May/June 2026 Paper 12

2026 · 10 questions · 19 parts · 75 marks

0/75 marks

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–/3 mks

–/7 mks

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4(a)(i)4(a)(ii)4(b)

–/7 mks

–/7 mks

–/4 mks

7(a)7(b)(i)7(b)(ii)

–/10 mks

–/11 mks

–/11 mks

10(a)10(b)(i)10(b)(ii)

–/9 mks

Context for question 9

the curve with equation y = 3 times the square root of (2x + 1), rising from the origin O through the point R(4, 9); the normal to the curve at R, drawn as a straight line crossing the y-axis above O and sloping down to cross the x-axis to the right of R; and the horizontal line y = a crossing both the curve and the normal. The region bounded by the curve, the y-axis, the line y = a and the vertical line through R is shaded.

The diagram shows the curve with equation

y = 3 2 x + 1

, the normal to the curve at the point

R (4, 9)

and the line

y = a

, where

a

is a positive constant.

9(a)Areas Volumes Arc LengthMedium4 marks

Find the area of the shaded region.

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0 words

Area of the shaded region

9(b)Differentiation Rules Tangents NormalsHard7 marks

Find the exact value of

a

for which the triangular area enclosed by the

y

-axis, the normal to the curve at

R

and the line

y = a

is equal to the area found in 9(a).

Show your working

0 words

Exact value of a