Skip to content

Course home

Sign up

1 Unit 1: Pure Mathematics A

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357
Question 76

The temperature of water (w∘Cw^\circ\text{C}w∘C) in a kettle t t\,t minutes after it was boiled is recorded in the table below

ttt1369111520
www92766550463325

The data is coded using the changes of variable x=tx = tx=t and y=log⁡10wy = \log_{10} wy=log10​w

The regression line of x x\,x on y y\,y is found to be y=1.99−0.031xy = 1.99 - 0.031xy=1.99−0.031x

a.

Given that the data can be modelled by an equation in the form w=abtw = ab^tw=abt where a a\,a and b b\,b are constants. Find the values of a a\,a and b b\,b to 3 significant figures.

[3]
b.

Give an interpretation of the constant a a\,a in this equation.

[1]
c.

Explain why this model is not reliable for calculating the temperature after 1 hour.

[1]
Markscheme

1 Unit 1: Pure Mathematics A Questions

  1. A Level
  2. /Maths
  3. /1 Unit 1: Pure Mathematics A

Question bank