Differentiation, summation sign manipulation, infinite series, logarithms.

[STEP III 2012 Question 4 (Pure)]

Sum of squares, algebraic manipulation, inequalities.

[STEP III 2010 Question 1 (Pure)]

Product, binomial expansion, differentiation.

[STEP III 2007 Question 2 (Pure)]

Differentiation, binomial expansion, general term, series.

[STEP II 2005 Question 6 (Pure)]

Simultaneous equations, sum of squares and cubes.

[STEP I 2003 Question 1 (Pure)]

Geometric series, differentiation, sum of squares.

[STEP II 1995 Question 1 (Pure)]

Trigonometry, binomial coefficients, sum.

[STEP III 1992 Question 8 (Pure)]

Integration by parts, reccurence formula, binomial coefficient.

[STEP III 1991 Question 8 (Pure)]