Analysis and Approaches for IBDP Maths Ebook 2 | Page 142

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b) (i) 5x� 2y� 24 � 0
2y�24 � 5x
y�12 � 2.5x
(M1) for valid approach
� � � � � � (M1) for substitution
2 2
3x 4(12 2.5 x) 2 x(12 2.5 x) 48
2 2 2
3x � 4(144 �60x � 6.25 x ) � 24x �5x
� 48
2 2 2
3x �576 � 240x � 25x � 24x �5x
� 48
2
33x
264x
528 0
x
2
� � � A1
�8x�16 � 0
2
( x �4) � 0
x � 4
� y �12 � 2.5(4)
y � 2
Thus, the coordinates of P are (4, 2) .
A1
(c)
(ii)
The gradient of the tangent at P
3(4) � 2
� (M1) for substitution
4 � 4(2)
5
�� A1
2
The gradient of the tangent
� �1��
4
1
� (A1) for correct value
4
1 3x�
y
� � (M1) for setting equation
4 x � 4y
x � 4y � 4(3 x � y)
x � 4y �12x � 4y
0 � 11x
x � 0
2 2
�3(0) � 4y
� 2(0) y� 48
(M1) for substitution
2
4y � 48
2
y �
12
y �� 12 or y � 12
Thus, the required coordinates are (0, � 12) and
(0, 12) . A2
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