Equations & Problem Solving (Cambridge O Level Maths)

What is problem solving?

• 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

• 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 1.2
  • If the question was about money then your final answer should be £1.20

• A quadratic equation can have two solutions
  • Only one may be valid if only positive values are relevant (eg distance)

• 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