The H2 Accelerated Mathematics class has been focusing on the theory of integration which is both the antiderivative and area under the curve.
Initially, students worked through an investigation of linear functions and their areas to the x-axis by using geometrical shapes like rectangles, triangles, and trapeziums. During this productive class, students applied their understanding by coming up with their own functions so that the definite integral would equal zero. Students used Desmos, a graphical calculator app, to help them develop various functions and online integration calculators to check their work as some of the problems were quite complicated and beyond the scope of the course.
They then used spaghetti to show that the regions from their integration were equal. What was supposed to be a 30-minute activity turned into an extensive creative endeavour with wonderful discussions and self-imposed challenge that lasted the whole class. Even so, only one pair finished their work with a symmetrical cubic function (rotational symmetry of order 2 about the origin), coloured vibrantly with oil-based markers.
As these students continue to prepare for their IGCSE 0606 Additional Mathematics examinations, we will be further developing these calculus concepts.