ujian pertengahan tahun matematik tambahan tingkatan 4
1
Nama: .........................................
Kelas : .........................................
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
2
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
1.
x
b � b 2 4ac
2a
2.
a m �a n a m n
3.
a m �a n a mn
6.
7.
8.
4.
(a m ) n a mn
5.
log a mn log a m log a n
1.
log a
m
log a m log a n
n
log a m n n log a m
log a b
Diagram 1 shows the relation between set P and set Q.
log c b
log c a
8.
3
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 and 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 f : x → 6 x−
Find
(a)
marks]
(b)
the value of
2
x
,
x ≠ 0 and x > 0.
f −1 (4) .
[3
the value of k if f −1 ( k ) =−2 .
Answer:
[2 marks]
(a) ………………………………
(b) ………………………………
4.
Given that the function f : x → 2−3 x
Determine the values of m and n.
and f 2 : x → mx+ n .
[3 marks]
Answer:
m = ………………………….…
5
n =………………………………
5.
State the product of the roots of the quadratic equation 2 x 2 +7 x=10 .
Answer:
[2 marks]
…..………………………………
___________________________________________________________________________
6.
If x = a and x = 3 are the roots of the quadratic equation 2 x 2=7 x−3 b , find the
values of a and b.
[4
marks]
6
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 +5 mx+25 p=0 has only one root, find
(a) m in terms of p,
(b) the roots of the equation.
[3 marks]
[3 marks]
7
Answer:
(a) ………………………………
(b) ………………………………
9.
Given the quadratic function
of the function.
2
f ( x )=( x +1 ) + 3 , state the maximum or minimum value
[2 marks]
Answer:
…..………………………………
___________________________________________________________________________
10.
Given the maximum point of the quadratic function
when x = 4. Determine the value of p.
f ( x )=−x 2+2 px+ 6 happens
[3 marks]
8
Answer:
11.
Find the ranges of the value of x when
2
x +3 x 0 is such that
x−p
f ( 2 p )=2 p
[6 marks]
13
Answer:
22.
p = ………………………………
q =………………………………
The quadratic function f ( x )=x 2−4 x+ 2 can be written in the form
2
x+ p ¿ + q
, where a, p and q are constants.
f ( x )=a ¿
(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
2
2
x + y =8 and 2 x − y=2.
[6 marks]
15
END OF QUESTION PAPER
Nama: .........................................
Kelas : .........................................
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
2
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
1.
x
b � b 2 4ac
2a
2.
a m �a n a m n
3.
a m �a n a mn
6.
7.
8.
4.
(a m ) n a mn
5.
log a mn log a m log a n
1.
log a
m
log a m log a n
n
log a m n n log a m
log a b
Diagram 1 shows the relation between set P and set Q.
log c b
log c a
8.
3
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 and 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 f : x → 6 x−
Find
(a)
marks]
(b)
the value of
2
x
,
x ≠ 0 and x > 0.
f −1 (4) .
[3
the value of k if f −1 ( k ) =−2 .
Answer:
[2 marks]
(a) ………………………………
(b) ………………………………
4.
Given that the function f : x → 2−3 x
Determine the values of m and n.
and f 2 : x → mx+ n .
[3 marks]
Answer:
m = ………………………….…
5
n =………………………………
5.
State the product of the roots of the quadratic equation 2 x 2 +7 x=10 .
Answer:
[2 marks]
…..………………………………
___________________________________________________________________________
6.
If x = a and x = 3 are the roots of the quadratic equation 2 x 2=7 x−3 b , find the
values of a and b.
[4
marks]
6
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 +5 mx+25 p=0 has only one root, find
(a) m in terms of p,
(b) the roots of the equation.
[3 marks]
[3 marks]
7
Answer:
(a) ………………………………
(b) ………………………………
9.
Given the quadratic function
of the function.
2
f ( x )=( x +1 ) + 3 , state the maximum or minimum value
[2 marks]
Answer:
…..………………………………
___________________________________________________________________________
10.
Given the maximum point of the quadratic function
when x = 4. Determine the value of p.
f ( x )=−x 2+2 px+ 6 happens
[3 marks]
8
Answer:
11.
Find the ranges of the value of x when
2
x +3 x 0 is such that
x−p
f ( 2 p )=2 p
[6 marks]
13
Answer:
22.
p = ………………………………
q =………………………………
The quadratic function f ( x )=x 2−4 x+ 2 can be written in the form
2
x+ p ¿ + q
, where a, p and q are constants.
f ( x )=a ¿
(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
2
2
x + y =8 and 2 x − y=2.
[6 marks]
15
END OF QUESTION PAPER