Exact Values (Edexcel GCSE Maths: Foundation)

What are exact values?

• An exact value is one where the answer can be expressed exactly and is not rounded, truncated or an unending decimal 
  • It may be written as an integer, a fraction, a terminating decimal or as a multiple of a root or known constant such as

How do I give an answer in terms of π?

• In a question involving circles you may be asked to give an answer in terms of
  • Treat  like an algebraic term
• If calculating the circumference or area of a circle or part circle without a calculator
  • Substitute the values you know into the appropriate formula 
  • Simplify the expression by performing the operations on the numbers only
  • Leave your final answer as a multiple of 

What is a surd?

• A surd is the square root of a non-square integer
• Using surds lets you leave answers in exact form
  • E.g.   rather than 

• Your calculator may automatically give you an answer to a calculation in surd form
  • Make sure that you are confident interpreting answers in surd form and entering surds into your calculator

How do I work with surds?

• Adding or subtracting surds is very like adding or subtracting letters in algebra
  • You can only add or subtract multiples of 'like' surds
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• Be very careful, you can not add or subtract numbers under square roots
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• Remember that squaring is the inverse operation of taking the square root
  • If you square a surd, the result is the number without the root sign
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