21N.2.SL.TZ0.2

pestleMathematicsAASLPaper 221N· sl-2-3-graphingsource ↗

Consider the function $f (x) = e^{- x^{2}} - 0.5$ , for $- 2 \leq x \leq 2$ .

Find the values of $x$ for which $f (x) = 0$ .

[2]

Sketch the graph of $f$ on the following grid.

[3]

Markscheme / solution

$x = - 0.832554 \dots, x = 0.832554 \dots$

$x = - 0.833, x = 0.833$ A1A1

[2 marks]

A1A1A1

Note: Award A1 for approximately correct shape. Only if this mark is awarded, award A1 for approximately correct roots and maximum point and A1 for approximately correct endpoints.
Allow $- 1 < x \leq - 0.8, 0.8 \leq x < 1$ for roots, $x = 0, 0.4 \leq y \leq 0.6$ for maximum and $x = \pm 2, - 0.6 \leq y \leq - 0.4$ for endpoints.

[3 marks]

Examiners’ report

[N/A]