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Applying Mathematics across the GCSE/A curriculum

Physics (AS)

A particle of mass 10 kg is fired, parallel to the ground, at a velocity of 30 m/s toward a wooden object. If the force required to stop the particle is 500 N, find the depth to which the particle penetrates the wooden object.

Key concept : Energy is the capacity to do work.

Kinetic energy of particle = ½ mv² = ½ x 10 x 30² = 4,500 Joules

Work done in bringing particle to rest = Fs = 500s

=> 500s = 4500

s = 4500/500 = 9 metres

Chemistry (AS)

C H

n 2n + 2 This is the general formula of the hydrocarbon group, the alkanes, which are molecules consisting of chains of saturated

(ie single bonds only) carbon atoms, bonded with hydrogen atoms

(n = 1,2,3 etc). An example is Propane, C H .

3 8

Geography (GCSE/A)

As the populations of England and Wales are so unequal, in absolute terms, we need to obtain a relative measure of the rugby playing base in each country eg number of registered players per 1000 of population.

Country Population Registered players Registered players

per 1000 of population

England 53,000,000 166,762 166,762/53,000 = 3.15

Wales 2,900,000 22,408 22,408/2,900 = 7.73

Economics (AS)

Let q = quantity of product, p = price per unit, v = variable cost per unit,

F = total fixed costs (at any outpul level, Q), R = total revenue,

P = total profit, C = total costs (Fixed + Variable)

=> P = R - C

= pq - (F + vq)

= pq - vq - F

= q(p - v) - F (A)

At Breakeven, P = 0 and R = C.

Let Breakeven output = q*

=> In (A), 0 = q*(p - v) - F

F = q*(p - v) [+ F both sides]

=> q* = F/(p - v) [(p - v) is known as the CONTRIBUTION/unit]

Commercial insurance

If the probability of illness X for Andrea Pirlo is p and the treatment and administrative costs are T and A respectively, find an algebraic expression for the creative midfielder's annual premium, P.

P = probability x total costs = p x (T + A) = p(T + A)

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