Sequences, proof, counter-example.

[STEP III 2015 Question 2 (Pure)]

Differentiation, infinite series, sum, inequality, logarithm function.

[STEP II 2015 Question 1 (Pure)]

Inequalities, sum, positive integers, nubmer theory, decimal representation, sum of reciprocals.

[STEP III 2014 Question 8 (Pure)]

Differentiation, increasing and decreasing functions, inequality.

[STEP III 2014 Question 6 (Pure)]

Logarithm function, infinite series, inequalities, exponential function, limits.

[STEP II 2012 Question 4 (Pure)]

Curve sketching, trigonometry, integration, modulus function, differentiation, stationary, minimum, optimisation.

[STEP I 2011 Question 5 (Pure)]

Curve sketching, turning points, differentiation, exponential function, inequality.

[STEP II 2006 Question 2 (Pure)]

Approximating an integral, inequalities, sum, inverse square, bounds.

[STEP III 2004 Question 3 (Pure)]

Integration by parts, logarithmic function, limit, inequality, sum of inverse squares.

[STEP II 2003 Question 7 (Pure)]

AM-GM inequality, e, binomial theorem, limit, product, exponential function, C1-ish.

[STEP III 2000 Question 7 (Pure)]