SOALAN ADD MATHS KERTAS 2 PP ZON A 2007

8/14/2019 SOALAN ADD MATHS KERTAS 2 PP ZON A 2007

1/11

SULIT 1 3472/2

3472/2

Matematik

Tambahan

Kertas 2

SEPTEMBER

20072 jam

SEKOLAH-SEKOLAH KUCHING ZON A

PEPERIKSAAN PERCUBAAN SPM 2007

MATEMATIK TAMBAHAN

Kertas 2

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini mengandungi tiga bahagian : Bahagian A,

BahagianBdanBahagian C.

2. Jawab semua soalan dalam Bahagian A , empat soalan daripada Bahagian Bdan dua soalan daripada Bahagian C.

3. Bagi setiap soalan berikan satu jawapan/penyelesaian sahaja.

4. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantuanda untuk mendapatkan markah.

5. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan.

6. Markah yang diperuntukan bagi setiap soalan atau ceraian soalan ditunjukkandalam kurungan .

7. Satu senarai rumus disediakan di halaman 2 hingga 3.

8. Kertas graf dan buku sifir matematik empat angka disediakan.

9. Adalah dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

Kertas soalan ini mengandungi 10 halaman bercetak


2/11

SULIT 3472/2

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

the ones commonly used.

ALGEBRA

1

2 4

2

b b ac

x a

2 am an = a m + n

3 am an = a m n

4 (am)n = a nm

5 log amn = log am + log an

6 log an

m= log am log an

7 log amn = n log am

8 log a b = 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

rann

=

1

)1(

1

)1(, (r 1)

13 r

aS = 1 , r


3/11

SULIT 3472/2

STATISTICS

3

1 Arc length,s = r

2 Area of sector,A =21

2r

3 sin 2A + cos 2A = 1

4 sec2A = 1 + tan2A

5 cosec2A = 1 + cot2A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A sin2A

= 2 cos2A 1= 1 2 sin2A

8 tan 2A =A

A2

tan1

tan2

TRIGONOMETRY

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosBsinA sinB

11 tan (A B) =BA

BA

tantan1

tantan

12C

c

B

b

A

a

sinsinsin==

13 a2 = b2 + c2 2bc cosA

14 Area of triangle = Cabsin2

1

1 x =N

x

2 x =

f

fx

3 =2( )x x

N

=2

2x xN

4 =

2( )f x x

f

=

22fx x

f

5 m = Cf

FN

Lm

+ 2

1

61

0

100Q

IQ

71 1

1

w II

w

8)!(

!rn

nPrn

9!)!(

!

rrn

nCr

n

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

11 P(X=r) = rnrrn qpC , p + q = 112 Mean, = np

13 npq=

14 z=

x


4/11

Section A

[40 marks]

Answerallquestions in this section.

1 Solve the simultaneous equations 27x 9y = 7x2y2 = 18[5 marks]

2 (a) The sum of the first 5 terms of an arithmetic progression is 100 and the sum of the

next 3 terms is 24. Find

(i) the first term and the common difference, [3 marks]

(ii) the sum of all terms from the 5th term to the 12th term. [2 marks]

(b) Write the recurring decimal 0272727 as a single fraction in its lowest terms.[2 marks]

3 (a) The curvey = hx2 + kx has a gradient of 5 at (1, 2). Find

(i) the value of h and ofk,

(ii) the equation of the normal to the curve at (1, 2). [4 marks]

(b) Given thaty =x3, find the value ofdx

dywhenx = 6. Hence, estimate the value of 5.983

[3 marks]

4 Table 1 shows the Additional Mathematics monthly test marks for Azimah and Airina.

Name Test marks

Azimah 54 59 83 96 93

Airina 71 72 65 84 93

(a) Calculate the range of their marks. [2 marks]

(b) Calculate their mean and standard deviation. [3 marks]

(c) Hence, identify who has a more consistence result and why. [1 mark]

4

TABLE 1


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SULIT 3472/2

5 In Diagram 1, EAD is a sector of a circle with centre E, CDFis a straight line andAFis

the tangent to the circle at pointA. AB,BCand CD are three sides of a rectangle.

Given thatAB = 12 cm andBC= 20 cm.

Calculate

(a) AED, in radian, [2 marks]

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

6. In Diagram 2, ABCD is a quadrilateral, ACD = 90 and AEC is a straight line.

Given that 16xAB

, 4yBC

, 8 10x yAD

, and 3 AE EC .

(a) Express, in terms ofx and y :

(i)AC

(ii) BE

[3 marks]

(b) Show that BE is parallel to CD . [2 marks]

(c) If 5cmy and 60BCE , findAC

. [3 marks]

3472/2 2007 Hak Cipta Sekolah-Sekolah Kuching Zon A SULIT

DIAGRAM 2

B

A

E

C

D

DIAGRAM 1

AB

C F

E

D

[Lihat sebelah

5


6/11

Section B

[40 marks]

Answerfour questions from this section.

7 Use the graph paper to answer this question.

The variablesx andy are known to be related by the equationy = (a + b) 2 ax where a and

b are constants. The table 2 shows the experimental values of quantityx andy.

(a) Reduce the equation y = (a + b) 2ax to the linear form Y= mX+ c. [1 marks]

(b) Using a scale of 2 cm to 02 units on both axes, plot a graph of log 10y againstlog 10x and draw a line of best fit. [5 marks]

(c) Use your graph to find the value of

(i) a, [2 marks]

(ii) b. [2 marks]

8 (a) Prove thatsin 2 cos

1 sin cos 2

A A

A A

= cotA. [3 marks]

(b) Sketch the graph ofy = 5 sin 2x for 0 x 2. Hence, sketch a suitable straight line

to determine the number of solutions of the equation sin x cos x +1

2x =

3

5for

0 x 2. State the number of solutions. [7 marks]


x 20 32 71 158 631

y 30 40 63 100 224

TABLE 2


7/11

SULIT 3472/2

9 (a) Peter bought 12 mangoes. The probability that a mango bought by Peter is rotten is

20%. Find the probability that of the 12 mangoes, there is

(i) Find the probability that of the 12 mangoes, there is exactly 9 mangoes that arerotten,

(ii) Find the standard deviation of the rotten mangoes.[5 marks]

(b) The marks of Additional Mathematics of a certain examination is normally distributed

with mean 50 and variance 64. Find the probability that a student chosen at randomhas

(i) not more than 40 marks,

(ii) between 60 and 70 marks.

[5 marks]

10 Solution to this question by scale drawing will not be accepted.

Diagram 3 shows two straight linesPR andPS. The equation ofPR is 2 5 0.y x The

point Slies on thex-axis and Q is the midpoint ofPR.

y

Sx

OR

Q

P(3, 4)

DIAGRAM 3

(a) Find

(i) the coordinates ofS, [2 marks]

(ii) the equation of the perpendicular bisector ofPR. [3 marks]

(b) A point Mlies on the perpendicular bisector ofPR and the straight line SMis parallel

to the linePR.


7


8/11

(i) Find the coordinates of M. [3 marks]

(ii) Hence, show thatPQMSis a square. [2 marks]

11 (a) Diagram 4 shows a curvey2 = 2x + 1and straight linesx = 1 andx = k.

Given the volume of the solid generated when the shaded region is rotated about the

x-axis through 360 is 18 unit3

, find the value ofk. [6 marks]

(b) Find the equation of the normal to the curvey = 4x3 +2

5

x 4 atP(1, 5). [4 marks]

Section C

[20 marks]

Answertwo questions from this section.

12 Diagram 5 shows a cyclic quadrilateralABCD.

Given that = 130CBA , 7 cmAB = , 4 cmBC= and 8 cmCD = .Find

(a) the length, in cm, ofAC, [3 marks]


CD

4 cm

130

8 cm

B

y

O x1

y2 = 2x + 1

kDIAGRAM 4

7 cm DIAGRAM 5

[Lihat sebelah


9/11

SULIT 3472/2

(b) ACD , [3 marks]

(c) the area, in cm2, of the cyclic quadrilateral ABCD . [4 marks]

13 A particle moves along a straight line so that its velocity, v m s1, is given by

6104 2 += ttv , where tis the time in seconds after passing through O.

Find

(a) (i) the initial velocity of the particle,

(ii) the time at which the particle is at instantaneous rest,

[4 marks]

(b) the maximum velocity of the particle, [3 marks]

(c) the distance travelled from the beginning until the particle is at first instantaneousrest. [3 marks]

14 A bakery sells two types of biscuits, A andB. Table 3 shows the mass of flour and butter

required to make a pack of biscuitA and a pack of biscuitB.

BiscuitMass (g)

Flour Butter

A 120 300

B 240 200

The bakery makesx packs of biscuitA andy packs of biscuitB per day. The making of

biscuits per day is based on the following constraints :

I : The total mass of flour used is not more than 96 kg.

II : The total mass of butter used is at most 15 kg.

III : The ratio of the number of packs of biscuit A to the number of packs of

biscuitB is at most 4 : 1.

(a) Write three inequalities, other than 0x and 0y , which satisfy all of the aboveconstraints. [3 marks]

(b) Using a scale of 2 cm to 10 packs on both axes, construct and shade the region Rwhich satisfies all of the above constraints. [3 marks]

(c) By using your graph from 14(b), find

(i) the maximum and the minimum number of packs of biscuit B, if 20 packsof biscuitsA are produced per day.


TABLE 3

9


10/11

(ii) the maximum total profit per day if the profit from one pack of biscuitA is

RM1.00 and from one pack of biscuitB is RM1.50.

[4 marks]

15 Table 4 shows the prices of 3 items with their price per kg for the year 2004 and 2006.

Item Price per kg2004 2006

Weightage

A RM 1.00 RM 2.00 5

B RM 1.50 RM1.80 3

C RM2.50 RM3.00 2

(a) Find the composite index for the year 2006 based on the year 2004. [5 marks]

(b) If another item D is to be included with weightage 2, find the index number for the

item D for the year 2006 based on 2004 if the composite index number remains

unchanged. [3 marks]

(c) Find the price per kg of the itemD for the year 2004 if the price per kg for the year

2006 is RM6.00. [2 marks]

END OF QUESTION PAPER


TABLE 4

[Lihat sebelah


11/11

SULIT 3472/2

NAMA : ..

KELAS : ..

Arahan Kepada Calon

1 Tulis nama dan kelas anda pada ruang yang disediakan.

2 Tanda ( ) untuk soalan yang dijawab.

3

Ceraikan helaian ini dan ikat sebagai muka hadapan bersama-sama dengan buku

jawapan.


KodPemeriksa

Bahagian Soalan

Soalan

dijawab

Markah

Penuh Markah Diperoleh

A

1 5

2 7

3 7

4 6

5 7

6 8

B

7 10

8 10

9 10

10 10

11 10

C

12 10

13 10

14 10

15 10

Jumlah

11

SOALAN ADD MATHS KERTAS 2 PP ZON A 2007

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