Watch out
Choosing a method from a remembered keyword instead of reading the whole question.
Back to National 5 Mathematics
SQA National 5 Mathematics
Circle properties
Using radius, diameter, circumference and area relationships.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Read the command word and identify what is being asked.
- Write down the relevant formula, rule or algebraic structure before substituting values.
- Keep working set out line by line so method marks are clear.
Explanation
Circle properties is part of Geometry and Measurement in SQA National 5 Mathematics. The key skill is choosing a method and communicating the working clearly.
For circle properties, underline the values or algebraic terms you are given, choose the matching rule, then simplify one line at a time.
National 5 answers should show enough working for a marker to follow the method. Exact answers are expected where the question asks for exact form; otherwise round only at the end.
Key formulae and rules
- Calculator and non-calculator methods may both be useful.
- Pythagoras: a² + b² = c²
Check
Compare your answer with the size you expected from the question.
Exam tip
Method marks come from clear setup and correct mathematical notation, not just a final answer.
Calculator tip
Use brackets for fractions, powers and square roots, then round only at the final line.
Worked examples
Worked example 1
Use a geometry formula
Find the area of a circle with radius 5 cm.
- Area = πr²
- Area = π x 5²
- Area = 25pi
Answer: 25pi cm², about 78.5 cm²
Worked example 2
Use scale factor
Two similar shapes have length scale factor 3. A side of 4 cm becomes what length?
- Multiply by the length scale factor.
- 4 × 3 = 12
So: 12 cm.
Worked example 3
Check units
A sector has area in square centimetres.
- Area uses square units.
- Length uses ordinary units.
- Volume uses cubic units.
Answer: A sector area answer should be in cm².
Watch out
- Choosing a method from a remembered keyword instead of reading the whole question.
- Dropping negative signs, powers or brackets during the working.
- Giving a rounded decimal when an exact answer or algebraic form is needed.