## Maths

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### S16 P-value

Hypotheses can be tested by comparing the test statistic to the critical value or by comparing the p-value to the significance level, α.

### S17 One sided tests

How do we apply a test of proportions? Rather than comparing a sample mean to a population mean, we can compare a sample proportion to a population proportion.

### S18 Tests of proportion

Hypothesis tests can be either two-tailed (non-directional) suggesting that the sample mean is different to the population mean, or one- tailed (directional) suggesting that the sample mean is...

### S19 Poisson distribution

The Poisson Distribution deals with the number of random occurrences over a period of time (or distance or area or volume), such as the number of people who enter a shop every hour, or the number of...

### S2 Data

Data is everywhere and increasingly drives many aspects of our day-to-day lives. Here we explain the different types of data that can be collected and some ways of illustrating this data.

### S3 Mean, mode, median

The mean, the median and the mode are three different measures of central tendency. This module shows the three different ways in which you can find a single number to summarise a set of data.

### S4 Measures of spread

The range, the interquartile range and the standard deviation are three different measures of the spread of a set of data. This module shows three different ways to calculate a number to represent...

### S5 Probability rules

This module covers the rules of basic probability, including the multiplication and addition principles and complementary events.

### S6 Sample spaces

A sample space is a list of all the possible outcomes. There are a number of techniques that can be used to list the sample space.

### S7 Conditional probability

If two events are not independent then the outcome of one event can change the probability of the second event occurring.

### S8 Binomial probability

The binomial distribution is a discrete distribution consisting of repeated trials, where each trial has two possible outcomes.

### S9 Normal distributions

The normal distribution is a “bell-shaped”, symmetrical, continuous probability distribution.

### Statistics

### T1 Pythagoras’ theorem

Pythagoras’ Theorem shows the relationship between the sides of a right-angled triangle. Knowing the length of two sides of a right-angled triangle, the length of the third side can be calculated.

### T2 Right triangle trigonometry

Sine, cos and tan can be defined using side lengths of a right-angled triangle. These side lengths are identified as either the hypotenuse or the opposite or adjacent sides to the angle.

### T3 The sine rule

How can we apply trigonometry to triangles that do not possess a right-angle? The sine rule shows that the ratio of the length of a side, to the sine of its opposite angle, will be the same for all...

### T4 Cosine rule

The cosine rule is a generalisation of Pythagoras’ theorem. If you have any two sides of a triangle, as long as you know the angle between them, you can calculate the length of the third side.

### T5 Angular measurement and the unit circle

Angles are frequently measured in degrees. However, it is sometimes useful to define angles in terms of the length around the unit circle (a circle of radius = 1). This module introduces radians as a...

### T7 Trigonometric equations

If you know the value of a trigonometric function, how do I find all the possible angles that satisfy this expression? The calculator may only give you one answer to an inverse trig question...

### Trigonometry

Trigonometry is a branch of mathematics involving the study of triangles. Ancient builders and mariners used it for finding lengths that are not physically measurable (because they were so large) but...