2014 A-level H1 Mathematics (8864) Question 2 Suggested Solutions

By KS Teng

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

(i)
\frac{d}{dx} \mathrm{ln} (x^{2}+4)

= \frac{2x}{x^{2}+4}

(ii)
\frac{2x}{x^{2}+4} = k

kx^{2} - 2x +4k = 0

(iii)
For kx^{2} - 2x +4k = 0 to have equal roots,

Discriminant ~ = 0

(-2)^{2}-4(k)(4k) = 0

16k^{2}-4 = 0

(4k-2)(4k+2) = 0

k = \pm 0.5

KS Comments:

Question is well attempted and simple. Students just need to know the definition of discriminants well.

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