Skip to content

Course home

2.5 Data presentation and interpretation

2.5 Data presentation and interpretation

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193
Question 84

A biochemist is studying the effect of temperature, TTT in ∘C^\circ\text{C}∘C, on the rate of a catalytic reaction, VVV in units of 10−2 mol s−110^{-2} \text{ mol s}^{-1}10−2 mol s−1. Data from a random sample of 12 experiments are summarised as follows:

∑T=480∑T2=21200∑V=150∑V2=2025 \sum T = 480 \quad \sum T^2 = 21200 \quad \sum V = 150 \quad \sum V^2 = 2025 ∑T=480∑T2=21200∑V=150∑V2=2025

and the regression line of VVV on TTT has the equation V=2.5+0.25TV = 2.5 + 0.25TV=2.5+0.25T.

a.

Use the regression line to estimate the rate of reaction in mol s−1\text{mol s}^{-1}mol s−1 for an experiment conducted at 35∘C35^\circ\text{C}35∘C.

[2]
b.

Find the values of STTS_{TT}STT​ and SVVS_{VV}SVV​.

[2]
c.

Calculate the product moment correlation coefficient between TTT and VVV.

[3]
d.

A 13th experiment is performed. The temperature is recorded as 40∘C40^\circ\text{C}40∘C and the rate of reaction is measured as 0.125 mol s−10.125 \text{ mol s}^{-1}0.125 mol s−1.

Use the formula STV=∑(T−Tˉ)(V−Vˉ)S_{TV} = \sum (T - \bar{T})(V - \bar{V})STV​=∑(T−Tˉ)(V−Vˉ) to demonstrate that the value of STVS_{TV}STV​ for the 13 experiments will be identical to its value for the original 12 experiments.

[3]
e.

Determine the new equation of the regression line of VVV on TTT for the full set of 13 experiments.

[2]
f.

Comment on the reliability of using the new regression line to estimate the rate of reaction for an experiment conducted at 120∘C120^\circ\text{C}120∘C, providing a justification for your answer.

[2]
Markscheme

2.5 Data presentation and interpretation Questions

  1. A Level
  2. /Maths
  3. /2.5 Data presentation and interpretation

278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank