Some things that JC students should know.

In all these years of teaching, I realised that many JC students still do not know a handful of things. So I will list down a few random ones that I can recall off-hand, and of course expand a lot the way.

  1. You have MF26 formula booklet given. It contains your double angle formulas, some integration and differentiation formulas. Please review what you have so you don’t need to memorise them. Also, realise how to use them!

  2. 0 is neither positive nor negative. This is important when questions use terms like nonnegative or nonpositive to trick you. It is also important to remember that 0 is both an integer and real number.

  3. Solving for limits, when we have a \frac{0}{0} or \frac{\infty}{\infty}, we can just say that it gives us 1 or 0 respectively. A question you ask is, which 0 is smaller and which infinity is larger? An example will be \lim_{x \rightarrow 0} \frac{sinx}{x} = 1

  4. When dealing with Complex Number, z = x+ yi, x, y \in \mathbb{R} Many students can still write \mathrm{Im}(x)=yi, which shows that they have poor understanding of their definitions here.

  5. What is a variable and constant. For example when given a substitution y = 3(u-x) to do an integration, its alarming some students thing that u is a constant.

  6. n! = 1 \times 2 \times \ldots \times n and we can easily write it as (n+1)! = n! \times (n+1). Students should be able to identify with this comfortably.

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