Firstly, everything here will just be me talking to myself and I am not spotting any trends.
- Functions, good to know how to do piecewise composite functions. Checking for inverse algebraically. And to use discriminant to find range or domain of functions.
- Conics, good to be familiar and spot them. Finding graph of f(x) from given graph, like f’(x) with another. Good to test concepts of first derivative test here.
- System of linear equations need not have unique solutions always. Know what to do in the event we have no unique or more than one solution.
- Maclaurin’s expansions as a sum to infinity was tested last year so most students should be familiar with them by now. So perhaps learn what the general terms of these expansions are and better, how to derive them. Do also review how to do expansion in deceasing powers.
- Differentiation with first principles using the secant line. Inverse trigo differentiation without the formulae, but instead implicitly.
- Integration with partial fraction since factor formulae was already tested in the past years. Perhaps with a few unknown constants to confuse students in their partial fractions decomposition.
- Area / vol with parametric equations, finding Cartesian equations to resolve for volume. Also review how to find area/ volume if it is not about x or y axis, and transformations are required.
- Directional cosines. There are actually very fundamental concepts regarding vectors and it’s not that easy to use them. I know three planes are not in the syllabus; but what if we find the line of intersection between two planes and consider that line with a third plane.
All the best for paper 1!
