Analysis and Approaches for IBDP Maths Ebook 1 | Page 22

Your Practice Set – Analysis and Approaches for IBDP Mathematics
6
Paper 2 Section A – Find the unknown coefficients
of a curve with given number of intersections
Example
2
Let f ( x) �x � 2kx
and g( x) �6x
� 1. The graphs of f and g intersect at two distinct
points. Find the possible values of k .
[8]
Solution
2
x � 2kx � 6x
� 1
(M1) for setting equation
2
x � (2k �6) x �1� 0
M1
2
� � b � 4ac
� 0
(M1)R1 for discriminant
2
(2k �6) � 4(1)(1) � 0
(A1) for substitution
2
4k
� 24k� 32 � 0
2
k �6k�8 � 0
( k� 2)( k� 4) � 0
(M1) for factorization
k � 2 or k � 4
A2 N3
[8]
Exercise 6
2
1. Let f ( x) � �x � 4x
and g( x) �2kx
� 1. The graphs of f and g do not intersect with
each other. Find the possible values of k .
[8]
2
2. Let f ( x) � x � 4x � 4k
and g( x) �2kx
� 16 . The graphs of f and g intersect at two
distinct points. Find the possible values of k .
[8]
2
3. Let f ( x) �x � 1.5k
and g( x) � �16 � (8 � k)
x . The graphs of f and g intersect with
each other. Find the possible values of k .
[8]
2
4. Let f ( x) � x � 2x � 2k
and g( x) �9
� kx . The graphs of f and g intersect with each
other at most once. Find the possible values of k .
[8]
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