Some more STEP solutions

I/1999/4 – sketching regions

I/2007/9 – particle on an inclined plane

I/2007/13 – numbered discs

II/2007/6 – differentiation, square roots, ln

II/2007/7 – Jensen’s inequality

II/2007/8 – vectors, product of ratios = 1

II/2007/12 – throwing two dice and stopping

II/2011/1 – sketching and finding roots of square-root expressions

II/2013/4 – locus of midpoint of chord of circle

III/2007/6 – points round a circle

III/2007/8 – differential equation

III/2009/6 – e, e, e, e, and a circle

III/2011/6 – four definite integrals with tanh, sinh, coth, and ln

I/2009/13 – girls and boys in a row

Click here for answers (pdf)

For STEP I/2007/8 (sketching cubics) see


III/1999/11 – hoop rolling over the edge of a table

Click here for solution (from The Student Room)