Applied Mathematics Problem-Solving Strategies

Paper 2 optional topics span mechanics, statistics, and discrete mathematics. This lesson provides targeted strategies for each of the five optional areas, focusing on the most frequently examined question types and the most common errors.

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Further Mechanics Strategies

Circular Motion

The most common topic in Further Mechanics exam questions. Key formulas:

Quantity	Formula
Centripetal acceleration	$a = \frac{v^2}{r} = r\omega^2$a=rv2​=rω2
Centripetal force	$F = \frac{mv^2}{r}$F=rmv2​
Angular velocity	$\omega = \frac{v}{r} = \frac{2\pi}{T}$ω=rv​=T2π​

Strategy for "motion in a vertical circle":

1. Draw a force diagram at the relevant point (top, bottom, or angle $\theta$θ).
2. Resolve forces toward the centre: $\text{resultant toward centre} = \frac{mv^2}{r}$resultant toward centre=rmv2​.
3. Use energy conservation between two positions.
4. At the "critical" point (usually the top), the minimum speed occurs when the normal reaction or tension is zero.

Exam Tip: At the top of a vertical circle, weight acts toward the centre. At the bottom, weight acts away from the centre. Many marks are lost by resolving forces in the wrong direction.

Elastic Strings and Hooke's Law

$T = \frac{\lambda x}{l}$T=lλx​