In this task all the pupils need to do is write down the integrals with limits.  I won’t ask them to go on and find the areas in this one. 

We don’t have lots of time to practice in class. I want them to get lots of practice of the first parts of the questions, which is where the variety comes in.  If they were working on whole questions they’d never get through that many.  They can then do some full questions after completing this sheet.

For instance, for question 9 I’d want the pupils to calculate the x-coordinates of the points of intersection, then write the correct integral with the limits in the correct place. I then ask them to write if the evaluated integral would be positive or negative. That’s enough. The task is all about practicing what is different about each type of integration question and experiencing variety. It’s not about doing the parts which are the same technique in all questions: integrating and evaluating.

The questions themselves come from an old Tom Barr worksheet.