Gr 12 (Calculus)

1. Factorise third-degree polynomials. Apply the Remainder and Factor Theorems.

2. An intuitive understanding of the limit concept.

3. Use limits to define the derivative of a function, eg 1st principles

4. Understand intuitively that f '(a) is the gradient of the tangent 

to the graph of f at the point with x -coordinate a.

5. Use the derivative rule. 

6. Determine equations of tangents to graphs of functions.

7. Second derivative, and concavity

8. Sketch graphs of cubic functions using 1st and 2nd derivates.  Determine the x -intercepts of the graph using the factor theorem.

9. Solve practical problems concerning optimisation and rate of change