IGCSE Additional Mathematics (0606)

Transforming relationships to linear form

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

When the plotted variable is a function of y (here ln 2y), after solving for 2y you must divide by 2 to find y.
Common mistake: Students often forget this final step and give the value for 2y instead of y.
When solving for x in an equation involving x², both positive and negative roots must be considered.
Common mistake: Students often give only the positive value, missing the negative solution that also satisfies x² = k.
To estimate y for a new x value in a cubic relationship y = P x³ + Q, substitute the cube of x (not x itself) into the equation.
Common mistake: Students often mistakenly use x instead of x³, leading to significant error.
The domain of a logarithmic function y = ln(expression) is where the argument is positive.
Common mistake: Students often forget to solve the inequality for positivity or mistakenly include zero or negative values, or introduce unnecessary plus-or-minus when taking odd roots.
When one expression plotted against another gives a straight line, write Y = mX + c using those expressions, find m and c from the points, then take logs to make y the subject.
Common mistake: The common trap is to miss the need for this transformation or to mishandle the logarithm when isolating y.
Write the straight line as ln 2y = m(x²) + c using the two points, then undo the logarithm by exponentiating and divide by 2 to get y alone.

Work out y when x = 3.

Try it first, then show the working

Answer: y = 2.24

10 exam-style questions on Transforming relationships to linear form, each marked to the scheme.