# Maths

Content relating to Maths (primarily English GCSE and A-level)

## Straight line graphs Part 3

This is the final instalment of my series of tutorials on straight line graphs, and follows on from “Working with a coordinate grid“, “Straight line graphs Part 1” and “Straight line graphs Part 2“. We’ve covered most of the Foundation…

## Hypothesis testing for pmcc (A-level Maths)

This is the third of my series of three articles on hypothesis testing for A-level Maths, and covers hypothesis testing for pmcc (the product moment correlation coefficient). The first instalment introduced the concept of hypothesis testing and covered hypothesis testing…

## Straight line graphs Part 2

This tutorial follows on from “Working with a coordinate grid” and “Straight line graphs Part 1“. We’ve covered the basics of straight line graphs – enough to get you up to about Grade 3/4 level at GCSE – and now…

## What does “Integration as the limit of a sum” mean?

The English A-level Maths specification includes “integration as the limit of a sum” and “Fundamental Theorem of Calculus”. This article explains these expressions. Using strips to estimate the area under a curve To estimate the area under a curve, we…

## Working with a coordinate grid

In this tutorial we’re looking at working with a coordinate grid: what it looks like, terminology and plotting points, and the equations of simple vertical and horizontal lines. Once you’re comfortable with this basic content, you can move on to…

## Straight line graphs Part 1

This tutorial follows on from “Working with a coordinate grid“, where we covered plotting coordinate points and the equations of vertical and horizontal lines. We’re now moving on to look at plotting other straight line graphs, and understanding the general…

## Compound transformations of graphs (A-level Maths)

This is Part 3 of a three-part tutorial on graph transformations, and covers compound transformations. If you haven’t already worked through Part 1 and Part 2 then I recommend you look at those before trying to make sense of this…

## Hypothesis testing for Normal (A-level Maths)

This is part 2 of my series of three articles on hypothesis testing for A-level Maths. The first part can be found here; it gives an introduction to the concept of hypothesis testing and covers the Year 1 topic of…

## More graph transformations

This is Part 2 of a three-part tutorial on graph transformations; Part 1 can be found here. If you haven’t already worked through Part 1 then I recommend you look at it before trying to make sense of this one!…

## Graph transformations for GCSE and A-level Maths (Part 1)

In my tutoring, the topic of graph transformations is one that almost every Higher GCSE, IGCSE or A-level student wants to spend time on, so I thought I’d use it as the subject of a series of blog posts /…

## Hypothesis testing for Binomial (A-level Maths)

In the first year of the A-level Maths course you need to be able to carry out a hypothesis test to judge whether a Binomial probability has (probably) changed. In the second year, hypothesis tests are required (1) to decide…

## Directed numbers (positive and negative numbers)

Directed numbers are something that a lot of people find confusing. I hope that this article will help you to get your head round them! What are directed numbers? “Directed numbers” means positive and negative numbers. “Positive” or “negative” describes…

## Madness-themed fun carnival game for Maths practice

Something a little different this month, since it’s the summer holidays. This year I’m running a stall at a couple of local carnival-type events to promote my theatre company (STAMPS)’s show and use some carnival games to fundraise while I’m…

## Working with double angle formulae (A-level Maths)

The A-level Maths specification requires you to work with formulae for compound angles – sin (A ± B), cos (A ± B), tan (A ± B) – and use these to derive and use a range of double angle formulae,…

## Using Ratio mode on your Classwiz calculator

All the Casio Classwiz calculator models – both the original “X” and the new “CW” models – feature ratio mode, which didn’t exist on their predecessor the fx-83/85 GT Plus. Although it’s perfectly possible to get by without ever using…

## The new Casio Classwiz CW calculators

In early 2023, Casio replaced the popular Classwiz fx-83/85GT X and fx-991EX calculator models with the Classwiz fx-83/85GT CW and the fx-991CW. The change is a lot less trivial than you might think! A short (recent) history of Casio scientific…

## How to resolve a vector into components

In the first year of A-level Maths, all the vectors you deal with are given to you in component form, i.e. as two perpendicular components, e.g. $\begin{pmatrix}2\\-3\end{pmatrix}$ or 2i – 3j. In the second year, however, you’re more likely to…

## Direct and inverse proportion for Higher GCSE

For Foundation GCSE you just need to know what equations and graph shapes represent direct and inverse proportion, and work with equations given to you. That’s all covered in a previous article which you can find here. For Higher you…

## Direct and inverse proportion for Foundation GCSE

For Foundation GCSE you need to know what equations and graph shapes represent direct and inverse proportion, and work with equations given to you, but you don’t have to actually derive the equations, as you do at Higher. You also…

## Strategies for listing/calculating possible outcomes

The GCSE Maths topic of systematic listing strategies is all about working out how many possible outcomes there are – i.e. how many ways there are for something to happen – for example when finding probabilities. Sometimes the simplest way…

## Equilibrium and resultant forces (A-level Maths Year 1)

This article, on equilibrium and resultant forces, follows on from my recent post on Forces and Newton’s Laws of Motion, and covers part of the Mechanics content of the first year of A-level Maths – though I’m sure that a…

## How to answer Rate of Flow questions (GCSE Maths)

Rate of flow is a topic that’s sometimes omitted in GCSE Maths text books, or perhaps included in the form of just a question or two in the section on compound measures. It’s only needed for the Higher Tier so…

## Mathematical notation you need for A-level – part 3

This is part 3 of a series covering the mathematical notation you need for A-level Maths. Click the links below for the previous parts:Part 1: set notation and miscellaneous symbolsPart 2: other Pure Maths notation This final instalment covers vectors…

## More mathematical notation you need for A-level

Much of the mathematical notation that you need to know for A-level, you’ll already have come across at GCSE, but there are some symbols that you may not be familiar with and others that you certainly won’t have used before…