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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Advanced Problem Solving Module 6

##### 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.
### The Why and How of Substitution

### Agile Algebra

### Symmetrically So

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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.

Age 16 to 18

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.

Age 16 to 18

Challenge Level

Observe symmetries and engage the power of substitution to solve complicated equations.

Age 16 to 18

Challenge Level

Exploit the symmetry and turn this quartic into a quadratic.