2010 A-level H2 Mathematics (9740) Paper 1 Question 6 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)
Using GC, \beta = 0.347, \gamma = 1.532

(ii)
Using GC, Area = |\int_0.347^1.532 x^3 - 3x + 1 dx| = 0.781

(iii)
Area = \int_{-\sqrt{3}}^0 x^3 -3x + 1 dx - \sqrt{3} \times 1

= \frac{9}{4}

(iv)
\frac{dy}{dx}=2x^2 - 3 = 0

x = \pm 1

y = 3 \mathrm{~or~}-1

Thus, -1 \textless k \textless 3

KS Comments:

Take note to give (i) to 3 decimal places! For (iii), students can use GC to check their answers too! (iv), Students might want to consider using the GC to graph it out to help yourself find an efficient method

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