In this post, let’s look at curve sketching as tested in H2 A Level Math.
What’s tested in Curve Sketching
I would divide the portion on curve sketching to cartesian equations and parametric equations.
Cartesian equation
In curve sketching, students are expected to know the characteristics of the following:
- Circles: (x-a)² +(y-b)² = r²
- Ellipses: (x-a)²/c² +(y-b)²/d² = 1
- Hyperbolas
- Rectangular Hyperbolas: y= (ax+b)/(cx+d)
- y= (ax²+bx+c)/(dx+c)
For the above graphs, students are expected to be familiar with the following properties of each graph:
- shape
- symmetry
- intersections
- turning points
- asymptotes
The graphic calculator is able to give the shape, points of intersections, turning points. However, the equations of the asymptotes will not be provided by the graphic calculator.
Parametric Equations
Under the section on parametric equations, students are expected to be able to draw parametric equations and their graphs. Notes for sketching of parametric equations can be found here.