Year 10 - Maths
Checking and securing understanding of circles
2D and 3D shape: compound shapes
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Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, knowledge of circles and polygons is drawn upon to find the arc length and area of a circle sector and areas of complex compound shapes.
Lesson Summary
You will learn to identify the parts of a circle and calculate the perimeter and area of a circle.
Key Notes
- A chord splits the circle into two uneven pieces.
- The smaller piece is the minor segment and the larger is the major segment.
- Sectors look familiar as you broke a circle into sectors to draw a pie chart.
- The circumference of a circle is found using C = πd or C = 2πr
- The area of a circle is found using A = πr²
Vocabulary To Learn
- Chord: A chord is any line segment joining two points on the circumference of a circle.
- Segment: Two segments are created when dividing a circle into two parts using a chord.
- Sector: A sector is the region formed between two radii and their connecting arc.
- Arc: An arc is part of a curve. An arc of a circle is part of the circle's circumference.
Common Mistakes To Avoid
- "Any line segment starting from the centre of a circle is a radius."
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A chord splits the circle into two uneven pieces. The smaller piece is the minor segment and the larger is the major segment.
2. Use this key word in a maths sentence and explain it clearly. 'Chord'
A chord is any line segment joining two points on the circumference of a circle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: "Any line segment starting from the centre of a circle is a radius.". Correction: It is true that one endpoint of a radius must be at the centre of a circle. However, the other endpoint must be on the circumference of the circle. This second endpoint cannot be inside or outside of the circle.
More Lessons In This Unit
- Area of a sector Study Guide
- Area of compound shapes Study Guide
- Calculating arc length Study Guide
- Checking and securing understanding of area for compound shapes Study Guide
- Checking and securing understanding of area for standard shapes Study Guide
- Checking and securing understanding of converting between metric and imperial measures Study Guide
- Checking and securing understanding of perimeter for compound shapes Study Guide
- Checking and securing understanding of perimeter for standard shapes Study Guide
- Checking and securing understanding of scales and conversion Study Guide
- Equations from complex shapes Study Guide
- Perimeter and area in a contextual setting Study Guide
- Problem solving with 2D shapes Study Guide
- Problem solving with complex 2D shapes Study Guide
- Shapes on coordinate grids Study Guide
- Shapes within shapes Study Guide
Browse all guides in the Year 10 Maths guide library.