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Mathematics

We develop mathematical thinkers through deep, structured training — building logic, creativity, and confidence from Primary all the way to Senior level. Our Olympiad approach goes far beyond the classroom syllabus.

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The Mathematics pathway

PrimaryJuniorIntermediateSenior
Ages 11–13 · Years 7–8

Building the Olympiad toolkit

Junior students are introduced to the core topics of competitive mathematics. We move beyond school-level content into the problem-solving techniques that distinguish strong mathematical thinkers — parity, extremal principles, modular arithmetic and more.

What we cover

  • Number theory fundamentals
  • Algebraic identities and equations
  • Combinatorics and pigeonhole principle
  • Geometry: congruence, similarity, angles
  • Proof by contradiction and invariants

Competitions & exams we prepare for in United Kingdom

  • Junior Mathematical Challenge — JMC (UK)
  • Junior Kangaroo (UK)
  • Junior Mathematical Olympiad — JMO (UK)
  • Bebras Computational Thinking

Topics we explore

ParityYou, of course, know that there are even and odd numbers.Even numbers are those that are divisible by 2 without a remainder (for example, 2, 4, 6, etc.). Each such number can be written as 2K by choosing a suitable integer K (for example, 4 = 2 x 2, 6 = 2 x 3, etc.).Odd numbers are those that, when divided by 2, leave a remainder of 1 (for example, 1, 3, 5, etc.). Each such number can be written as 2K + 1 by choosing a suitable integer K (for example, 3 = 2 x 1 + 1, 5 = 2 x 2 + 1, etc.).Even and odd numbers have remarkable properties:a) the sum of two even numbers is even;b) the sum of two odd numbers is even;c) the sum of even and odd numbers is odd number.View on ProblemsWorst Case ScenarioView on ProblemsRacingView on ProblemsEquationsView on ProblemsPigeonhole principlePigeonhole Principle (Dirichlet's principle) is a simple, intuitive, and often useful method for proving statements about a finite set. This principle is often used in discrete mathematics, where it establishes a connection between objects (“rabbits”) and containers (“cells”) when certain conditions are met.‍View on ProblemsKnights and LiarsThere are two types of inhabitants on the Island of Knights and Liars. Knights always tell the truth. Liars always lie.View on ProblemsNumber Placement GraphsPlace numbers in circles or cells on a graph while satisfying equal-sum, side-sum, target-answer, or adjacency constraints.View on ProblemsBase Numbers ProblemsView on ProblemsSquare DissectionsView on ProblemsChessboard ColouringClassic board-colouring problems where a simple colour or weight pattern proves an impossibility, or shows the right construction.View on ProblemsClock — Hours and MinutesExplore clock-hand angle problems: when the hands overlap, point at right angles, or line up in other ways. Touch and drag the clock to set the time directly.View on ProblemsColouringsColour grids, cube faces, vertices, and edges subject to neighbour and count constraints — hands-on entry to construction and proof.View on ProblemsDoubling the MedianLearn how to apply the method of doubling the median in triangle geometry. Includes proofs and ratio problems involving triangle medians.View on ProblemsExponents (Last Digit)Explore deep-thinking maths problems involving last digits, powers, prime numbers, and digit tricks. Perfect for ages 11–16 and ideal for UKMT, AMC, and GCSE enrichment. Includes Olympiad-style theory with modular arithmetic, Diophantine equations, and factorial analysis.View on ProblemsKnight ReturnsExact-move knight return problems built around colouring invariants and closed walks in the knight graph.View on ProblemsMagic SquaresA classic number puzzle where rows, columns, and diagonals all add up to the same magic sum.View on ProblemsMatchsticks ProblemsMove or remove matchsticks to build target figures with no dangling sticks.View on ProblemsMaximum Non-Attacking PiecesExtremal chessboard placement problems solved by combining upper bounds with constructions.View on ProblemsPatterns in Numbers and DigitsProblems on periodicity. Spot patterns in them!View on ProblemsRatioView on ProblemsRiver Crossing RiddlesClassic brain teasers where you transport items or people across a river while following specific rules to avoid dangerous combinations.View on ProblemsRoman Numeral Matchstick EquationsMove one matchstick in a Roman numeral equation to make it true, or to keep it true.View on ProblemsRotational SymmetryView on ProblemsWater Pouring PuzzlesClassic brain teasers where you measure exact amounts using unmarked containers through filling, emptying, and pouring.View on Problems

Courses in Mathematics

Olympiad Mathematics
MathematicsAge 8+

Olympiad Mathematics

Join our Olympiad Maths training for ambitious students. Build skills in key topics like algebra, geometry, and combinatorics while practising with real past papers and simulated challenges.

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Curriculum Mathematics
MathematicsAge 8+

Curriculum Mathematics

A complete maths course for exam success. Strengthen core skills, tackle advanced topics, and prepare for school, GCSE, or A-Level maths exams with confidence.

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Introduction to Financial Mathematics
MathematicsAge 16+

Introduction to Financial Mathematics

Financial Mathematics is a course that teaches students the mathematical principles and techniques needed to understand and analyze financial data. It is an essential subject for anyone interested in pursuing a career in finance or economics, as it helps students develop skills in problem-solving, critical thinking, and data analysis.

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