CAIE A-Level Mathematics 3.2.4 Linearising Relationships

Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise taking logarithms of power and exponential models, matching the result to a straight-line equation and using plotted gradients and intercepts to recover constants.

How this is tested

take logarithms and rearrange the relationship into Y = mX + c for the plotted axes
calculate the graph gradient and intercept from two points without confusing logged variables
match m and c to model parameters, then exponentiate an intercept to recover its constant

[Maximum number: 4]

Figure for Question 3 — CAIE A-Level Mathematics

The variables x and y are related by the equation $y=a b^{x}$ , where a and b are constants. The diagram shows the result of plotting $\ln y$ against x for two pairs of values of x and y. The coordinates of these points are ( 1,3.7 ) and ( 2.2,6.46 ).

Use this information to find the values of a and b.

How this is tested

Question 3