01Multiple choice
Medium
Real numbers a and b satisfy a + b = 47 and ab = 552. Find a² + b².
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24 October 2026 · new at 8 am UK time
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02Proof
Hard
How many subsets of {1, 2, …, 15} contain no two consecutive integers? Include the empty set, and justify your count.
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03A-level pure
Challenge (A*)
Let a = 10. The curve C has equation y = x⁴ + 3ax³ − 3a²x² − 7a³x + 6a⁴. The tangent to C at its only stationary point with positive x-coordinate meets C at two other points. Find the total exact area of the finite regions bounded by C and this tangent. Show how you found the intersections and handled any change of sign.
10 marks · Proposed working allocation
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