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GCSE Trial & Improvement Questions - easy when you know how.

Updated: Aug 30, 2023



In ‘trial & improvement’ questions, there are steps you can use to guarantee full marks. The idea is to gradually zero in on a reasonable answer. A methodical approach is needed to gain a relatively easy 4+ marks.


Let’s look at an example…


Using the following equation, find a solution for x using a trial and improvement method



Give your answer to 1 decimal place.


To maximise your marks, you need to show step -by-step reasoning.

First, draw a table like this…



For x values, you are looking for two consecutive numbers between which the target number lies... We'll try x = 2 and 3



The target lies more towards x=3 value so it is reasonable to try x = 2.8 or 2.9



2.8 is too low - try 2.9…



So now we know the x lies between 2.8 and 2.9 but does it lie more to 2.8 or 2.9? Time for one last calculation to find out. Try a value halfway between these values… 2.85.



The value for x must be greater than 2.85, so the answer is…


x = 2.9 (to 1 d.p.)


Maximise the marks

  • Draw a table (if it's not done for you!)

  • Find two consecutive numbers so that the value for x lies between them (this may be given in the question)

  • Make small, incremental adjustments to narrow the values - don’t ‘fly around’ using, say, 5 then 8 or 4.4 then 4.9.

  • Examiners want to see a methodical, step-by-step approach to finding a value for x.


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