Factorisation, curve sketching, differentiation, inequality, C1.

[STEP I 2014 Question 5 (Pure)]

Curve, tangent, positive integers, C1.

[STEP I 2009 Question 2 (Pure)]

Proof by contradiction, inequality, curve sketching, C1.

[STEP II 2008 Question 3 (Pure)]

Quadratic equations, factor, perfect square, root, C1.

[STEP I 2007 Question 4 (Pure)]

Quadratic equations, curve sketching, necessary and sufficient conditions, turning points, C1-ish.

[STEP III 2003 Question 5 (Pure)]