Mensuration Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about mensuration for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Area Formulas
Rectangle = length x width. Triangle = (1/2) x base x height. Parallelogram = base x height. Trapezium = (1/2)(a + b) x h where a and b are the parallel sides. Circle = pi x r squared.
Key Formulas
- Rectangle: A = lw
- Triangle: A = (1/2)bh
- Parallelogram: A = bh
- Trapezium: A = (1/2)(a+b)h
- Circle: A = pi r squared
Exam Tips
- The height must be PERPENDICULAR to the base
- For compound shapes, split into simpler shapes and add/subtract areas
- Always include units squared for area
Arc Length and Sector Area
An arc is part of the circumference, and a sector is the region between two radii and an arc. Both use the fraction angle/360 of the full circle formulas.
Key Formulas
- Arc length = (theta/360) x 2 pi r
- Sector area = (theta/360) x pi r squared
- Perimeter of sector = arc length + 2r
Exam Tips
- The fraction theta/360 represents the proportion of the full circle
- For the perimeter of a sector, do not forget the two straight edges (radii)
- These formulas are on the formula sheet but practise using them quickly
Volume of 3D Shapes
Prism: cross-section area x length. Cylinder: pi r squared h. Cone: (1/3) pi r squared h. Sphere: (4/3) pi r cubed. Pyramid: (1/3) x base area x height.
Key Formulas
- Prism: V = area of cross-section x length
- Cylinder: V = pi r squared h
- Cone: V = (1/3) pi r squared h
- Sphere: V = (4/3) pi r cubed
- Pyramid: V = (1/3) x base area x h
Exam Tips
- A cone is one-third of a cylinder with the same base and height
- A hemisphere is half a sphere: V = (2/3) pi r cubed
- For compound solids, find each part separately then add
Surface Area
The total surface area is the sum of all face areas. For curved surfaces: cylinder curved surface = 2 pi r h, cone curved surface = pi r l (where l is slant height), sphere = 4 pi r squared.
Key Formulas
- Cylinder (closed): SA = 2 pi r h + 2 pi r squared
- Cone: SA = pi r l + pi r squared
- Sphere: SA = 4 pi r squared
Exam Tips
- For closed shapes, include both ends (e.g., two circles for a cylinder)
- The slant height of a cone (l) is different from the vertical height (h): l squared = r squared + h squared
- For open shapes, omit the relevant circular faces
Similar Shapes: Length, Area, Volume
When two shapes are similar with length scale factor k: all lengths scale by k, all areas scale by k squared, all volumes scale by k cubed.
Key Formulas
- Lengths: factor k
- Areas: factor k squared
- Volumes: factor k cubed
Exam Tips
- If given an area ratio, square root to find the length ratio
- If given a volume ratio, cube root to find the length ratio
- This applies to all similar shapes, not just simple ones
Revision Checklist
- I understand all key concepts in mensuration
- I have memorised the essential mensuration formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on mensuration
- I know the common mistakes to avoid in mensuration questions
Frequently Asked Questions
What mensuration topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers mensuration across both Core and Extended tiers. Key areas include area formulas. Key areas include arc length and sector area. Key areas include volume of 3d shapes.
How important is mensuration in the IGCSE exam?
Mensuration is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine mensuration with other topics.
What are the most common mistakes in mensuration?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For mensuration specifically, make sure you understand the underlying concepts rather than just memorising procedures.
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