The equation of a curve is y = 4 cos2x + 3 for 0 ≤ x ≤ 2π.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [2] B1B1 B2 for answers of -1 and 7 only. B1 for one correct value. Ignore incorrect identification/inequality. [Greatest] 7, [least] -1
2. [1] B1 for two complete cycles, one from 0 to approximately π and the other finishing at approximately 2π. Starting at their greatest value and initially decreasing. Condone straight lines and minimum above the x-axis or joining points with straight lines.
3. [1] B2 for correct curve; condone any incorrect x-axis intercepts. Graph must start to level off at both 0 and 2π. Ignore any y-labels, but the curve should be more above the x-axis than below.
4. [1] B1 Ignore any graphs drawn. 3 [solutions]