O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2015 · Q108 Marks
The relationship between experimental values of two variables, x and y, is given by y = Abˣ, where A and b are constants.
- (i)By transforming the relationship y = Abˣ, show that plotting lny against x should produce a straight line graph.[2]
- (ii)The diagram below shows the results of plotting lny against x for 7 different pairs of values of variables, x and y. A line of best fit has been drawn. [Figure 10.1] By taking readings from the diagram, find the value of A and of b, giving each value correct to 1 significant figure.[4]
- (iii)Estimate the value of y when x = 2.5.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [M1] ln y = ln(Abˣ) ⇒ ln y = ln A + ln bˣ
- [A1] ⇒ ln y = ln A + x ln b
- [M1] ln A = 11.4 ⇒ A=e^(their 11.4) condone misread of scale for M1 (11.2 only)
- [A1] A = 90000 cao
- [M1] ln b = -1 Allow awrt -1
- [A1] b = 0.4 cao
- [M1] x = 2.5 ⇒ ln y = 9
- [A1] y = e⁹ or 8000 to 1 sf Allow awrt 8100
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