Problem solving techniques

 

All of the questions that you will come across in your homework or exams are based on work that you have covered, you may just have to think about  which part of the course is being tested.

     

 

A common error is to rush straight in and write down a solution, without any planning ,  working or thought to it being a sensible answer.

 

1.Clarify the problem

                                

Read the question.
Make sure that you answer what the question is asking,  not what you think it is asking.

Some examples

Words used in question	Meaning
Calculate	Work out an answer, showing your working! (Even if it is in a calculator paper !)
Do not use a scale diagram	Use Trigonometry, Pythagoras or Similar Triangles.
Estimate	Do not work out the exact answer
Expand	Multiply out the brackets
Factorise	Take out a common factor or put a quadratic into brackets.
Find	Calculate an answer
Give an exact value	Do not give decimals, use surds or fractions as necessary
Give your answer to 2dp	You must have 2 digits after the decimal point.
Hence	Use the previous answer to continue
Show that	You must work through the steps necessary to arrive at the given answer.
Simplify	Collect all like terms or fully reduce a fraction
Solve Satisfy	Work out the values that make the equation true.
Solve algebraically	Use algebra. A graph will not get you marks.
Write down	No calculations required.

 

Read the question again

If necessary, write down two columns

*What I want                       * What I know

 

and write down what you want, and also the information that you know.

This can help focus your thinking.

Don’t forget to write down any formulae that you may have  been given or are expected to know.

 

Is it a hidden Pythagoras or Trig question ?
Is it work from previous years ?

 

             

 

 

2.Plan your attack

 

• Look for keywords.

E.g. find the area , differentiate, find the max/min

• Draw a diagram.

You can then use it to write in information.

• Make lists if necessary

 

• Eliminate Possibilities

 For example, if  you know that the answer lies in a
certain range, you can ignore answers outside that range.

• Look for a pattern

  It might help you see what is going on.

• Trial and error

Put in numbers to see what happens.

• Unit analysis

Make sure that all your units are the same!

• Act it out if necessary.
• Use a logic grid if necessary
• Use Algebra if it helps.

3.Solve the problem

Go ahead and find a solution.

Organise your work so that it is easy to read by the person who will be marking.

Remember – working is important to get full marks.

 

Remember : you still have to show working even in a calculator paper.

 

 

4.Check your answer
                                   
Is it sensible ? 
Is it to the correct number of decimal places ?
Does it work  ?