Quelpr
4 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2 · Question 6(a)(i)

The function f is defined on the set of real numbers by f(x) = x³ - 6x² + 9x.

Determine the coordinates of the points where the curve y = f(x) intersects the x-axes and y-axes.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 6(a)(ii)a)Determine the coordinates of the stationary points on y = f(x).[4 marks]
  2. 6(a)(ii)b)Classify EACH of the stationary points on y = f(x) as a maximum point, minimum point or point of inflection.[3 marks]
  3. 6(a)(iii)Hence, sketch a carefully labelled graph of y = f(x).[3 marks]
  4. 6(b)Calculate the area of the shaded region.[6 marks]
  5. 6(c)The gradient at any point (x, y) on a curve is equal to (5x + 1)². Given that the curve passes through the point (1, 0.2), determine the equation of the curve.[5 marks]

More practice: the rest of this paper · more Algebraic Operations questions · all CAPE Pure Mathematics Unit 1 past papers