Intermediate Maths Challenge-Style Mock Paper 2 (UKMT-Style Practice) with Full Worked Solutions

A second full-length Intermediate Maths Challenge-style mock paper with complete worked solutions, built to the exact format of the real UKMT Intermediate Challenge: 25 multiple-choice questions (A to E), 60 minutes, no calculator, 135 marks, with Questions 1 to 15 worth 5 marks and Questions 16 to 25 worth 6 marks, plus the real negative marking (minus 1 on Questions 16 to 20, minus 2 on Questions 21 to 25). Every question is original, written fresh in the style and at the genuine difficulty of the Intermediate Challenge, with all-new contexts so it pairs perfectly with Mock Paper 1. What’s inside: a cover with instructions, the scoring table and a key-facts panel, 25 questions ramping from quick warm-ups to genuine Gold-level problems, a printable answer sheet and a one-glance answer key. The paper is built around six high-yield themes: surds and indices (comparing huge powers, a surd value that collapses a cubic), circle geometry (angle in a semicircle, chords, a circle inscribed in a quarter-circle), sequences (cycling recurrences, Fibonacci-style puzzles), rates and speed (filling with a leak, the average-speed trap), 3D shapes (the painted cuboid, a drilled cylinder, the octahedron inside a cube) and probability (complements, inclusion-exclusion, remainder classes), finishing with a completing-the-square number theory problem. The worked solutions are the real value: every question gets a step-by-step solution that explains the key insight, names the trap behind each tempting wrong option, and shows a fast elimination route, so students learn exactly when to guess and when to leave a box blank under negative marking. Ideal for Year 9 to 11 students preparing for the Intermediate Mathematical Challenge (and the Kangaroo and Olympiad follow-on rounds), for maths club practice, and for tutors and teachers setting a timed mock. Original UKMT-style practice material; not official UKMT papers.