STUDENT'S COPY MODULE 1-FUNCTIONS
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ADDITIONAL MATHEMATICS FORM 4 MODULE 1 PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI
FUNCTIONS
MINISTRY OF EDUCATION MALAYSIA
MODULE 1: FUNCTIONS Arahan: 1. Modul ini mengandungi tiga puluh lima soalan. Semua soalan adalah dalam bahasa Inggeris. 2. Modul merangkumi lima konstruk yang diuji K3 - Memahami istilah matematik dalam bahasa Inggeris K5 - Menguasai konstruk pengetahuan K6 - Menguasai konstruk kefahaman K7 - Menguasai konstruk kemahiran K8 - Mengungkapkan idea/informasi dalam bahasa Inggeris 3. Murid hendaklah menulis maklumat diri dalam kertas jawapan objektif disediakan. Murid juga perlu memastikan maklumat konstruk, nombor soalan dan jumlah soalan seperti yang dibaca oleh guru di dalam ruangan disediakan dalam kertas jawapan objektif sebelum ujian. 4. Bagi soalan objektif, anda perlu menandakan jawapan dengan menghitamkan pilihan jawapan pada pilihan jawapan A , B , C atau D pada kertas jawapan objektif. Contoh: Antara berikut, yang manakah haiwan? A. Pokok A
B. B
Kambing
C.
C
D
5. Jawab semua soalan.
Modul ini mengandungi 17 halaman bercetak
2
Kereta E
D.
Pe n
1.
Refer to the diagram below P
‘is the capital of’
Q
Kangar
Perlis
Kuantan
Pahang
Which of the following is written in correct ordered pairs ?
2.
A
{(Kangar, Kuantan)}
B
{(Kangar,Perlis)}
C
{(Perlis, Pahang)}
D
{(Pahang. Kuantan)}
Figure shows an arrow diagram P
4
2
9
3
25
5
36
6
Which of the following is the image of 4? A
2
B
3
C
5
D
6
Q
‘is the square of’
3
3.
4.
Which of the following is the symbol for absolute value of p? A
{p}
B
(p)
C
p
D
|p|
The arrow diagram below shows that set X is mapped to set Y and set Y is mapped to set Z. Which of the following arrow represent an inverse function? A
X
Y
Z D
B
C 5.
Which of the following arrow diagram shows many-to-one relation? M
N
A
C p
x
q
y
M
N D x
q
y
N
p
x
q
B p
M
r
y
M
N
p
x y
q
4
z
6.
Figure shows an arrow diagram P
Q
‘is the factor of’
2
4 6
3
●7 9
{4, 6, 9} is known as
7.
A
Domain
B
Codomain
C
Range
D
Images
Figure shows an arrow diagram. P
‘can be divided by’
4
Q 2
6 8 10
5
Identify the type of relation between set P and set Q. A
One-to-one
B
Many-to-one
C
One-to-many
D
Many-to-many 5
8.
From the arrow diagram, determine the codomain. K
9.
p
s
q
t
r
u
A
{s,t,u}
B
{p,q,r}
C
s,t,u
D
p,q,r
Given f ( x) A
4
B
2
C
4
D
16
L
x . W hat is the value of f (4) ?
6
10.
Based on the arrow diagram, gf is known as
gf P
R
Q g
f x
11.
z
y
A
Multiple function
B
Combine function
C
Inverse function
D
Composite function
Which of the following arrow diagram is a function? M
M
N B
A p
x
q
y
p
N x
q r
y
M
N
p
x
r
M
N D
C p
x
q
y
y q
7
z
12.
Based on the arrow diagram. M
N
p
x
q
y
r
z
Which of the following are known as objects?
13.
A
{ p,q,r}
B
{ x, y, z}
C
p ,q a n d r
D
x,y and z
The graph shows a relation mapping X to Y. Y
3 2 1
0 1
2
3 4
X
State the type of relation. A
One-to-one
B
One-to-many
C
Many-to-one
D
Many-to-many
8
14.
Based on the arrow diagram. M
P
Q
R
g
f
x
y
z
Which of the following function is correct to represent M? gf fg
A B C
g 1 f gf 1
D
Se t Y
15.
14 12 10 4
5
6
7
Se t X
Set X and set Y have the relation ‘multiple of’. W hat are the objects of 12? A
5 and 6
B
4 and 6
C
4 and 12
D
6 and 12
9
16.
Given g ( x)
x 2 5 x is the relation between set P and set Q.
P
Q
1
6
-1
-4
From the above diagram, which of the following answer is correct?
17.
A
g (6) 6 2 5(6)
B
g (4)
C
g (1) 12 5(1)
D
g (1)
Given h( x) defined. A
3
B
1
C
2
D
3
(4) 2 5(4)
(1) 2 5( 1) 2x 1 , x z k . Find the value of k such that the function is not x3
10
18.
The diagram shows the relation of set P and set Q. Q
P
1
2
2
4
3
6
Determine the relation when set P is mapped onto set Q.
19.
A
2x
B
x2
C
1 x 2
D
x2
Given f ( x) x 1 and g ( x) Then fg ( x) f (3 2 x)
3 2x
=Q What is Q?
20.
A
3 2( x 1)
B
(3 2 x) 1
C
3 2 x( x 1)
D
x(3 2 x) 1
Given f ( x) 2 x 5 . W hich of the following is the correct step to find the image of 4? A 2(4) 5 B
2 5(4)
C
2x 5
4
D
2x 4
5
11
21.
Figure shows the function g : x o x 2 5 .
1
6
2
w
3
14
Find the value of w.
22.
A
2
B
5
C
7
D
9
Given g ( x) 2 x 4. Below are the steps in finding g 1 ( x). Determine the step 4. S te p 1 g ( x ) y S te p 2 2 x 4 y S te p 3 2 x y 4 Step 4 …………. A
x
y42
B
x
2y 4
C
x
y4 2
D
x
y 4 2
12
23.
The diagram shows function f ( x)
2x 3
f
x
2x 3
2
1
5
p
8
13
Find the value of p.
24.
A
4
B
5
C
7
D
13
Given a function f ( x) Find f (2) .
4x 2 3 .
A 67 B 19 C 13 D 61 25.
Given the absolute value function f ( x) Find the value of f (3) . A
11
B
7
C
7
D
11
13
3x 2 .
26.
27.
28.
Given f ( x) 2 x 1 and g ( x) Find fg (2) . A
3
B
11
C
17
D
21
7 2x .
Given a function g ( x) 3 x 2 . Find the object when the image is 4. A
2 3
B
3 2
C
2
D
10
If 2 x 5
3 is an absolute value function, then 2 x 5
3 or 3 .
Find the possible values of x ?
29.
A
1
B
4
C
1 and 4
D
4 and 4
The functions f and g are defined as f ( x) Find the composite function fg . A
1 x4
B
1 4x x
C
1 4 x
D
x4 x
14
x 4 and g ( x )
1 , x z 0. x
30.
Given a function f ( x) 3 2 x . The inverse function f 1 can be determined by the following steps. f 1 ( x) f ( y)
y x P
3 2y 2y
x3
y
Q
What are the values of P and Q?
31.
A
P
x, Q
x3 , 2
B
P
x, Q
3 x 2
C
P
y, Q
x3 2
D
P
y, Q
3 x 2
Why does the relation in the arrow diagram is a function? M
N
1
2
2
4
3
6
A
Each object is mapped to one and only one image.
B
There is an image without object.
C
The type of relation is one-to many.
15
32.
Figure shows an arrow diagram. M
N
9
3
16
4
Which of the following is the relation that maps set M to N?
33.
A
The square root of 9 is 3.
B
The cube root of 9 is 3.
C
The square of 16 is 4.
D
The cube of 16 is 4.
Figure shows an arrow diagram. Q
P
x
f
f (x)
R g
Which of the following defines the composite function gf ? A
set Q maps to set R
B
set P maps to set Q
C
set P maps to set R
D
set R maps to set Q
16
gf (x)
34.
35.
Given that f ( x) 2 x 1 and f (1) 3 , f (3) 5 . Therefore, the image of an absolute value function is always A
positive
B
negative
C
zero
D
infinity
Function g (x) does not have an inverse function. What is the type of relation of function g? A
Function g has one-to-one relation.
B
Function g has one-to- many relation.
C
Function g has many-to-one relation.
D
Function g has many to many relation.
END OF QUESTIONS PAPER
17
KEMENTERIAN PELAJARAN M ALAYSIA
KERTAS JAWAPAN OBJEKTIF Ujian Diagnostik
Nama Pelajar: Tahun/ Tingkatan :
4
Mata Pelajaran:
MATEMATIK TAMBAHAN
Modul:
Nama Sekolah:
1
GUNAKAN PENSIL 2B ATAU BB SAHAJA. TENTUKAN TIAP-TIAP TANDA ITU HITAM DAN MEMENUHI KESELURUHAN RUANG.
PADAMKAN HINGGA HABIS MANA-MANA TANDA YANG ANDA UBAH
SILA HITAMKAN JAWAPAN DI BAWAH MENGIKUT HURUF JAWAPAN YANG ANDA PILIH 1
A
B
C
D
E
31
A
B
C
D
E
46
A
B
C
D
E
2
A
B
C
D
E
32
A
B
C
D
E
47
A
B
C
D
E
3
A
B
C
D
E
33
A
B
C
D
E
48
A
B
C
D
E
4
A
B
C
D
E
34
A
B
C
D
E
49
A
B
C
D
E
5
A
B
C
D
E
35
A
B
C
D
E
50
A
B
C
D
E
6
A
B
C
D
E
36
A
B
C
D
E
51
A
C
D
E
B
C
D
E
1 52
B
A
A
B
C
D
E
7
A
B
C
D
E
37
8
A
B
C
D
E
38
A
B
C
D
E
53
A
B
C
D
E
9
A
B
C
D
E
39
A
B
C
D
E
54
A
B
C
D
E
10
A
B
C
D
E
40
A
B
C
D
E
55
A
B
C
D
E
11
A
B
C
D
E
41
12
A
B
C
D
E
13
A
B
C
D
14
A
B
C
D
15
A
B
C
D
E
16
A
B
C
D
E
17
A
B
C
D
E
18
A
B
C
D
E
19
A
B
C
D
E
20
A
B
C
D
E
21
A
B
C
D
E
22
A
B
C
D
E
23
A
B
C
D
E
24
A
B
C
D
E
25
A
B
C
D
E
6
26
A
B
C
D
E
7
27
A
B
C
D
E
28
A
B
C
D
E
29
A
B
C
D
E
30
A
B
C
D
E
A
B
C
D
E
56
A
1 42
B
C
D
E
A
B
C
D
E
57
A
B
C
D
E
E
43
A
B
C
D
E
58
A
B
C
D
E
E
44
A
B
C
D
E
59
A
B
C
D
E
45
A
B
C
D
E
60
A
B
C
D
E
Konstruk
No. Soalan
Jumlah Soalan
1
K3
1-6
6
2
K5
7 - 15
9
3
K6
16 - 22
7
4
K7
23 - 30
8
5
K8
31 - 35
5
8 9 10
Bilangan Soalan Gagal Dijawab
Kegunaan Guru
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