Higher Tier Paper Math Formulas Lecture

Introduction

• Video covers formulas needed only for the higher tier paper.
• Previous video covers formulas needed for both foundation and higher tiers.
• Links to all relevant videos are provided for deeper exploration.

Volume of a Pyramid

• Formula: ( \text{Volume} = \frac{1}{3} \times \text{Area of base} \times \text{Height} )
• Example:
  • Base: 6 x 6 (square)
  • Height: 8
  • Calculation: ( \frac{1}{3} \times 36 \times 8 = 96 \text{ cm}^3 )

Quadratic Equation

• Formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )
• Example:
  • Equation: ( 3x^2 + 5x - 4 = 0 )
  • Values: ( a = 3, b = 5, c = -4 )
  • Solutions rounded to 2 decimal places: ( x = 0.59, x = -2.26 )

Sine Rule

• Formula: ( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} )
• Used for: Non-right angled triangles.
• Example:
  • Find missing length with known angle and opposite pairs.
  • Result: 2.8 cm when rounded to 1 decimal place.

Cosine Rule

• Formula: ( a^2 = b^2 + c^2 - 2bc \cdot \cos A )
• Used for: Non-right angled triangles without opposite pairs.
• Example:
  • Result after calculation and rounding: 7.2 cm.

Area of a Triangle Using Sine

• Formula: ( \frac{1}{2}ab \sin C )
• Used when height is unknown.
• Example calculation yields: 14 cm².

Area of a Sector

• Formula: ( \text{Area} = \frac{\theta}{360} \pi r^2 )
• Example:
  • Angle: 62°, Radius: 8
  • Area: 34.6 cm²

Direct Proportion

• Formula: ( x = ky^n )
• Example:
  • Relationship: ( x \propto y^2 )
  • Find k: Sub in known values and solve.

Inverse Proportion

• Formula: ( x = \frac{k}{y^n} )

Frequency Density in Histograms

• Formula: ( \text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}} )
• Example calculation for a given table.

Coordinate Geometry

• Equation of a Line: ( y = mx + c )
• Gradient: ( m = \frac{y_2 - y_1}{x_2 - x_1} )
• Perpendicular gradients: Negative reciprocal.
• Example of finding equation of a perpendicular line.

Conclusion

• Extra topics and formulas are given as bonus content.
• Encouragement to check out full videos for detailed explanations.