| Date | May 2009 | Marks available | 4 | Reference code | 09M.1.sl.TZ2.11 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 11 | Adapted from | N/A |
Question
Consider \(f:x \mapsto {x^2} - 4\).
Find \(f ′(x)\).
Let L be the line with equation y = 3x + 2.
Write down the gradient of a line parallel to L.
Let L be the line with equation y = 3x + 2.
Let P be a point on the curve of f. At P, the tangent to the curve is parallel to L. Find the coordinates of P.
Markscheme
\(2x\) (A1) (C1)
[1 mark]
3 (A1) (C1)
[1 mark]
\(2x = 3\) (M1)
Note: (M1) for equating their (a) to their (b).
\(x =1.5\) (A1)(ft)
\(y = (1.5)^2 - 4\) (M1)
Note: (M1) for substituting their x in f (x).
(1.5, −1.75) (accept x = 1.5, y = −1.75) (A1)(ft) (C4)
Note: Missing coordinate brackets receive (A0) if this is the first time it occurs.
[4 marks]
Examiners report
This question was generally answered well in parts (a) and (b).
This question was generally answered well in parts (a) and (b).
This part proved to be difficult as candidates did not realise that to find the value of the x coordinate they needed to equate their answers to the first two parts. They did not understand that the first derivative is the gradient of the function. Some found the value of x, but did not substitute it back into the function to find the value of y.
