2024 BTYSS P2 Q9

Secondary 4

9 marks

The variables \(x\) and \(y\) are connected by the equation \(y=\dfrac{1}{x^2}+\dfrac{3x}{2}-2\).

Some corresponding values of \(x\) and \(y\) are given in the table below.

\(x\)	\(0.4\)	\(0.45\)	\(0.5\)	\(0.6\)	\(0.8\)	\(1\)	\(1.5\)	\(2\)	\(2.5\)	\(3\)
\(y\)	\(4.85\)		\(2.75\)	\(1.68\)	\(0.76\)	\(0.5\)	\(0.69\)	\(1.25\)	\(1.91\)

Complete the table.[2]
Draw the graph of \(y=\dfrac{1}{x^2}+\dfrac{3x}{2}-2\) for \(0.4\leq x\leq3\).
The graph of \(y=\dfrac{1}{x^2}+\dfrac{3x}{2}-2\) for \(-0.75\leq x\leq-0.3\) has been drawn for you.[2]

Explain why the graph does not exist when \(x=0\).[1]
By drawing a tangent, find the gradient of the curve at \(x=0.7\).[2]
Use the graph to find the solutions to the equation \(\dfrac{1}{x^2}+\dfrac{3x}{2}-2=2\).[2]

Similar questions are unavailable for this question.

Answer:(a) \(3.61,\ 2.61\) (b) See graph. (c) Division by zero is undefined. (d) Approximately \(-4.3\). (e) Approximately \(-0.46,\ 0.56,\ 2.57\).

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