Quadratic equation, functional equation, integer, C1.

[STEP I 1992 Question 7 (Pure)]

Differentiation, logarithmic function, functional equations.

[STEP II 1991 Question 7 (Pure)]

Algebraic manipulation, C1.

[STEP II 1991 Question 3 (Pure)]

Rotating curves, funnels, surfaces, inverse hyperbolic function, water tap.

[STEP II 1987 Question 4 (Pure)]

Lagrange's identity, inverse functions, root of equation, exponential function, derivatives, series, sequences.

[STEP II 1987 Question 5 (Pure)]