Barney Maunder-Taylor
RECOMMENDED LEVEL: A-level
5) ARCHIMEDEAN SPIRAL: the spiral you see if you roll up a carpet and look side-on. Constant separation distance between each coil. See my video of how to draw one here or use your favourite free graph sketching software (e.g Geogebra or Desmos). For A-level Further Maths students: the polar equation is $r=aθ$ where the parameter a makes the (constant) separation distance between each coil larger or smaller.
4) LOGARITHMIC SPIRAL: a spiral in which
IN THIS VIDEO: all eight Circle Theorems needed for GCSE maths demonstrated and explained. NOTE: students of IGCSE (“International GCSE”) also need to know the Intersecting Chords Theorem (not covered in this video).
THE TIN OF TUNA ON THE LEFT: is the traditional shape: quite wide and not very tall. I was intrigued to see recently (2024) that one producer of tuna (can on the right!) has recently
Thinking of taking A-level maths? Here are some key differences you’ll find from the style of GCSE maths, all designed to make our life easier not harder:
Maths is ultimately about spotting patterns, and algebra is the language we use to write down patterns. A simple example: $A=l \times w$ is a formula to tell you how big a rectangle is. ANY rectangle. At GCSE, it is reasonable to develop clever tools to avoid having to use algebra; but at A-level, we must embrace algebra: it’s our friend and is there to make maths easier! An example:
A QUICK REMINDER: The reciprocal of a number is: either: turn it upside down or (equivalently): one divided by that number. So the reciprocal of $\frac{2}{3}$ is $\frac{3}{2} = 1.5$ and the reciprocal of $5$
AT GCSE: introducing Greek letters (α, β, γ, δ, …) leaves the more familiar Roman letters (a, b, c, d, …) free to represent other quantities and unknowns. To start with, here are two Greek
TARGET AUDIENCE: A-level statistics or A-level Further Maths. A Real World example of a chi-squared test in action follows: this sort of test is extremely useful in a huge range of real-world scenarios!At our board
INTUITIVELY:
Let’s see if we can find a rule for dividing by $\frac{1}{2}$.
First of all, it’s easy to see that a 2000 piece jigsaw is more than twice as hard as a 1000 piece jigsaw. To see why: imagine having two 1000 piece jigsaws that are of
I was delighted to find this quote at the start of Seán M. Stewart‘s book “How to Integrate it“. One of the main differences between GCSE and A-level maths is the introduction of calculus. This