Curve sketching, roots of equations, turning points, C1.

[STEP II 2013 Question 3 (Pure)]

Curve sketching, turning points, differentiation, area enclosed, symmetry, C1.

[STEP II 2007 Question 2 (Pure)]

Roots of equation, geometric progression, polynomial, C1.

[STEP III 1999 Question 1 (Pure)]

Curve sketching, roots of equation, inequality, C1.

[STEP I 1993 Question 7 (Pure)]

Differentiation, logarithmic function, functional equations.

[STEP II 1992 Question 7 (Pure)]

Algebra, polynomial equation, trigonometry, substitution, counterdatabase.

[STEP II 1989 Question 1 (Pure)]