20N.1.SL.TZ0.T_4

pestleMathematicsAISLPaper 120N· sl-2-4-key-features-of-graphs-intersections-using-technologysource ↗

Consider the graph of the function $f (x) = x + \frac{12}{x^{2}}, x \neq 0$ .

Write down the zero of $f (x)$ .

[2]

a.i.

Write down the coordinates of the local minimum point.

[2]

a.ii.

Consider the function $g (x) = 3 - x$ .

Solve $f (x) = g (x)$ .

[2]

Markscheme / solution

$0 = x + \frac{12}{x^{2}}$ (M1)

Note: Award (M1) for equating the function to zero.

$(x =) - 2.29 (- 2.28942 \dots)$ (A1) (C2)

Note: Award (C1) for a correct $x$ -value given as part of a coordinate pair or alongside an explicitly stated $y$ -value.

[2 marks]

a.i.

$(2.88, 4.33)$ $((2.88449 \dots, 4.32674 \dots))$ (A1)(A1) (C2)

Note: Accept $x = 2.88, y = 4.33$ .

[2 marks]

a.ii.

$3 - x = x + \frac{12}{x^{2}}$ (or equivalent) (M1)

Note: Award (M1) for equating the functions or for a sketch of the two functions.

$(x =) - 1.43 (- 1.43080 \dots)$ (A1) (C2)

Note: Do not award the final (A1) if the answer is seen as part of a coordinate pair or a $y$ -value is explicitly stated, unless already penalized in part (a).

[2 marks]

Examiners’ report

[N/A]

a.i.

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a.ii.

[N/A]