CAIE IGCSE Mathematics Extended Differentiation Questions

Cambridge IGCSE Mathematics 0580 syllabus for exams in 2028, 2029 and 20302028–2030

Practise differentiating polynomial functions, finding and classifying stationary points and forming tangent equations from derivative gradients.

How this is tested

differentiate each ax^n term as anx^(n−1) and simplify the derived function
solve dy/dx = 0 and substitute each x-value into the original curve for stationary coordinates
classify stationary points or use the derivative gradient with a point to form a tangent equation

[Maximum number: 3]

The table shows some values for $y=x^{3}+4 x^{2}-4$ .

(a)

Draw the tangent to the graph at the point (1,1).

[ 1 ]

(b)

Use your tangent to estimate the gradient of the curve at the point (1,1).

[ 2 ]