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MAKTAB SABAH, KOTA KINABALU__________________________________

PEPERIKSAAN PERTENGAHAN TAHUN 2009

MATEMATIK TAMBAHANTINGKATAN 4

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. This question paper consists of 23 questions.

2. Answer all questions.

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

4. Write your answers clearly in the space provided 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 diagrams in the questions provided are not drawn to scale unless stated.

8. The marks allocated for each questions and sub-part of a question are shown in brackets.

9. A list of formulae is provided on page 2.

10. A booklet of four-figure mathematical tables is provided.

11. You may use a non-programmable scientific calculator.

12. This question paper must be handed in at the end of the examination.

Kertas soalan ini mengandungi 14 halaman bercetak

Nama: .........................................

Kelas : .........................................

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

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1. Diagram 1 shows the relation between set P and set Q.Rajah 1 menunjukkan hubungan antara set P dan Q.

DIAGRAM 1

State(a) the range of the relation,

julat hubungan itu [1 mark](b) the type of the relation.

Jenis hubungan itu [1 mark]

Answer: (a) ………………………………

(b) ………………………………

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2. Diagram 2 shows the relation between set X and set Y.Rajah 2 menunjukkan hubungan antara set X dan Y

DIAGRAM 2

State

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Nyatakan(a) the type of the relation,

Jenis hubungan itu [1 mark](c) the object of f.

objek bagi f [1 mark]

Answer: (a) ………………………………

(b) ………………………………

3. A function f is defined by f : x →6 x− 2x

, x≠ 0 and x > 0.

Fungsi f ditakrifkan oleh f : x →6 x− 2x

, x≠ 0 and x > 0.

FindCari(a) the value of f−1(4 ).

Nilai f−1(4 ). [3 marks] (b) the value of k if f−1 (k )=−2 . [2 marks]

Nilai k jikaf−1 (k )=−2 .

Answer: (a) ………………………………

(b) ………………………………

4. Given that the function f : x →2−3 x and f 2: x →mx+n.Determine the values of m and n. [3 marks]Diberi fungsi f : x →2−3 x dan f 2: x →mx+n. Tentukan nilai m dan n.

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Answer: m = ………………………….…

n =………………………………

5. State the product of the roots of the quadratic equation 2 x2+7 x=10. [2 marks]Nyatakan hasil darab punca-punca bagi persamaan kuadratik 2 x2+7 x=10.

Answer: …..………………………………

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6. If x = a and x = 3 are the roots of the quadratic equation 2 x2=7 x−3b, find the values of a and b. [4 marks]Jika x = a dan x = 3 ialah punca-punca bagi persamaan kuadratik 2 x2=7 x−3b, cari nilai-nilai a dan b.

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Answer: a = ………………………………

b = ………………………………

7. Given that the two roots of the quadratic equation x(x + m) = 2m + 3 are equal, determine the possible values of m. [4 marks]Diberi kedua-dua punca bagi persamaan kuadratik x(x + m) = 2m + 3 ialah sama, tentukan nilai-nilai yang mungkin bagi m.

Answer: …..………………………………

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8. The quadratic equation px2+5 mx+25 p=0 has only one root, findPersamaan kuadratik px2+5 mx+25 p=0 mempunyai satu punca sahaja, cari(a) m in terms of p,

m dalam sebutan p [3 marks](b) the roots of the equation. [3 marks]

punca-punca bagi persamaan itu.

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Answer: (a) ………………………………

(b) ………………………………

9. Given the quadratic function f ( x )= (x+1 )2+3, state the maximum or minimum value of the function. [2 marks]Diberi persamaan kuadratik f ( x )= (x+1 )2+3, nyatakan nilai maksimum atau minimum bagi fungsi itu.

Answer: …..………………………………

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10. Given the maximum point of the quadratic function f ( x )=−x2+2 px+6happens when x = 4. Determine the value of p. [3 marks]Diberi titik maksimum berlaku apabila persamaan kuadratik f ( x )=−x2+2 px+6 mempunyai nilai x=4. Cari nilai p.

Answer: …..………………………………

11. Find the ranges of the value of x when x2+3 x<4. [3 marks]

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Cari julat nilai bagi x apabila x2+3 x<4.

Answer: …..………………………………

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12. The graph below shows the ranges of the value of x for which the quadratic function

f ( x )=ax2+bx+c is positive.Graf menunjukkan julat nilai bagi x apabila f ( x )=ax2+bx+c ialah positif.

(a) Find the values of a, b and c.Cari nilai a, b dan c. [3 marks]

(b) Determine the value of x when the function is at the minimum point. [2 marks]Tentukan nilai x apabila fungsi itu berada di titik minimum.

Answer: (a) ………………………………

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(b) ………………………………13. Solve the equation log2 (logx9) = 1. [3 marks]

Selesaikan persamaan log2 (logx9) = 1.

Answer: …..………………………………

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14. Solve the equation log3(x – 2) = 3 – log3(x + 4). [4 marks]Selesaikan persamaan log3(x – 2) = 3 – log3(x + 4).

Answer: …..………………………………

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15. Given that loga2 = p and loga3 = q, express loga36 in terms of p and q. [3 marks]Diberi loga2 = p dan loga3 = q, ungkapkan loga36 dalam sebutan p dan q.

Answer: …..………………………………

16. Given that log43 = h and log45 = k, express the following in terms of h and k.Diberi log43 = h dan log45 = k, ungkapkan yang berikut dalam sebutan h dan k(a) log445 [2 marks](b) log40.75 [2 marks]

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Answer: (a) ………………………………

(b) ………………………………

17. A function f is defined by f : x →q

x−p, x ≠ p where p > 0 is such that f (2 p )=2 p and

f ( q )=q. Find the value of p and q.

Fungsi f ditakrif oleh f : x →q

x−p, x ≠ p dimana p > 0 dan f (2 p )=2 p dan f ( q )=q.Cari

nilai p dan q. [6 marks]

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Answer: p = ………………………………

q =………………………………18. The quadratic function f ( x )=x2−4 x+2 can be written in the form

f ( x )=a¿ , where a, p and q are constants.Fungsi kuadratik ( x )=x2−4 x+2 boleh ditulis dalam bentuk ( x )=a¿, dimana a, p, dan q ialah pemalar.(a) Determine the values of a, p and q.

Tentukan nilai a, p, dan q. [3 marks](b) State the maximum or the minimum point and the axis of symmetry of the

function.Nyatakan nilai maksimum atau minimum dan persamaan paksi simetri bagi fungsi itu. [3 marks]

(c) Sketch the graph of the function.Lakarkan graf fungsi itu [4 marks]

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19. Solve the simultaneous equations x2+ y2=8 and 2 x− y=2. [6 marks]Selesaikan persamaan serentak x2+ y2=8 dan 2 x− y=2

20. A particular type of muffin is made by using four ingredients, P, Q, R and S. Table 3 shows the prices of the ingredients.Sejenis kek muffin dibuat menggunakan empat bahan-bahan, P, Q, R dan S. Table 3 menunjukkan harga bahan-bahan itu.

IngredientsPrice per kilogram (RM)

Year 2005 Year 2008

P 4.00 x

Q 2.50 3.00

R y z

S 2.00 2.20

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Table 3

(a) The index number of ingredient P in the year 2008 based on the year 2005 is 125.Calculate the value of x.

Nombor indeks bagi P pada tahun 2008 berasaskan tahun 2005 ialah 125. Cari nilai x. [2 marks]

(b) The index number of ingredient R in the year 2008 based on the year 2005 is 140. The price per kilogram of ingredient R in the year 2008 is RM2.00 more than its corresponding price in the year 2005. Calculate the value of y and z.Nombor indeks bagi R pada tahun 2008 berasaskan 2005 ialah 140. Harga sekilogram bahan R pada tahun 2008 ialah RM2.00 berbanding dengan harga sepadan pada tahun 2005. Hitungkan nilai y dan z. [3 marks]

(c) The composite index for the cost of making the muffin in the year 2008 based on the year 2005 is 126.CalculateIndeks gubahan untuk kos membuat kek muffin pada tahun 2008 berdasarkan tahun 2005 ialah 126. Hitung

(i) the price of the muffin in the year 2005 if its corresponding price in the year 2008 is RM 6.30harga muffin pada tahun 2005 jika harga sepadannya pada tahun 2008 ialah RM 6.30

(ii) the value of r if the quantities of ingredients P, Q, R and S used are in the ratio of 6 : 3 : r : 2 nilai r jika kuantiti-kuantiti bagi bahan P, Q, R dan S digunakan dalam nisbah 6: 3: r: 2 [5 marks]

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END OF QUESTION PAPER