PEPERIKSAAN PERTENGAHAN TAHUN
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
Nama: ...
The following formulae may be helpful in answering the questions. The symbols given are the
DIAGRAM 1 2. Diagram 2 shows the relation between set X and set Y.
3. A function f is defined by f:x →6x−2
x , x ≠0 and x > 0.
Find
(a) the value of f−1
(4) . [3
marks]
(b) the value of k if f−1(k)=−2 . [2 marks]
Answer: (a) ……… (b) ………
4. Given that the function f:x →2−3x and f2:x → mx+n .
Determine the values of m and n. [3 marks]
n =………
5. State the product of the roots of the quadratic equation 2x2
+7x=10 . [2 marks]
Answer: …..……… ___________________________________________________________________________
6. If x = a and x = 3 are the roots of the quadratic equation 2x2
=7x−3b , find the
values of a and b. [4
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]
Answer: …..……… ___________________________________________________________________________ 8. The quadratic equation px2
+5mx+25p=0 has only one root, find
(a) m in terms of p, [3 marks]
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]
Answer: …..……… ___________________________________________________________________________
10. Given the maximum point of the quadratic function f(x)=−x2
Answer: …..……… 11. Find the ranges of the value of x when x2+3x<4 . [3 marks]
Answer: …..……… ___________________________________________________________________________
12. The graph below shows the ranges of the value of x for which the quadratic function
f(x)=ax2+bx+c is positive.
Answer: (a) ……… (b) ……… 13. Solve the equation log2 (logx9) = 1. [3 marks]
Answer: …..……… ___________________________________________________________________________
14. Solve the equation log3(x – 2) = 3 – log3(x + 4). [4 marks]
Answer: …..……… ___________________________________________________________________________
Answer: …..………
Answer: …..……… 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]
Answer: …..……… ___________________________________________________________________________
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.
Answer: …..……… ………..
21. A function f is defined by f:x → q
x−p, x ≠ p where p > 0 is such that f(2p)=2p
and f(q)=q .
Answer: p = ………
q =……… 22. The quadratic function f(x)=x2−4x+2 can be written in the form
x+p¿2+q
f(x)=a¿ , 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]
23. Solve the simultaneous equations x2
+y2
