2013 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.

y= \frac{x^{2}+x+1}{x-1}
y(x-1) = x^{2}+x+1
0 = x^{2}+x-xy+y+1
For x\in \mathbb{R}, y exists only when b^{2}-4ac \ge 0

(1-y)^{2}-4(1)(1+y) \ge 0

1-2y+y^{2}-4-4y \ge 0

y^{2}-6y-3 \ge 0

y \le 3-2\sqrt{3}~\mathrm{or}~y \ge 3+2\sqrt{3}

KS Comments:

When I first saw this, I was really surprised as O’levels had something really similar. The above method is the most direct, yes, 5 marks for that. Students can also go and find the turning point (and justify they are maximum or minimum) to decide the range.

Showing 3 comments
    pingbacks / trackbacks

    Leave a Comment

    one + one =

    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