Analysis and Approaches for IBDP Maths Ebook 1 | Page 204

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Solution
(a)
(i)
(ii)
(iii)
1
f�( a) �� � � 1
(M1) for perpendicular slope
3
f�( a) � 3
A1 N2
2
� � M1
f ( x) 3x
f �( a) � 3a
2
2
�3a
� 3
A1
2
a � 1
a � 1
AG N0
3
1 � 0 1
1�
b ��
3
(M1) for slope formula
1 1
1� b �� 3
�3�1�
b
b � 4
A1 N2
(b)
(iv)
The equation of [PQ]:
1
y � � x � c
3
1
0 � � (4) � c
3
(M1) for substitution
4
c �
3
1 4
� y� � x� 3 3
A1 N2
The required area
1 (4 �1)(1 �0)
�� f ( x)dx
�
M1A1
0
2
1
3 (3)(1)
��
x dx�
0
2
1
�1 4 � 3
�
�
x
4 �
�
� �0
2
A2
1 4 1 4 3
� (1) � (0) �
4 4 2
(M1) for substitution
1 3
� � 0 �
4 2
7
�
4
A1 N3
[8]
[6]
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