1

N1

10

12(a)

(b)

(c)

(d)

Use 100

0

1 u

P

PI

x = 135, y = 80, z = 140

141842

)8(140)4(125150)2(150

m

m

m = 6

141100350

2005 uP

P2005 = 493.50

100141

11502005/2006 uuI

= 106.38

K1

N2,1,0

K1K1

N1

K1

N1

K1

N110



47/106


48/106

Substitute t = 3 or t = 5 into ttt

s 182

9

3

23

S3 = 22.5

S5 =6

119

Total distance traveled= )

6

1195.22()05.22(

6

525

OR5

3

233

0

23

182

9

318

2

9

3

ttt

tt

)3(18

2

)3(9

3

3)5(18

2

)5(9

3

50)3(18

2

)3(9

3

3232323

=6

525

K1

K1

N1

K1K1

K1

N1

10



49/106

7(a)

14(b)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8 lg y

(0.15,0.52)

(0.28,0.72)

(0.40,0.90)

(0.51,1.08)

(0.61,1.20)

(0.74,1.42)



50/106

Rx+y=40

x2y

4x+3y=36



51/106

1

PEPERIKSAAN PERCUBAAN SPM TAHUN 2010

KERTAS SELARAS NEGERI MELAKA

JADUAL SPESIFIKASI UJIAN MATEMATIK TAMBAHAN

(PAPER 1 & PAPER 2)

TOPICSTotal

Question

s PAPER 1PAPER 2

Section A Section B Section C

No

Marks

No

Marks

No

Marks

No

Marks

1) A1 Functions (F4) 3

1 2

2 4

3 3

2) A2 Quadratic Equations (F4) 1 4 3 2 7

3) A3 Quadratic Functions (F4) 25 2

6 3

4) A4 Simultaneous Equations (F4) 1 - - 1 5

5) A5 Indices and Logarithms (F4) 27 3

8 3

6) A6 Progressions (F5) 3

9 3 6 6

10 2

11 4

7) A7 Linear Law (F5) 1 - - 8 10

8) T1 Circular Measure (F4) 1 12 4 10 10

9) G2 Vectors (F5) 213 4 5 8

14 4

10) G1 Coordinate Geometry (F4) 1 15 3 9 10

11) T2 Trigonometric Functions (F5) 216 3 4 617 3

12) C2 Integration (F5) 218 3 7 10

19 4

13) C1 Differentiation (F4) 1 20 3 3 7

14) S2 Permutations/Combinations (F5) 1 21 4

15) S3 Probability (F5) 1 22 3

16) Statistics ( F4) 1 23 3

17) S4 Probability Distributions (F5) 324 3 11 10

25 4

18) AST1 Solution of Triangles (F4) 1 - - 12 1019) ASS1 Index Number (F4) 1 - - 13 10

20) AST2 Motion Along a Straight Line

(F5)1 - - 15 10

21) ASS2 Linear Programming (F5) 1 - - 14 10

TOTAL 25 80 6 40 5 50 4 40



52/106

2

TEST SPECIFICATION TABLE

KERTAS SELARAS NEGERI MELAKA

JADUAL SPESIFIKASI UJIAN MATEMATIK TAMBAHAN

(PAPER 1 & PAPER 2)

Paper 1

Question Topics Construct Level ofDifficulty Marks

1 Functions

Knowledge

Interpret from ordered pairs.

Find object and determine the type of relation.Find the range of relation

L 2

2 FunctionsUnderstanding

Inverse function and composite function.L 4

3. Function

Understanding

Determine one of the functions in a given

composite function given the other related

function..

L 3

4QuadraticEquations

Understanding

Find the roots for the equation that cannot be

factorized.

I 3

5QuadraticFunctions

Understanding

Find the range of values for quadratic

inequalities.

I 3

6Quadratic

Functions

Application

Find the axis of symmetry and minimum point

from completing the square method.

H 3

7Indices and

LogarithmsApplication

Solving equation involving indices.L 3

8Indices andLogarithms

ApplicationSolve problems involving the change of base and

laws of logarithms

H 3

9 ProgressionsApplication

Find the value a and Sun to n terms for API 3

11 Progressions

Application

Find the value of n, given the sum of the first nterms of G P

I 4

12 ProgressionApplication

Geometric Progression: Sum to infinityI 2

13 Linear LawApplication

Given the line of best fit; convert to linear formand find the gradient andy-intercept .

H 4



53/106


54/106

4


PAPER 2

TEST SPECIFICTION TABLE

Question Topics Construct Level of Difficulty Marks

1 SimultaneousEquations

Application

Solving two simultaneous equations :

one linear equation and one non-linear

equation.

L 5

2 Integration (a) Application

Find the unknown from gradient

function.

(b) Application

By integration, find the the equation

of the curve.

L

I

3

3

3 Progressions (a) Problem Solving / Application

Find the a from Tn.

Application

(b) Find the Sn(c) Find n from given Tn

L

I

I

2

2

2

4 Trigonometric

Functions

(a) Application

Prove the identity.

(b) Application

Sketch the trigonometric graph and a

straight line.Find the number of solutions from the

graph.

L

H

2

6

5 Coordinate

Geometry

Application

(a) Find the coordinate of a point

divides a segment internally at a

ratio.

(b) Find the equation of a

perpendicular line.

(c) Find the area of parallelogram

L

I

I

2

3

3

6 Statistics (a) Application

Find the mean and standard deviation

from the Histogram.

(b) Understanding

The effect of change to the mean and

standard deviation.

I

L

4

3

7 Linear Law (a) Understanding

Plot the graph and draw the line of best

fit.

(b) Application

Change the equation to linear form.

Use the gradient and y-intercept to find

the unknowns.

I

H

4

6



55/106

5

8 Vectors (a) Application

Find the resultant vector using polygon

law.

(b) Application

Express a vector as a combination ofother vectors.

(c) Understanding

Solve simultaneous equations to find theconstants.

(d) UnderstandingNegative vector.

L

I

I

L

2

3

4

1

9 Circular

Measure

(a) Application

Find the angle of sector using

trigonometry.

(b) Application

Find the perimeter of shaded region.

(c) Application

Find the area of triangle.

(d) ApplicationFind the area of shaded region.

L

I

L

H

2

3

2

3

10 Progressions (a) Understanding

Show the areas form a geometric

progression.

(b) Problem Solving/Application

(i) Find n from Tn.

(ii) Find the sum of specific terms.

(iii) Find Sum to Infinity

L

I

I

L

2

3

3

2

11 Probability

Distributions

(a) Application

Find the area of the shaded region.(b) Application

Find the minimum point of the curve.

(c) Application

Find the volume generated.

H

I

H

3

3

4

12 Solutions of

Triangle

(a) Application

Use the Sine Rule or Cosine Rule to find

the length.(b) Application

Use the Sine Rule or Cosine Rule to find

the angle.

(c) Application

Use the area formula to find the area oftriangle.

(d) Application

Use the Cosine Rule to find the length.

L

L

L

H

2

3

2

3

13 Index Number Problem solving(a) (i) Find the price of the base year.

(ii) Find the price index.

(b) (i) Given the composite function,

find the price index.

(ii) Find the cost of item in the base

L

H

I

L

2

3

3

2



56/106

6

year, given the composite index.

14 Motion Along a

Straight Line

Problem solvinga). Determine displacement of a particlefrom a fixed point.b). Determine the total distance traveledby a particle over a time interval using

graphical methodc). Determine velocity function of aparticle by differentiation.d) Determine instantaneous velocity of aparticlee ) Determine acceleration function of aparticle by differentiation

L

L

H

L

H

2

2

2

2

2

15 Linear

Programming

Problem solving

a) writing linear inequalities and

equations describing asituation.

b) shading the region of feasible

solutions.

c) determining and drawing the

objective functionax + by = k where a, b and k

are constants.

d) determining graphically the

optimum value of the

objective function.

L

L

H

H

3

3

2

2

Level of Difficulty : L LowI Intermediate

H- High

JOB DISTRIBUTION

Paper 1

No 1 - 7 Horsiah No 8 - 14 Saripah

No 15 20 GanNo 21 24 Kee

Paper 2

Part A and B

No 1 4 Horsiah

No 5 7 Saripah

No 8 9 KeeNo 10 - 11 Gan

Paper 2

Part C

No 12 Horsiah

No 13 Kee

No 14 GanNo 15 Saripah



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SPM Trial 2010 AddMath Q&A (Melaka)

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Transcript of SPM Trial 2010 AddMath Q&A (Melaka)