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. questions.
2.
Answer all
3.
Give
4.
rite W rite
your answers clearly in the space provided in the question paper.
5.
how S how
your working. It may help you to get marks. marks.
questions. questions.
only one answer / solution to each question. question.
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 th e questions provided a re not drawn to scal e 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 page2 page 2.
10.
A
booklet of four-figure mathematical tables is provided.
11.
ou Y ou
12.
This question paper must be handed in at the end of the examination.
may use a non-programmable scientific calculator.
Kertas soalan ini mengandungi 14 halaman bercetak
2
The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.
b 2 4ac
b s
1.
x !
2.
a m v an
!
am
3.
am
!
am
log a
7.
log
8.
log a b !
2a
za
4.
( a m )n
5.
log a
n
!
n
n
amn
mn ! log a m log a
n
m
6.
a
n
m
!
n
loga
!
m loga
n log a m 8.
log c b log c a
n
3
1.
Diagram 1 shows the relation between set P and set Q.
DIAGRAM 1
State (a) (b)
the range of the relation, the type of the relation.
[1 mark ] [1 mark ]
Answer:
(a) «««««««««««« (b) ««««««««««««
__________________________________________________________________________________
2.
Diagram 2 shows the relation between set X a nd set Y.
DIAGRAM 2
State (a) (b)
the type of the relation, the object of f.
[1 mark ] [1 mark ]
Answer:
(a) «««««««««««« (b) ««««««««««««
4
3.
A function f is defined by Find (a) (b)
, and x > 0.
the value of . the value of k if .
Answer:
[3 marks ] [2 marks ]
(a) «««««««««««« (b) ««««««««««««
4.
Given that the function and . Determine the values of m and n.
Answer:
[3 marks ]
m = ««««««««««.« n =««««««««««««
5
5.
State the product of the roots of the quadratic equation .
Answer:
[2 marks ]
«..««««««««««««
___________________________________________________________________________ 6.
If x = a and x = 3 are the roots of the quadratic equation , find the values of a and b. [4 marks ]
Answer:
a = «««««««««««« b = ««««««««««««
6
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 has only one root, find (a) m in terms of p, (b) the roots of the equation.
Answer:
[3 marks ] [3 marks ]
(a) «««««««««««« (b) ««««««««««««
7
9.
Given the quadratic function , state the maximum or minimum value of the function. [2 marks ]
Answer:
«..««««««««««««
___________________________________________________________________________ 10.
Given the maximum point of the quadratic function happens when x = 4. Determine the value of p. [3 marks ]
Answer:
«..««««««««««««
8
11.
Find the ranges of the value of x when .
Answer:
[3 marks ]
«..««««««««««««
___________________________________________________________________________ 12.
The graph below shows the ranges of the value of x for which the quadratic function is positive.
(a) (b)
Find the values of a, b and c. [3 marks ] Determine the value of x when the function is at the minimum point. [2 marks ]
Answer:
(a) «««««««««««« (b) ««««««««««««
9
13.
Solve the equation log 2 (logx9) = 1.
[3 marks ]
Answer:
«..««««««««««««
___________________________________________________________________________ 14.
Solve the equation log 3 ( x ± 2) = 3 ± log3 ( x + 4).
Answer:
[4 marks ]
«..««««««««««««
___________________________________________________________________________ 15.
Given that loga2 = p and log a3 = q, express log a36 in terms of p and q.
Answer:
[3 marks ]
«..««««««««««««
10
16.
Given that log4 3 = h and log4 5 = k , express the following in terms of h and k. (a) log445 [2 marks ] (b) log40.75 [2 marks ]
Answer:
(a) ««««««««««««
(b) «««««««««««« ___________________________________________________________________________ 17.
Show that the lines and
are parallel.
[2 marks ]
Answer:
«..««««««««««««
___________________________________________________________________________ 18.
Find the gradient of the line joining the points R(2, ± 4) and S ( ± 3, 5).
P (1,
2) to the midpoint of the line joining the [3 marks ]
Answer:
«..««««««««««««
11
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.
S olutions
to this question by scale drawing will not be accepted .
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 ] ABCD
Answer:
«..«««««««««««« «««««««««««««..
12
21.
A function f is defined by
where p > 0 is such that and
. Find the value of p and q.
[6 marks ]
Answer:
p = «««««««««««« q =««««««««««««
13
22.
The quadratic function can be written in the form , 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 ]
14
23.
Solve the simultaneous equations and
END OF QUESTION PAPER
[6 marks ]
