17M.1.SL.TZ1.S_4

pestleMathematicsAISLPaper 117M· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

Jim heated a liquid until it boiled. He measured the temperature of the liquid as it cooled. The following table shows its temperature, $d$ degrees Celsius, $t$ minutes after it boiled.

M17/5/MATME/SP1/ENG/TZ1/04

Jim believes that the relationship between $d$ and $t$ can be modelled by a linear regression equation.

Write down the independent variable.

[1]

a.i.

Write down the boiling temperature of the liquid.

[1]

a.ii.

Jim describes the correlation as very strong. Circle the value below which best represents the correlation coefficient.

$0.992\quad \quad \quad 0.251\quad \quad \quad 0\quad \quad \quad - 0.251\quad \quad \quad - 0.992$

[2]

Jim’s model is $d = - 2.24t + 105$ , for $0 \leqslant t \leqslant 20$ . Use his model to predict the decrease in temperature for any 2 minute interval.

[2]

Markscheme / solution

$t$ A1 N1

[1 mark]

a.i.

105 A1 N1

[1 mark]

a.ii.

$- 0.992$ A2 N2

[2 marks]

valid approach (M1)

eg $\,\,\,\,\,$ $\frac{{{\text{d}}d}}{{{\text{d}}t}} = - 2.24;{\text{ }}2 \times 2.24,{\text{ }}2 \times - 2.24,{\text{ }}d(2) = - 2 \times 2.24 \times 105,$

finding $d({t_2}) - d({t_1})$ where ${t_2} = {t_1} + 2$

4.48 (degrees) A1 N2

Notes: Award no marks for answers that directly use the table to find the decrease in temperature for 2 minutes eg $\frac{{105 - 98.4}}{2} = 3.3$ .

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]