Exact Values
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
Exam Tip
- If you are using your calculator to work out a problem involving , it will often give you your final answer in terms of .
- You just need to write down what you see on the calculator display!
Worked example
Find the perimeter of the semicircle shown below.
Leave your answer in terms of .
The perimeter of the semicircle is made up of the arc of the semicircle and the diameter
Find the circumference of a circle with diameter 8 cm
Use the formula,
Find the arc length of the semi-circle by dividing the circumference by 2
Add the diameter (8 cm) to the arc length to find the perimeter of the semi-circle
Leave the answer as an expression in terms of