📘 Formula Sheet

This page summarises helpful formulas for solving problems in measurement, geometry, and algebra at Level 5.

📏 Measurement

• Perimeter of a rectangle:
  \( P = 2 \times (\text{length} + \text{width}) \)
• Area of a rectangle:
  \( A = \text{length} \times \text{width} \)
• Area of a triangle:
  \( A = \frac{1}{2} \times \text{base} \times \text{height} \)
• Volume of a rectangular prism:
  \( V = \text{length} \times \text{width} \times \text{height} \)

📐 Geometry

• Angles on a straight line add to \(180^\circ\)
• Angles around a point add to \(360^\circ\)
• Angles in a triangle add to \(180^\circ\)
• Angles in a quadrilateral add to \(360^\circ\)

🔄 Transformations

• Enlargement: Multiply each side by the scale factor
• Scale factor of enlargement:
  \( \text{new length} = \text{original length} \times \text{scale factor} \)

🧮 Number & Algebra

• Fraction to decimal: Divide numerator by denominator
• Percentage of amount:
  \( \frac{\text{percent}}{100} \times \text{amount} \)
• Solving simple equations:
  Use inverse operations to isolate the unknown
• Using formulae: Substitute numbers into letters (e.g. \( A = lw \))

🧭 Metric Conversions

• \(1 \text{ km} = 1000 \text{ m}\)
• \(1 \text{ m} = 100 \text{ cm}\)
• \(1 \text{ cm} = 10 \text{ mm}\)
• \(1 \text{ kg} = 1000 \text{ g}\)
• \(1 \text{ L} = 1000 \text{ mL}\)