## WHAT SHAPE OF CYLINDER IS BEST?

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

## KEY DIFFERENCES BETWEEN GCSE MATHS AND A-LEVEL MATHS?

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:

### 1)  EMBRACE THE ALGEBRA!

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:

## WHAT’S THE POINT OF A “RECIPROCAL”?

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 $5$

## WHAT’S THE POINT OF USING GREEK LETTERS IN MATHS?

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

## WHAT’S THE POINT OF CHI-SQUARED GOODNESS OF FIT TEST?

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

## WHY DO YOU “KEEP, CHANGE, FLIP” WHEN DIVIDING FRACTIONS?

### Aimed at: KS3, GCSE and A-level

#### First we will see why it seems to make sense that you can divide by a fraction by simply flipping it upside down and multiplying; then we will prove it works.

INTUITIVELY:
Let’s see if we can find a rule for dividing by $\frac{1}{2}$.

## HOW MUCH HARDER IS A 2000 PIECE JIGSAW THAN A 1000 PIECE JIGSAW?

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

## Quote of the week: DIFFERENTIATION IS A SKILL. INTEGRATION IS AN ART.

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

## WHAT’S THE POINT OF INTEGRATION BY SUBSTITUTION?

A PUZZLE: which of these shapes is larger: a square of side 7cm or a circle or diameter 8cm? Well that’s easy to answer if you know that the area of a circle is \$A=\pi

## TOP TEN SAMPLING METHODS

A quick reminder: if there are 1200 students at our school, it would be very time-consuming (if not impossible) to interview them all for your Sociology project. Here the population is everyone at the school,