2014 A-level H1 Mathematics (8864) Question 5 Suggested Solutions

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

5.
(i)
\frac{dy}{dx} = 3x^{2} + 2kx + 7

When x = 1, ~ \frac{dy}{dx} = 0

\Rightarrow 3 + 2k + 7 = 0

k = -5

\Rightarrow 1^{3} - 5 (1)^{2} + 7 + c = 2

\therefore, c = -1

(ii)
\frac{dy}{dx} = 3x^{2} - 10 x + 7 = 0

x= \frac{7}{3} \mathrm{~or~} x = 1

When x = \frac{7}{3}, y = \frac{22}{27}

\therefore, (\frac{7}{3}, \frac{22}{27})

(iii)

Graph of 5

Graph of 5(iii)

(iv)
Area = \int_1^2 x^{3} - 5 x^{2} + 7x - 1 dx

= \frac{x^{4}}{4} - \frac{5x^{3}}{3} + \frac{7x^{2}}{2} - x \biggl|_1^2

= \frac{19}{12}

KS Comments

Students must be careful to leave answers in fractions and not just decimals. They should also check their answers with the Graphing Calculator.

Comments
pingbacks / trackbacks

Leave a Comment

2 × 2 =

Contact Us

CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

Not readable? Change text. captcha txt

Start typing and press Enter to search