EXN.1.SL.TZ0.8

pestleMathematicsAISLPaper 1EXN· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

The water temperature $(T)$ in Lake Windermere is measured on the first day of eight consecutive months $(m)$ from January to August (months $1$ to $8$ ) and the results are shown below. The value for May (month $5$ ) has been accidently deleted.

Assuming the data follows a linear model for this period, find the regression line of $T$ on $m$ for the remaining data.

[2]

Use your line to find an estimate for the water temperature on the first day of May.

[2]

Explain why your line should not be used to estimate the value of $m$ at which the temperature is $10.0$ $° C$ .

[1]

c.i.

Explain in context why your line should not be used to predict the value for December (month $12$ ).

[1]

c.ii.

State a more appropriate model for the water temperature in the lake over an extended period of time. You are not expected to calculate any parameters.

[1]

Markscheme / solution

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$(T = 1.517 \dots m + 3.679 \dots) T = 1.52 m + 3.68$ A1A1

[2 marks]

$11.3 (11.2671 \dots) (° C)$ (M1)A1

[2 marks]

Because the line should only be used to estimate $T$ from $m$ and not $m$ from $T$ . R1

[1 mark]

c.i.

Because the temperatures are no longer going up at a steady rate, or because we know that winter is approaching so the temperature will go down, or temperatures are not likely to continue increasing. R1

[1 mark]

c.ii.

Trigonometric or sinusoidal A1

[1 mark]

Examiners’ report

[N/A]

c.i.

[N/A]

c.ii.

[N/A]