SPM Questions for functions

Frequently Asked Questions in SPM for Functions

We will discuss some pass year SPM exam questions based on the four concepts :

Relations – SPM 2010
Functions – SPM 2007
Composite Functions – SPM 2007
Composite & Inverse Functions – SPM 2010


 

Relations – SPM 2010 Paper1 Question 1

Diagram 1 shows the relation between set X and set Y in the graph form.

SPM 2010 Paper1- Question 1

State

(a)    The relation in the form of ordered pairs.
(b)   The type of the relation
(c)    The range of the relation

(3 marks)

Solution:

a)      Analysis

  • The question required you to state the relation in the form of ordered pairs, eg: {(a,b),(c,d)},
  • Hence we can state it as {(1,p),(2,r),(3,s),(4,p)}.
  • Remember that the element of set X come first, follow by the element from set Y, eg: (element from set X, element from set Y).  

b)      Analysis

  • We need to know the objects and images
  • Objects – 1,2,3,4 (from set X) 
  • Images – p,r,s      (from set Y) 
  • 1 & 4 could be mapped to p, so we can state the relation as many to one relation.

c)      Analysis

  • The range is all the images being mapped, in this case the range = {p,r,s}
  • Take note that q is not included as it does not belong to any object

SPM 2010 arrow diagram
 
 

Functions – SPM 2007 Paper1 Question 2

Given that f : x –> | x – 3 |, find the values of x such that f(x) =5. [2marks]

Solution:

Analysis

Given | x – 3 | and f(x) = 5, meant that you have both positive (5) and negative (-5) image value, so,

x – 3 = 5 or x – 3 = -5

        x = 8 or      x = -2  

Thus, x = 8 or x = -2
 
 

Composite Functions – SPM 2007 Paper1 Question 3

The following information is about the function h and the composite function h2.

h : x –> ax + b, where a and b are constants, and a > 0h2 : x –> 36x – 35

Find the value of a and b [3marks]

Solution:

Given h(x) = ax + b

h2(x)    = hh(x)

= h( ax + b )

= a( ax + b ) + b [ insert ax + b into the function h(x) again ]

= a2x + ab + b

If we compare both composite functions

h2(x) = 36x – 35

h2(x) = a2 x + ab + b

you will see that a2 = 36,

a = 6 [ Since a > 0, so we do not accept -6 here ]

ab + b = -35

6b + b = -35 

        7b = -35

          b = -5

So a = 6, b = -5
 
 

Composite Functions & Inverse Functions – SPM 2010 Paper1 Question 2

Given the functions g:x –> 2x + 1 and h:x –> 3x + 6, find

(a) g-1(x)

(b) hg-1(9)

(3 marks)

Solution:

 

Solution for SPM2010 Question 2

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About Cedric Low

MBA holder from University of Southern Queensland Australia (USQ) in 2009. Studied for IT and graduated from University of Hertfordshire in UK back to 2005. A system engineer turned to become a full time Maths tutor and researcher. Living in Malaysia. Editor of Perfectmaths.com

Posted on 16/06/2011, in Functions, SPM Additional Maths and tagged , , , . Bookmark the permalink. 1 Comment.

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