'My son has just received his 'A' level Maths result and got an 'A' ! We worried about the prospect of a tricky Pure C4 paper, but my son sailed through it after some excellent coaching on exam technique from Ian. Regular tuition, even for one part of the syllabus, really helped to cement what my son learned at school, and coupled with plenty of exam question practice from Ian, he achieved the grade he needed. Thanks, Ian, for seeing him through, and getting him exam ready.'

Sue Bartlett, Pontprennau, Cardiff

More examples may be found on my Facebook page (under 'Photos')

a) GCSE model answers The total cost of coffee & milk in an office is £72/month and staff pay according to whether they drink 1,2 or 3 cups per day.

Three drinks per day - 8 staff

Two " " " - 5 "

One " " " - 2 "

Assuming that Sharon makes no profit from the transaction, how much will she charge the three groupings ? Show every step in your calculations.

Let cost of one cup per person = c, cost of two cups per person = 2 x c = 2c, cost of three cups per person = 3 x c = 3c

=> 8(3c) + 5 (2c) + 2c = 72

24c + 10c + 2c = 72

36c = 72

=> c = 72/36 = 2

b) 'A' level basic Trigonometry proof

From Pythagoras Theorem, c² = a² + b² (1)

Divide both sides of (1) by c² , c² /c² = a² /c² + b² /c²

1 = (a/c)² + (b/c)² (2)

But sinx = a/c, cosx = b/c (3)

Substitute (3) into (2), 1 = sin² x + cos² x

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