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Generally Geometric

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.


What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

Exponential Trend

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

Integration Matcher

Age 16 to 18 Challenge Level:
If you have not yet met integration, here are two ways to approach the problem:
Integration can be considered as anti-differentiation, so see if you can match each function with a function showing its gradient.

Alternatively, integration shows the area under a curve, so by estimating the areas in each interval, you can deduce the shape of the integral function.