17N.1.SL.TZ0.T_12

pestleMathematicsAISLPaper 117N· sl-2-5-modelling-functionssource ↗

Sejah placed a baking tin, that contained cake mix, in a preheated oven in order to bake a cake. The temperature in the centre of the cake mix, $T$ , in degrees Celsius (°C) is given by

$T(t) = 150 - a \times {(1.1)^{ - t}}$

where $t$ is the time, in minutes, since the baking tin was placed in the oven. The graph of $T$ is shown in the following diagram.

N17/5/MATSD/SP1/ENG/TZ0/12

The temperature in the centre of the cake mix was 18 °C when placed in the oven.

The baking tin is removed from the oven 15 minutes after the temperature in the centre of the cake mix has reached 130 °C.

Write down what the value of 150 represents in the context of the question.

[1]

Find the value of $a$ .

[2]

Find the total time that the baking tin is in the oven.

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

the temperature in the oven (A1)

the maximum possible temperature of the cake mix (A1) (C1)

Note: Award (A0) for “the maximum temperature”.

[1 mark]

$18 = 150 - a( \times 1.1^\circ )$ (M1)

Note: Award (M1) for correct substitution of 18 and 0. Substitution of 0 can be implied.

$(a) = 132$ (A1) (C2)

[2 marks]

$150-132 \times {1.1^{ - t}} = 130$ (M1)

Note: Award (M1) for substituting their a and equating to 130. Accept an inequality.

Award (M1) for a sketch of the horizontal line on the graph.

$t = 19.8{\text{ }}(19.7992 \ldots )$ (A1)(ft)

Note: Follow through from part (b).

34.8 (minutes) (34.7992…, 34 minutes 48 seconds) (A1)(ft) (C3)

Note: Award the final (A1) for adding 15 minutes to their $t$ value.

In part (c), award (C2) for a final answer of 19.8 with no working.

[3 marks]

Examiners’ report

[N/A]