The twin prime conjecture states that there are infinitely many consecutive primes ( eg. It involves understanding the modulo operation.ġ8) Fermat’s last theorem: A problem that puzzled mathematicians for centuries – and one that has only recently been solved.ġ9) Natural logarithms of complex numbersĢ0) Twin primes problem: The question as to whether there are patterns in the primes has fascinated mathematicians for centuries. This is a puzzle that was posed over 1500 years ago by a Chinese mathematician. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions?ġ6) Euler’s identity: An equation that has been voted the most beautiful equation of all time, Euler’s identity links together 5 of the most important numbers in mathematics.ġ7) Chinese remainder theorem. Why do magic squares work?ġ4) Egyptian fractions: Egyptian fractions can only have a numerator of 1 – which leads to some interesting patterns. 3,4,5 triangle).ġ1) Mersenne primes: These are primes that can be written as 2^n -1.ġ2) Magic squares and cubes: Investigate magic tricks that use mathematics. There is a $1 million prize for solving the Riemann Hypothesis and $250,000 available for anyone who discovers a new, really big prime number.ġ0) Pythagorean triples: A great introduction into number theory – investigating the solutions of Pythagoras’ Theorem which are integers (eg. The great Indian mathematician Ramanujan discovered some amazing examples of these.ħ) Patterns in Pascal’s triangle: There are a large number of patterns to discover – including the Fibonacci sequence.Ĩ) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics.

Fermat’s Last Theorem is one of the most famous such equations.Ħ) Continued fractions: These are fractions which continue to infinity. For example, Mod 3 means the remainder when dividing by 3.Ģ) Goldbach’s conjecture: “Every even number greater than 2 can be expressed as the sum of two primes.” One of the great unsolved problems in mathematics.Ĥ) Applications of complex numbers: The stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers.ĥ) Diophantine equations: These are polynomials which have integer solutions. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL).ġ) Modular arithmetic – This technique is used throughout Number Theory. A large number of enrichment activities such as treasure hunts, quizzes, investigations, Desmos explorations, Python coding and more – to engage IB learners in the course.Ī list with over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework.Original Paper 3 investigations (with full worked solutions) to develop investigative techniques and support both the exploration and the Paper 3 examination.These make great homework sheets or in class worksheets – and are each designed to last between 40 minutes and 1 hour. Original pdf worksheets (with full worked solutions) designed to cover all the syllabus topics.The content now includes over 3000 pages of pdf content for the entire SL and HL Analysis syllabus and also the SL and HL Applications syllabus.

My new site has been designed specifically for teachers of mathematics at international schools. If you are a teacher then please also visit my new site:. All free!Īlso make sure to visit my page for Exploration Guides to download 3 specific guides to support the whole coursework process for IB students. Make sure to also visit my page on Paper 3s to download 13 different Paper 3s (which would also make excellent coursework starting points) complete with full markschemes.

Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL). Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework.

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