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SULIT 3472/1 Matematik Tambahan Kertas 1 2 Jam Mei 2006 SEKTOR SEKOLAH BERASRAMA PENUH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 4 2006 NAMA:…………………………………………………… TINGKATAN: …………….. Kod PemeriksaSoalanMarkah PenuhMarkah Di peroleh122333435462738393104113 1231331431531631731841932042142 23233244254Total80 MATEMATIK TAMBAHAN Kertas 1 Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. Kertas soalan ini mengandungi 25 soalan. 2. Jawab semua soalan. Bagi setiap soalan berikan SATU jawapan sahaja. Jawapan hendaklah ditulis pada ruang yang disediakan dalam kertas soalan. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk mendapatkan markah. Sekiranya anda hendak menukar jawapan, batalkan kerja mengira yang telah dibuat. Kemudian tulislah jawapan yang baru. Rajah yang mengiringi soalan ini tidak dilukiskan mengikut skala kecuali dinyatakan. Markah yang diperuntukan bagi setiap soalan atau ceraian soalan ditunjukkan dalam kurungan. Satu senarai rumus disediakan di halaman 2 10. Buku sifir matematik empat angka disediakan. 11. Penggunaan kalkulator saintifik yang tidak boleh diprogramkan adalah dibenarkan. 12. Kertas soalan ini hendaklah diserahkan pada akhir peperiksaan .

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SULIT 3472/1MatematikTambahan Kertas 12 Jam Mei 2006

SEKTOR SEKOLAH BERASRAMA PENUHKEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 4 2006

Kertas soalan ini mengandungi 12 halaman bercetak[Lihat sebelah

NAMA:…………………………………………………… TINGKATAN: ……………..

Kod PemeriksaSoalanMarkah PenuhMarkah Di

peroleh122333435462738393104113123133143153163173184193204214223233244254Total

80

MATEMATIK TAMBAHANKertas 1Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini mengandungi 25 soalan.

2. Jawab semua soalan. Bagi setiap soalan berikan SATU jawapan sahaja.

Jawapan hendaklah ditulis pada ruang yang disediakan dalam kertas soalan.

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

Sekiranya anda hendak menukar jawapan, batalkan kerja mengira yang telah dibuat. Kemudian tulislah jawapan yang baru.

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

Markah yang diperuntukan bagi setiap soalan atau ceraian soalan ditunjukkan dalam kurungan.

Satu senarai rumus disediakan di halaman 2

10. Buku sifir matematik empat angka disediakan. 11. Penggunaan kalkulator saintifik yang tidak boleh diprogramkan adalah dibenarkan.

12. Kertas soalan ini hendaklah diserahkan pada akhir peperiksaan .

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SULIT

INFORMATION FOR CANDIDATES

1. This question paper consists of 25 questions.2. Answer all questions.3. Give only one answer for each question. 4. Write the answers clearly in the space provide in the question paper. 5. Show your working. It may help you to get marks. 6. If you wish to change your answer, cross out the work that you have done. Then write down the new answer.7. The diagram in the questions provided are not drawn to scale unless stated. 8. The marks allocated for each question and sub-part of a question are shown in brackets. 9. A list of formulae is provided on page 2. 10. You may use a non-programmable scientific calculator. 11. This question paper must be handed in at the end of the examination.

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

ALGEBRA

1 x =

2 am an = a m + n

3 am an = a m - n

4 (am) n = a nm

5 loga mn = log am + loga n

6 loga = log am - loga n

7 log a mn = n log a m

8 logab =

[ Lihat sebelah3472/1 SULIT

2

3 A point dividing segment of a line ( x, y) =

4 Area of triangle =

GEOMETRY

1 Distance =

2 Midpoint , (x , y) = ,

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Answer all questions1 Diagram 1 shows the relation between set A and set B.

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1

3

2

4

5

2Set A

4 6 8 10

Set B

DIAGRAM 1

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State

(a) the image of 6, (b) the range of the relation. [2 marks]

Answer : ( a) …..…..………………

( b) ………………………..

2 A function f is defined by for the domain . Find

(a) the image of 2,

(b) the object of 9, (c) the corresponding range.

[3 marks]

Answer: ( a) . …..…..………………

( b) ……………………….

( c ) ………………………

3 Given the function Determine(a) the composite function fg,

(b) the value of gf(- 2). [3 marks]

1

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[4 markah]

Answer : ( a) …………………

( b) ………………….

4 The function f is defined as and the composite function

. Find g (x) . [3 marks]

Answer : ……………………

5 Given that and .

Find(a) the value of k,

(b) the function . [4 marks]

Answer : (a) ………………………

(b) ….. ………………….

6 Simplify and express the quadratic equation in the general form.

[2 marks ].

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Answer : …………………………

7 Determine the roots of the quadratic equation 3x = x + 1. Give your answer correct to four significant figures.

[ 3 marks ]

Answer : …………………………

8 Form a quadratic equation which has the roots and .

Give your answer in the form of ax + bx + c = 0, where a , b and c are constants .

[ 3 marks ]

Answer:………………………….

9 The quadratic equation 3px – 2x = 8 has two equal roots. Find the values of p.

[ 3 marks ]

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Answer : …………………………………

10 Given that and are the roots of equations 2x2 + 7x + 5 + k = 0 , where = 3 .

Find (a) the value of k ,

(b) the value of and .

[ 4 marks ]

Answer: (a) …………………………... (b) …………………………..

11 Given that the graph of the quadratic function f(x) = 2x2 + 4x + k intersects the x – axis at two different points. Find the range of values of k. [ 3 marks ]

Answer : . …………………12 Given that f(x) = -2x2 + 8x + 3 has a maximum value at the point P (a, b), where a

and b are constants. Find the value of a and b. [3 marks]

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(0 , -6 )

(5 , -1 )x

DIAGRAM 2

0

y

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Answer: a = …………………………

b = ………………………

13 Diagram 2 shows that (5 , -1) is the maximum point of the graph f(x) = a (x + p ) 2 + q.

Find the value of a, p and q.

[3 marks ]

Answer : a = ………………

p = ……………...

q = ………………

14 Find the range of values of x when (x - 3)(x + 5) < - 12 .

[ 3 marks ]

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Answer : ……………………..

15 Given that f(x) = 5 + 4x – x 2 , find the range of values of x which satisfies . [ 3 marks ]

Answer: ………………………

16 Solve the equation .

[3 marks]

Answer : …………………….

17 Solve the equation = 3 m -1 .

[3 marks]

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Answer : ………………

18 Express in the simplest form. [4 marks]

Answer : ………………

19 Given that logx3 = h and logx5 = k , express in terms of h and k .

[3 marks]

Answer : ………………..

20 Solve the equation .

[4 marks]

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Answer : ……………………….

21 The point A ( 3, 2 ) is the mid point of RS and the coordinates of R is (-1 , 5). Find (a) the distance between point A and R , (b) the coordinates of point S.

[ 4 marks]

Answer : (a) ……………………..

(b) ……………………..

22 Given that A (3,2) B (6, 4) and C (x , y ) are three points on a straight line such that AB : BC = 1 : 3 . Find the coordinates of C

[3 marks]

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Answer : ……………………

23 Find the equation of the straight line that passes through point P(3, -4) and point Q( 5, 9) .

[ 3 marks]

Answer : ……………………

24 The points A ( - 4 , -1) , B ( 2 , 5 ) and C ( 3, t ) are the vertices of the triangle which has the area of 6 unit2. Calculate the possible values of t.

[4 marks]

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Answer : ……………….……………….

25 The point R is ( -1 , 3 ) and the point S is ( 4, 8 ). The point P moves such that

. Find the equation of the locus of P .

[4 marks]

Answer : …………………………………

END OF QUESTION PAPER

SULIT