Working through this module will help you to consolidate your existing knowledge before extending your thinking. For more details about the Advanced Problem Solving programme, READ THIS.
One important mathematical technique that can be really useful in solving STEP and other advanced mathematics examinations questions is being able to spot a clever substitution. The right substitution can make an equation or integral that seems intractable at first glance into something straightforward to solve. This collection of problems and articles showcase the technique of the clever substitution.
article
The why and how of substitution
Step back and reflect! This article reviews techniques such as
substitution and change of coordinates which enable us to exploit
underlying structures to crack problems.
problem
Agile algebra
Age
16 to 18
Challenge level
Observe symmetries and engage the power of substitution to solve complicated equations.
problem
Symmetrically so
Age
16 to 18
Challenge level
Exploit the symmetry and turn this quartic into a quadratic.
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Prepare for university - pure mathematics
Helpful preparation for those intending to study a course involving pure mathematics at university.
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Prepare for university - applied mathematics
Helpful preparation for university for those intending to study a
course involving applied mathematics at university.
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Nrich and olympiads
A useful entry point into the NRICH site for those students interested in Mathematical Olympiad problems or the Maths Challenges.