- Problem solving in mathematics involves using several stages, across a variety of topics, to answer a question
- In this set of notes all the problems will involve
**equations**- These could be
**linear**equations,**quadratic**equations or**simultaneous**equations and**other**, relatively straightforward equations

- These could be

- You may notice there are not many subheadings in these notes
- That is deliberate so the examples are not labelled or dealt with in an order
- This is the nature of problem solving questions!
- You never know exactly what’s coming ... !

- In an ordinary mathematics question you would be given an equation to solve
- In a problem solving question you would have to
**generate**the equation ...- ... using information from the question
- ... using your knowledge of standard mathematical results

- A key feature of problem solving questions is to
**interpret**the answer in**context** - An answer on a calculator may be
**2**- If the question was about money then your final answer should be
**£1.20**

- If the question was about money then your final answer should be
- A
**quadratic**equation can have**two**solutions- Only
**one**may be valid if**only**positive values are relevant (eg distance)

- Only

- In problem solving questions you are typically given less information about the type of maths involved
- It is impossible to list every type of problem solving question you could see
- There are endless contexts questions can be set in
- There is no one-fits-all step-by-step method to solving problems

**Practice**,**experience**and**familiarity**are the keys to solving problems successfully

- Do
**not**necessarily expect whole number (**integer**) or “nice” solutions- Especially where a calculator is allowed

**Rounding****appropriately**may be one of the skills being tested- eg Rounding a value in
**cm**only needs to be to one decimal place;so it indicates

**mm**

- eg Rounding a value in

- Do
**not**start by focusing on what the question has asked you to find, but on what maths you**can**do - If your attempt turns out to be unhelpful, that’s fine, you may still pick up some marks
- If your attempt is relevant it could nudge you towards the full solution – and full marks!
- Add information to a
**diagram**as you work through a problem- If there is no diagram, try
**sketching**one

- If there is no diagram, try

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