CAIE A-Level Mathematics 2.2.4 Linearising Relationships

Practise transforming power or exponential relationships into straight-line form and interpreting gradient and intercept.

Exam points

take logarithms and rearrange the relationship into a straight-line equation
match transformed variables to Y=mX+c and identify the gradient and intercept
use two graph points to calculate constants, then reverse logarithms where required

[Maximum number: 3]

The variables x and y satisfy the equation $y=3^{2 a} a^{x}$ , where a is a constant. The graph of $\ln y$ against x is a straight line with gradient 0.239 .

Find the value of a correct to 3 significant figures.

State or imply equation is $\ln y=\ln 3^{2 a}+x \ln a$

B1

Equate gradient of line involving a to 0.239

М1

Obtain $\ln a=0.239$ and hence a=1.27

A1

3

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2.2.4—Linearising relationships question 1