Vectors: Ratio Theorem

As we all know, the Ratio Theorem is given in MF15. But some students struggle to fit in the and every time. They will then attempt to draw a bit and see it helps. Here’s a solution for [...]

What does unbiased in Math mean?

Some of your school notes will mention and explain the definition of unbiased and consistency. But let us just discuss what unbiased means as we do see it quite often in A-level. What does its [...]

Intuition of Mathematical Induction

Many students have asked me about Mathematical Induction, like whats the idea behind it. Especially since I always emphasize the importance of . So lets try to make some sense of this long and [...]

Will it ever converge?

If KS travels half the distance to the bus stop for every move, will he ever reach the bus stop? The answer is that I will never reach the bus stop, but could make arbitrarily close to it. This [...]

What is r-value

Many students asked me what exactly is r-value. They are always confused with the idea of correlation and causation. If you’re still confused, let me first establish that r-value implies [...]

Why can’t we extrapolate regression lines

Many students memorise the standard answer, that is, when the estimated data is not within range, we are extrapolating so it is not reliable. But why is it unreliable! Consider an example of [...]

Completing the square

This is a very old-school and technical method we learnt in secondary school. However, many students are unable to do it accurately still. The trick of completing the square is realising that it [...]

Vectors: Cross vs Dot Product

Many students have asked me why is there a difference between cross(vector) and dot(scalar) product, after all it is like multiplying. For starters, the former produces a resultant vector while [...]