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Date May 2017 Marks available 2 Reference code 17M.1.SL.TZ1.S_4
Level Standard Level Paper Paper 1 Time zone Time zone 1
Command term Predict Question number S_4 Adapted from N/A

Question

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 0.251 0 0.251 0.992

[2]
b.

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

[2]
c.

Markscheme

t     A1     N1

[1 mark]

a.i.

105     A1     N1

[1 mark]

a.ii.

0.992     A2     N2

[2 marks]

b.

valid approach     (M1)

eg d d d t = 2.24 ;   2 × 2.24 ,   2 × 2.24 ,   d ( 2 ) = 2 × 2.24 × 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 105 98.4 2 = 3.3 .

 

[2 marks]

c.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.4—Pearsons, scatter diagrams, eqn of y on x
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Topic 4—Statistics and probability

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