Differentiation, trigonometry, approximation, small angle.

[STEP II 1999 Question 8 (Pure)]

Inequality, integral, logarithm function, harmonic series, sum, limit.

[STEP I 1999 Question 8 (Pure)]

Telescoping sum, limit, ratio of terms.

[STEP II 1998 Question 3 (Pure)]

Factorisation, algebraic manipulation, integration, inequality, C1.

[STEP I 1997 Question 6 (Pure)]

Telescoping sum, trigonometry, integration.

[STEP I 1996 Question 6 (Pure)]

Trigonometric series, inequality.

[STEP III 1995 Question 4 (Pure)]

Integration by parts, recurrence relation, curve sketching, trigonometry, inequality, limit.

[STEP II 1995 Question 4 (Pure)]

Binomial coefficient, differentiation, integral, harmonic sum.

[STEP I 1995 Question 5 (Pure)]

Sum, inequality, approximation, analysis, C1.

[STEP I 1991 Question 9 (Pure)]

Taylor series of arctan function with remainder, inequality, modulus function, series, error approximation.

[STEP II 1987 Question 7 (Pure)]