2014 A-level H2 Mathematics (9740) Paper 1 Question 2 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

$x^{2}y+xy^{2}+54=0$
differentiating with respect to x,
$2xy+x^{2}(\frac{dy}{dx})+y^{2}+2xy(\frac{dy}{dx})=0$
When $\frac{dy}{dx}=-1$
$-x^{2}+2xy+y^{2}-2xy=0$
$y^{2}=x^{2}$
$y=\pm{x}$

When $y=x$ ,
$y^{3}+y^{3}+54=0$
$y^{3}=-27$
$y=-3$
$x=-3$

When $y=-x$
$-y^{3}+y^{3}+54=0$
There is no solutions.

Therefore, required coordinates are $(-3,-3)$

Personal Comments:
This question tests students on their understanding of basic differentiations. First pitfall was when students forget to introduce $\pm{ }$ . And to SHOW there is only one such point baffled many as they didn’t know how to go about. But the most direct way is to solve for them and find there is only one. Lastly, read the question carefully and you will see they require the answers to be COORDINATES.

A-level Differentiation H2 Mathematics Paper 1 Pure Mathematics Suggested Solution Year 2014

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

Comments

pingbacks / trackbacks

2014 H2 Mathematics (9740) Suggested Solutions | The Culture
[…] 1: Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question […]
July 28th, 2015 12:59 PM

Cart

2014 A-level H2 Mathematics (9740) Paper 1 Question 2 Suggested Solutions

Leave a Comment
Cancel reply

2014 A-level H2 Mathematics (9740) Paper 1 Question 2 Suggested Solutions

Leave a Comment Cancel reply

Leave a Comment
Cancel reply