May/June 2026 Paper 32

2026 · 10 questions · 20 parts · 75 marks

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Context for question 7

y = \frac{3 + sin 3 x}{2 - cos 3 x}

The equation of a curve is given above, for

0 \leq x \leq π

. The gradient of the curve is equal to

- \frac{3}{2}

when

x = a

7(a)Differentiation Rules Tangents NormalsMedium4 marks

Show that

a

satisfies the equation

sin^{2} 3 a + 6 sin 3 a - 3 = 0

Working

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7(b)Trigonometric Identities EquationsMedium3 marks

Hence find the values of

a

for

0 \leq a \leq π

Working

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