1 Nama:... Kelas :... MAKTAB SABAH, KOTA KINABALU PEPERIKSAAN PERTENGAHAN TAHUN 2009 MATEMATIK TAMBAHAN TINGKATAN 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

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. 2 1. ± x = 2 b b 4ac 2a m 6. log log m log n = a a a n 2. m n m n a a = a + n 7. log m = nlog m8. a a 3. m n m n a a = a 8. log a logc b b = log a c 4. ( a ) = a m n mn 5. log mn = log m + log n a a a

3 1. Diagram 1 shows the relation between set P and set Q. DIAGRAM 1 State (a) the range of the relation, [1 mark] (b) the type of the relation. [1 mark] (a) (b) 2. Diagram 2 shows the relation between set X and set Y. DIAGRAM 2 State (a) the type of the relation, [1 mark] (b) the object of f. [1 mark] (a) (b)

3. A function f is defined by ff: xx 6xx 2, xx 0 and x > 0. xx Find (a) the value of ff 1 (4). [3 marks] (b) the value of k if ff 1 (kk) = 2. [2 marks] 4 (a) (b) 4. Given that the function ff: xx 2 3xx and ff 2 : xx mmmm + nn. Determine the values of m and n. [3 marks] m =. n =

5 5. State the product of the roots of the quadratic equation 2xx 2 + 7xx = 10. [2 marks] 6. If x = a and x = 3 are the roots of the quadratic equation 2xx 2 = 7xx 3bb, find the values of a and b. [4 marks] 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] 6 8. The quadratic equation pppp 2 + 5mmmm + 25pp = 0 has only one root, find (a) m in terms of p, [3 marks] (b) the roots of the equation. [3 marks] (a) (b)

9. Given the quadratic function ff(xx) = (xx + 1) 2 + 3, state the maximum or minimum value of the function. [2 marks] 7 10. Given the maximum point of the quadratic function ff(xx) = xx 2 + 2pppp + 6 happens when x = 4. Determine the value of p. [3 marks]

8 11. Find the ranges of the value of x when xx 2 + 3xx < 4. [3 marks] 12. The graph below shows the ranges of the value of x for which the quadratic function ff(xx) = aaaa 2 + bbbb + cc is positive. (a) Find the values of a, b and c. [3 marks] (b) Determine the value of x when the function is at the minimum point. [2 marks] (a) (b)

9 13. Solve the equation log2 (logx9) = 1. [3 marks] 14. Solve the equation log3(x 2) = 3 log3(x + 4). [4 marks] 15. Given that loga2 = p and loga3 = q, express loga36 in terms of p and q. [3 marks]

16. Given that log43 = h and log45 = k, express the following in terms of h and k. (a) log445 [2 marks] (b) log40.75 [2 marks] 10 (a) (b) 17. Show that the lines 3xx 4yy + 8 = 0 and xx 4 yy 3 = 1 are parallel. [2 marks] 18. Find the gradient of the line joining the P(1, 2) to the midpoint of the line joining the points R(2, 4) and S( 3, 5). [3 marks]

19. The point P(2, t) is equidistant from the points Q(3, 2) and R(1, 4). Find the value of t. [3 marks] 11 20. Solutions to this question by scale drawing will not be accepted. ABCD is a rectangle and the coordinates of A, B, and C are ( 3, 2), (0, 4) and (4, 2) respectively. Find the coordinates of point D and calculate the area of the triangle formed by joining points A, C and D. [5 marks]..

21. A function f is defined by ff: xx qq ff(qq) = qq. Find the value of p and q. xx pp 12, xx pp where p > 0 is such that ff(2pp) = 2pp and [6 marks] p = q =

22. The quadratic function ff(xx) = xx 2 4xx + 2 can be written in the form ff(xx) = aa(xx + pp) 2 + qq, where a, p and q are constants. (a) Determine the values of a, p and q. [3 marks] (b) State the maximum or the minimum point and the axis of symmetry of the function. [3 marks] (c) Sketch the graph of the function. [4 marks] 13

23. Solve the simultaneous equations xx 2 + yy 2 = 8 and 2xx yy = 2. [6 marks] 14 END OF QUESTION PAPER