CAIE A-Level Mathematics AS 2.2.4 Linearising Relationships Questions

Allow inclusion of $\ln \mathrm{e}$.

Equate A-B to gradient of line
Obtain A-B=4.2
Substitute appropriate values to find value of $\ln A$
Obtain $\ln A=1.92$ and hence A=6.82 and B=2.62
or greater accuracy.

Alternative Method 1

State or imply equation $\ln y=\ln A+(A-B) x$
Allow inclusion of $\ln \mathrm{e}$.

Use of coordinates to obtain equation of line $\frac{\ln y-3.6}{14.1-3.6}=\frac{x-0.4}{2.9-0.4}$
condone use of y in place of $\ln y$.

Obtain gradient equal to 4.2
Substitute appropriate values to find value of $\ln A$

М1

Obtain $\ln A=1.92$ and hence A=6.82 and B=2.62
or greater accuracy.

Alternative Method 2

State or imply equation $\ln y=\ln A+(A-B) x$
Allow inclusion of $\ln \mathrm{e}$.

$3.6=\ln A+0.4(A-B)$
For one correct equation.

$14.1=\ln A+2.9(A-B)$
For both correct equations.

Obtain A=6.82 and B=2.62
For attempt at solution by elimination of $\ln A$ to obtain
both values. SC B1 for y=4.2 x+1.92.

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