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Chapter 8 of 10

📦 Mensuration, Coordinates & Vectors

6 min+15 XP

This chapter covers area and perimeter of 2D shapes, volume and surface area of 3D solids, arc length and sector area, radian measure, coordinate geometry, and vectors. These are popular Paper 2 topics with questions often worth 8-12 marks each. Many formulas are given in the formula sheet, but you must know when and how to apply each one.

Mensuration and vectors are often combined in complex, multi-step problems. For example, you might need to find the volume of a combined solid (cone + hemisphere), then calculate coordinates using vectors. The key to these questions is breaking them down into manageable steps and being systematic about which formula to use for each part.

Areas of 2D Shapes

You should know the area formulas for all standard shapes. While some are given in the formula sheet, being familiar with them saves time during the exam. Always draw a diagram and label all dimensions clearly before calculating.

📏Areas of 2D Shapes

Area formulas for common 2D shapes. All must be memorised.

Rectangle
A = l \times b
Triangle
A = \frac{1}{2} \times b \times h
Parallelogram
A = b \times h
Trapezium
A = \frac{1}{2}(a + b) \times h
Circle
A = \pi r^2
Circumference of circle
C = 2\pi r = \pi d
🎯Key Takeaway
Mensuration formulas are given in the formula sheet, but you must know WHEN to use each one. For combined solids, calculate each part separately and watch for internal faces. For vectors, remember: AB = OB - OA (destination minus start). Parallel vectors are scalar multiples of each other.

What the full chapter covers

  • Areas of 2D Shapes

  • Arc Length & Sector Area

  • Volumes & Surface Areas of 3D Solids

  • Coordinate Geometry

  • Vectors in Two Dimensions

  • 3D Solids Exam Strategy

  • Common Vector Mistakes

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