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Additional Maths FUNCTION SMKBBSL_2010
1
PAPER 1(SET 1)
JOHOR 2009
1. Diagram 1 shows the graph of the function = + 1 , for the domain
2 5.
State:
(a) 1 5
(b) 3 [2 marks]
2. Given the functions 7 + 1 and
3 1. Find
(a) 1 8
(b) [4 marks]
3. Given the functions =3
2 and = 5 4 . Find . [3 marks]
KEDAH 2009
4. Diagram 2 shows the relation between set A and set B.
Diagram 2
(a) State the image of 9.
(b) Find the value of . [2 marks]
Additional Maths FUNCTION SMKBBSL_2010
2
5. Given 1 3
5 , find the value of
(a) 3 ,
(b) if = 7. [4 marks]
6. Given that 2 + and 2: 9.
Find the value of and . [3 marks]
MELAKA 2009
7. Given function 7 2 and function 2 5.
Find :
(a) 1
(b) the value of 2 . [4 marks]
8. Given the function 3 + 2 and 2 + 1 , find the values of if
= 17. [3 marks]
MRSM 2009
9. Given that 2
4, 4, where and are constants and
1: 43
, 0, find the value of and . [3 marks]
10. Function is defined as
21+ 3,
1
2 and is a constant. Find the value
of such that only one image maps onto itself under function . [4 marks]
Additional Maths FUNCTION SMKBBSL_2010
3
PAHANG 2009
11. Diagram 3 shows the relation between set P and set Q
Diagram 3
State
(a) the type of relation between set P and set Q.
(b) the value of if
2+ 1. [2 marks]
12. Given the function 3 1 , find
(a) the value of 2 4 , [2 marks]
(b) the function of if = 6. [2 marks]
PERAK 2009
13. Diagram 4 shows the graph of the function = 3 2 for the domain
3 4.
Diagram 4
Additional Maths FUNCTION SMKBBSL_2010
4
State
(a) the value of ,
(b) range of corresponding to the given domain. [3 marks]
14. Given the function 2
+3. If =
3
2, find the value of . [2 marks]
15. Given the composite function = 32 5 and function = 2 2,
find 4 . [3 marks]
PERLIS 2009
16. Given that = 2, 1, 1, 2 , = 1, 4, 9 and the relation between set A and set B
is defined as the set of ordered pairs 2, 4 , 1, 1 , 1, 1 , 2, 4 .
State
(a) the range of the relation,
(b) the type of relation. [2 marks]
17. Given that 3 + 1 and 2
+3, 3, find
(a) 5 ,
(b) [3 marks]
18. Given that = 3 2 and = + 4, find
(a) 1 ,
(b) the value of if 1 2 = 4. [4 marks]
SABAH 2009
19. Given the function = 2 5 , find the value of 1 . [2 marks]
20. Given the function = 3 and composite function = 2 5, find the
function . [3 marks]
21. Given = 3 4 and 1 = + , find the value of and of .
[3 marks]
Additional Maths FUNCTION SMKBBSL_2010
5
SARAWAK 2009
22. Diagram 5 shows a graph of the relation between two variables and .
Diagram 5
State
(a) the object of 8,
(b) the type of relation between and . [2 marks]
23. Given that the function = 2 + 5, = 2 4, find
(a)
(b) 2 [3 marks]
24. Given that the function : 3+2
5 , find
(a) 1
(b) the value of such that 1 = 3 [3 marks]
Additional Maths FUNCTION SMKBBSL_2010
6
SELANGOR 2009
25. Given the function = 1 3 , for the domain 2 1,
(a) sketch the graph of the function on the axes in the answer space,
(b) state the range of corresponding to the given domain. [3 marks]
26. Given the functions 1 = 3 2 and = 3, find
(a) ,
(b) the value of , given 1 2 = 7 [4 marks]
27. Diagram 6 shows an arrow diagram that represents the function =
21,
Diagram 6
Find the value of
(a)
(b) [3 marks]
Additional Maths FUNCTION SMKBBSL_2010
7
TERENGGANU 2009
28. Diagram 7 shows the function that maps to and the function that
maps to .
Diagram 7
Determine
(a) 1 6
(b) 4 [2 marks]
29. The functions and are defined by 1 3 and 2 + 3
Find
(a) 2 ,
(b) 1 2 [3 marks]
WP 2009
30. Diagram 8 shows the relation of set A and set B.
Diagram 8
Additional Maths FUNCTION SMKBBSL_2010
8
State
(a) the image of 2
(b) the object that maps onto itself [2 marks]
31. Given that 7 3 and 2 .
Find
(a) 2 ,
(b) the possible values of , if 1 = 4. [4 marks]
32. Given the function =5
21,
1
2 and = 2 3.
(a) Find 1 .
(b) Hence, find . [4 marks]
KELANTAN 2009
33. Diagram 9 shows the relation between set A and set B.
Diagram 9
(a) State
(i) the value of ,
(ii) the range of the relation.
(b) Using the function notation, write a relation between set A and set B.
[3 marks]
34. Given the functions 3 + and 1: +4
3 , where and are
constants, find the value of and . [3 marks]
Additional Maths FUNCTION SMKBBSL_2010
9
35. The following information refers to the functions and .
3 , where is a constant,
2+4
12
(a) Given that 4 = 10, find the value of .
(b) Find . [4 marks]
Additional Maths FUNCTION SMKBBSL_2010
10
PAPER 1 (SET 2)
KELANTAN 2008
1. Diagram 10 shows the relation between set A and set B.
Diagram 10
State
(a) the object of 12,
(b) the range of the relation. [2 marks]
2. Diagram 11 shows the function
2 , 2, where is a constant.
Diagram 11
Find the value of . [2 marks]
3. The following information refers to the functions and .
3 2
6 + 1
Find 1 . [3 marks]
Additional Maths FUNCTION SMKBBSL_2010
11
JOHOR 2008
4. Diagram 12 shows the relation between set P and set Q.
State
(a) the codomain of the relation,
(b) the type of the relation. [2 marks]
5. Given the inverse of function is 1: 7
2, 2,
(a) Calculate the value of 3 .
(b) State the value of where function is not defined. [3 marks]
6. Diagram 13 shows the function that maps set A to set B and the function that
maps set B to set C.
Diagram 13
Given = + 1 and = 2 + . Find the values of and .
[3 marks]
Additional Maths FUNCTION SMKBBSL_2010
12
PERAK 2008
7.
Based on the relation defined by the ordered pairs {(3, 5), (3, 8), (5, 7), (5, 13)} , state
(a) the object of 7,
(b) the range of the relation. [2 marks]
8. Diagram 14 shows part of the mapping + 3.Find the values of [2 marks]
Diagram 14
WP 2008
9.
Based on the above information, the relation between R and S is defined by the set
of ordered pairs {(2, 6), (3, 8), (3, 10), (4, 12)}.
State
(a) the images of 3,
(b) the object of 12. [2 marks]
10. Function and are defined as 3 2 and 1
, 0, find .
[3 marks]
11. Given the function 3 and 1: 2 + where and are
constants, find the value of and of . [3 marks]
R = {2, 3, 4}
S = {6, 8, 10, 12}
Additional Maths FUNCTION SMKBBSL_2010
13
KEDAH 2008
12.
Refer to arrow diagram above for the function : 3. Find the value of
(a)
(b) [3 marks]
13. Given : 3 2 and : 32 + 4. Find
(a) 1 2 ,
(b) . [4 marks]
14. Given that the inverse function of : 3 + is 1: 7
, find the value of
(a)
(b)
(c) 1 5 [3 marks]
PAHANG 2008
15. Two functions are defined by : 1 and : 2 + 3 + 1. Given that
: 2 + + , find the value of and of . [3 marks]
16. Given the function : 2 3 and : 8
, 0. Find 1 5 .
[3 marks]
Additional Maths FUNCTION SMKBBSL_2010
14
17. Diagram 15 shows the linear relation f.
Diagram 15
(a) If the image of 6 is , state the value of .
(b) State the type of relation as shown in Diagram 15. [2 marks]
18. Given the function : 3
2, find
(a) the composite function 2, [2 marks]
(b) the inverse function, 1 . [2 marks]
19. Given the function = + 2 and = 2 + . If = 22 + 8 5,
find the value of and . [3 marks]
SABAH 2008
20. Given that 7 + 4. Find the value of if 2 = 5 + 3. [2 marks]
21. Given that 1: + 2, and = 3
2. Find the values of and .
[3 marks]
SELANGOR 2008
22. Given : 6
5 , find 4 . [2 marks]
23. Given the functions : + 3 and : 2 + 6 + 2. Find .
[3 marks]
Additional Maths FUNCTION SMKBBSL_2010
15
24. In Diagram 16, set P is the domain and set Q is the codomain of a relation.
Diagram 16
(a) State the type of relation between set P and set Q.
(b) Using function notation, state the relation between set P and set Q
[2 marks]
SBP 2008
25. A function maps the elements from set P = 3, 4, 9, 16, 25 to
set Q = 0, 3, 8, 15, 24 as shown below in ordered pairs:
3, 0 , 4, 3 , 9, 8 , 16, 15 , 25, 24
(a) Write down the function notation for .
(b) State the value of
(c) State the codomain. [3 marks]
26. Given that function 3
, 0, and 1:
4
+, , find the value
of and . [3 marks]
Additional Maths FUNCTION SMKBBSL_2010
16
TERENGGANU 2008
27. Diagram 17 shows the relation between set A and set B.
Diagram 17
State
a) the range of the relation
b) the type of relation [2 marks]
28. Diagram 18 shows the arrow diagram.
Diagram 18
Find
a) the value of
b) the object of -9 [2 marks]
Additional Maths FUNCTION SMKBBSL_2010
17
MRSM 2008
29. A function is defined by : 3 +6
1, 1.
Find
a) the image of 2,
b) the object that has image 0. [3 marks]
30. Given the functions : 4 3 and : 162 24 + 14,
find the function . [3 marks]
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