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SULIT NAMA: TINGKATAN: .. 3472/1 Matematik Tambahan Kertas 1 2 Jam Mei 2006 SEKTOR SEKOLAH BERASRAMA PENUH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 4 2006 MATEMATIK TAMBAHAN Kertas 1 Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU1. 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 .

Kod PemeriksaSoalanMarkah PenuhMarkah Di peroleh12233343546273839310411312313314 3153163173184193204214223233244254Total 80

SULIT Kertas soalan ini mengandungi 12

2 halaman bercetak [Lihat sebelah

INFORMATION FOR CANDIDATES 1. 2. 3. 4. 5. 6. This question paper consists of 25 questions. Answer all questions. Give only one answer for each question. Write the answers clearly in the space provide in the question paper. Show your working. It may help you to get marks. 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 5 loga mn = log am + loga n m 6 loga = log am - loga n n 7 log a mn = n log a m 8 logab = log c b log c a

x=

b b 4ac 2a2

2 am an = a m + n 3 am an = a m - n 4 (am) n = a nm

GEOMETRY1 Distance = 2 Midpoint , (x , y) = ,

3 A point dividing segment of a line ( x, y) = 4 Area of triangle = 3472/1 [ Lihat sebelah SULIT

1

For Examiners Only

1

Answer all questions Diagram 1 shows the relation between set A and set B. Set B 5 4 3 2 1 2 4 6 8 (b) the range of the relation. DIAGRAM 1 10 State (a) the image of 6, Set A [2 marks]

Answer : ( a) .... ( b) .. 2 A function f is defined by f : x 2 x 1 for the domain 1 x 4 . Find (a) the image of 2, (b) the object of 9, (c) the corresponding range. [3 marks]For Examiners Only

Answer: ( a) . .... ( b) . ( c ) 3 Given the function f : x 2 x + 3 and the function g : x 1 5 x. Determine (a) the composite function fg, (b) the value of gf(- 2). [3 marks]

[4 markah]

For Examiners Only

Answer : ( a) ( b) .

4

The function f is defined as f : x 5 x and the composite function x 1 fg : x , x 0 . Find g (x) . [3 marks] 2x

5

Given that g : x

x+k and g (5) = 4 . 3

Find (a) the value of k, (b) the function g 1 ( x) . [4 marks]

Answer : (a) (b) .. . x3 = x + 6 in the general form. Simplify and express the quadratic equation 2x 5 [2 marks ]

6

.For Examiners Only

7

Determine the roots of the quadratic equation 3x 2 = x + 1. Give your answer correct to four significant figures. [ 3 marks ]

8

2 1 and . 3 4 2 Give your answer in the form of ax + bx + c = 0, where a , b and c are constants . Form a quadratic equation which has the roots [ 3 marks ]

9

The quadratic equation 3px 2x 2 = 8 has two equal roots. Find the values of p. [ 3 marks ]

For Examiners Only

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 ]

y Answer: (a) ... 0 11 (b) .. x (5 , -1 )

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. (0 , -6 ) [ 3 marks ]

DIAGRAM 2

12

Answer : . 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]

13

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

f(x)

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 ]For Examiners Only

15

Given that f(x) = 5 + 4x x 2 , find the range of values of x which satisfies f ( x) 8 . [ 3 marks ]

16

Solve the equation 33 x 1 = 6x . [3 marks]

For Examiners Only

17

1 Solve the equation 9

2 m+5

= 3 m -1 . [3 marks]

For Examiners Only

Answer : Express 2n +3 2n + 5(2n 1 ) in the simplest form. [4 marks]

18

19

Given that logx3 = h and logx5 = k , express log x

15 x2

in terms of h and k . [3 marks]

20

Solve the equation 2 log 4 3 + log 4 (2 + x) log 4 5 x =

1 . 2 [4 marks]

For Examiners Only

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]

For Examiners Only

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

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]