Analysis and Approaches for IBDP Maths Ebook 2 | Page 93

Solution
(a)
� � �
OR �OP� PR
(M1) for valid approach
� �
7
�
OR �OP�
PQ
10
� �
7
� �
OR � OP � (OQ�
OP)
10
�
7
OR � p � ( q �p
)
10
(A1) for substitution
�
7 7
OR � p � q � p
10 10
�
3 7
OR � p�
q 10 10
A1
(b)
� � �
TR �OR� OT
(M1) for valid approach
�
3 7
TR � p � q � � q 10 10 (A1) for substitution
�
3 � 7 �
TR � p� � ��
�q A1
10 � 10 �
� � �
(c) ST �OT� OS
(M1) for valid approach
� � �
�
ST �OT�
PQ
� � � �
�
ST � OT � (OQ�
OP)
�
ST � � q � �( q �p
)
(A1) for substitution
�
ST � � q � � q � � p
[3]
[3]
8
�
ST � � p� ( � � �)
q A1
[3]
(d) ST :TR � 3:5
ST 3
� M1
TR 5
5ST � 3TR
�
�
5ST � 3TR
A1
� 3 � 7 � �
�5( �p � ( � � �) q) � 3�
p � � ��
�q � A1
� 10 � 10 � �
9 7
5� 5( � �) 3
� �
p � � q � p � � ��
�q M1
10 �10
�
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