above, below, over and under
Area and Slope
To infinity and beyond

For secondary school kids they like the notion of infinity and like to puzzle over 'what is the largest number?' and 'what is the biggest, furthest, and so on?'

With calculus we do have a link to infinity in that we split our x-axis to ever narrower sections making more and more of them. This allows us to develop methods for working out the rate of change at a point on a line graph (differential calculus). It also allows us to work out the area under a curve (integral calculus). Using our knowledge of mathematics we can use these skills along with tables for standard derivatives and integrals.

Calculus leverages the power of algebra to work out real world real life problems. Numerical methods have been developed so that even though solutions to calculus problems are difficult by hand they can be resolved by computer.