# Archive | AQA

## Problem Solving I

Problem solving may involve interpreting a real situation, representing it mathematically and finding an equation to solve. Other problems may involve fractions, percentages, ratios and probabilities all mixed up in so many different ways. Whatever the problem, you have to start by understanding it. Because of the variety of questions that can be asked, the […]

## Sampling Methods

Gathering statistics involves time and effeort. It is a necessary procecdure – governments need to know how many schools to build, or policemen to employ, and companies need to know which products people will buy. They could go out and ask everyone, but this would mean a lot of time and effort needed to be […]

## Constructing an Equilateral Triangle/60 Degree Angle

We can easily construct an equilateral triangle with a pair of compasses. Start by drawing a line AB. Open the compass to the same length as AB and put the compass needle at B. Draw an arc as shown. Now put the compass needle at A and draw another arc that crosses the first arc […]

## Constructing the Locus of Points a Fixed Distance From a Given Line

To construct the set of points a fixed distance x from a line AB, with a set of compasses draw circles of radius x with centres at A and B, then draw tangents from one circle to another, parallel to the line. For example, construct the set of points 2 cm from the line AB […]

## Number Sequences and Shapes

Number sequences and certain shapes are closely intertwined. Consider the number sequence 1, 3, 6, 10… The nth term of this number sequence isWe can picture the number sequences as triangles made up of dots. The nth triangle number is the number of dots in the nth triangle. Similarly, consider the number sequence 1, 4, […]

## Algorithms

An algorithm is a sequence of steps carried out in a certain order for solving a certain problem. There may be more than one way of solving the problem, of which an algorithm may be one. Not all problems can be solved by using an algorithm. For example, we want to solve the quadratic equation […]

## Moving Averages

Moving averages allow us to identify a trend when we have quantities that flucutate over time. For example, ice cream sales may fluctuate by season, with higher sales in the summer and lower sales in the winter. By finding the moving average it becomes much easier to find out if ice cream sales are increasing […]

## Constructing a Right Angle

To construct a right angle, we can use the circle theorem which says that a triangle inscribed in a circle, one edge of which is a diameter, is always a right angled triangle. Therefore, start by drawing a circle with a compass. The centre of the circle will be at the position of the compass […]

## Rational and Irrational Numbers

A rational number is any number that can be written as a fraction, one whole number divided by another. are all rational. Many decimals are rational too. If they only have so many decimal places then they are rational because they be written as something over 1 followed by some zeroes. For example 0.9786 is […]

## Constructing a Triangle With Given Sides

Suppose we want to construct a triangle with sides 5 cm, 6 cm and 7 cm. We use compass and ruler. Start with the base, and mark a line of 5 cm, PQ below. Open the compass to a length of 6 cm and draw an arc as shown below. Now open the compass to […]