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Additional Mathematics Trial 2013 : Topic 1 Functions
Citation preview
SULIT 5 3472/1
3472/1 [ Lihat halaman sebelah SULIT
2
The functions f –1 and fg are defined as f –1 : x → 4 − 3x and fg : x → x − 3. Find Fungsi-fungsi f –1 dan fg ditakrifkan sebagai f –1: x → 4 − 3x dan fg : x → x − 3. Cari (a) f −1(3). (b) g(x)
[3 marks] [3 markah]
Answer/Jawapan:
(a) (b)
3 Given that function 2 3f x x and g x k x . Find the value of
Diberi fungsi 2 3f x x dan g x k x . Cari nilai bagi (a) 2f ,
(b) k if 1 11fg .
k jika 1 11fg .
[3 marks] [3 markah]
Answer/Jawapan:
(a) (b)
3
3
3
2
For examiner’s
use only
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SULIT 4 3472/1
3472/1 SULIT
Answer all questions. Jawab semua soalan.
1
Diagram 1 shows the relation between x and f(x). Rajah 1 menunjukkan hubungan antara x dan f(x).
Diagram 1 Rajah 1 State Nyatakan (a) the object of 9 , objek bagi 9 , (b) the type of relation between x and f(x). jenis hubungan antara x dan f(x).
[2 marks] [2 markah]
Answer/Jawapan:
(a) (b)
For examiner’s
use only
2
1
9
6
3
0 1 2 − 1
f(x)
x ●
●
●
●
− 2
●
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SULIT 5 3472/1
3472/1 [ Lihat halaman sebelah SULIT
2
The functions f –1 and fg are defined as f –1 : x → 4 − 3x and fg : x → x − 3. Find Fungsi-fungsi f –1 dan fg ditakrifkan sebagai f –1: x → 4 − 3x dan fg : x → x − 3. Cari (a) f −1(3). (b) g(x)
[3 marks] [3 markah]
Answer/Jawapan:
(a) (b)
3 Given that function 2 3f x x and g x k x . Find the value of
Diberi fungsi 2 3f x x dan g x k x . Cari nilai bagi (a) 2f ,
(b) k if 1 11fg .
k jika 1 11fg .
[3 marks] [3 markah]
Answer/Jawapan:
(a) (b)
3
3
3
2
For examiner’s
use only
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11
3472/1
(Answer all questions) Jawab semua soalan
1. Diagram 1 shows the graph of function ( ) 2 4f x x for domain 0 5x
Rajah 1 menunjukkan graf bagi fungsi ( ) 2 4f x x , untuk domain 0 5x .
Diagram 1 / Rajah 1
State Nyatakan
(a) f (0), (b) range of f(x) corresponding to the given domain.
julat f(x) berdasarkan domain yang diberi. [2 markah] Answer / Jawapan :
(a) (b)
2. Given the function ( ) 3 2g x x and ( ) 12 4gh x x , Diberi fungsi ( ) 3 2g x x dan ( ) 12 4gh x x ,
find / cari
(a) h(x), (b) value of x such that h(x) maps onto itself.
nilai x dengan keadaan h(x) memeta kepada dirinya sendiri. Answer / Jawapan:
(a) (b)
[3 markah]
y
x O
4 ●
● (5, 6)
● 2
y = f(x)
2
1
3
2
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22
3472/1
3. Diagram 3 shows the function 5: kxxf , where k is a constant. Rajah 3 menunjukkan fungsi 5: kxxf , dengan keadaan k ialah pemalar.
Diagram 3 / Rajah 3 Find the value of k Cari nilai k. [3 markah]
Answer / Jawapan :
4. Straight line 1x2y is tangent to the curve 2 .y x p
Garis lurus 1x2y ialah tangen kepada lengkung 2 .y x p
Find the value of p Cari nilai p.
[3 markah] Answer / Jawapan :
3
14
kx+5 f
x
3
4
3
3
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3472/1 [ Lihat sebelah
Answer all questions.Jawab semua soalan
1 Diagram 1 shows the linear function f.Rajah 1 menunjukkan fungsi linear f.
Diagram 1Rajah 1
State:Nyatakan:
(a) value of mnilai m
(b) value of nnilai n
(c) image of 10imej bagi 10
[3 marks][3 markah]
Answer / Jawapan :
(a)
(b)
(c)
Forexaminer’s
use only
3
1
1 2
m 4
3 n
4 8
x f(x)
4
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3472/1 [ Lihat sebelah
2 Given function g and h as g(x) = 2x – 3 and h(x) = 2x2 + 2. Find hg(x).Fungsi g dan h diberi sebagai g(x) = 2x – 3 dan h(x) = 2x2 + 2. Cari hg(x).
[3 marks][3 markah]
Answer / Jawapan :
3 Find f – 1 (x) given f(x) = –2 x +10.Cari f – 1 (x) diberi f(x) = –2 x +10.
[2 marks][2 markah]
Answer/ Jawapan :
Forexaminer’s
use only
3
2
2
3
5
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SULIT 7 3472/1
Answer all questions. Jawab semua soalan.
1 The following information shows set A, set B and the relation between set A and set B
in the form of ordered pairs.
Maklumat berikut menunjukkan set A, set B dan hubungan antara set A dan set B dalam bentuk pasangan tertib.
A = {p, k, w}
B = {2, 3, 4, 5, 6}
{( p, 2 ),( p, 3 ),( k, 3 ),( w, x )}
Given that the range of the relation between set A and set B is { 2, 3, 4 }, state
Diberi julat hubungan antara set A dan set B ialah { 2, 3, 4 }, nyatakan
(a) the image of k,
imej bagi k,
(b) the value of x.
nilai x.
(c) the type of the relation.
jenis hubungan itu. [3 marks]
[3 markah]
Answer / Jawapan :
(a)
(b)
(c)
[Lihat sebelah]
For Examiner’s
Use
1
3
Negeri Sembilan SPM 2013 http://edu.joshuatly.com/
SULIT 8 3472/1
2 Given that xxh 5)( and 3)( kxxg , find
Diberi bahawa xxh 5)( dan 3)( kxxg , cari
(a) )1(h ,
(b) the value of k such that 7)1( gh .
nilai k dengan keadaan 7)1( gh [3 marks] [3 markah]
Answer / Jawapan :
(a)
(b)
3 Given that 56: xxf and 2
3:
xxg, find the function 1fg .
Diberi bahawa 56: xxf dan 2
3:
xxg, cari fungsi 1fg .
[3 marks]
[ 3 markah]
Answer / Jawapan :
For Examiner’s
Use
2
3
3
3
[Lihat sebelah] Negeri Sembilan SPM 2013 http://edu.joshuatly.com/
http://edu.joshuatly.com/ http://fb.me/edu.joshuatly
http://edu.joshuatly.com/ http://fb.me/edu.joshuatly
5
SULIT 3472/1
3472/1 ©2013 Hak Cipta BPSBPSK SULIT
Answer all questions.
Jawab semua soalan.
1. Diagram 1 shows the linear function f.
Rajah 1 menunjukkan fungsi linear f.
(a) State the value of k.
Nyatakan nilai k.
(b) Using the function notation, express f in terms of x.
Menggunakan tata tanda fungsi, ungkapkan f dalam sebutan x.
[ 2 marks ]
[2 markah]
Answer/Jawapan :
(a)
(b)
2. Given the function : 7 2g x x , find the value of n such that 1(3 1)g n n .
Diberi fungsi : 7 2g x x , cari nilai n dengan keadaan 1(3 1)g n n .
[ 3 marks ]
[3 markah]
Answer/Jawapan :
Diagram 1
Rajah 1
x f(x)
-1
4
1
2
-2
8
k
2
3
2
2
1
For Examiner’s
Use
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6
SULIT 3472/1
3472/1 ©2013 Hak Cipta BPSBPSK SULIT
3. Given the function ( ) 3h x px and 2 ( ) 49h x x q , where p and q are constants
and 0.p
Find the value of p and of q.
Diberi fungsi ( ) 3h x px dan 2 ( ) 49h x x q , dengan keadaan p dan q adalah
pemalar dan 0.p
Cari nilai p dan nilai q.
[ 3 marks ]
[3 markah]
Answer/Jawapan :
4. It is given that m and 2 are the roots of the quadratic equation
25 ( 1) 2 0x n x .
Find the value of m and of n.
Diberi bahawa m dan 2 adalah punca-punca bagi persamaan kuadratik
25 ( 1) 2 0x n x .
Cari nilai m dan nilai n.
[ 3 marks ]
[3 markah]
Answer/Jawapan :
3
3
For
Examiner’s Use
3
4
http://edu.joshuatly.com/ http://fb.me/edu.joshuatly
http://edu.joshuatly.com/
http://edu.joshuatly.com/