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Maths and Statistics

Site: Solent Online Learning
Course: Succeed@Solent
Book: Maths and Statistics
Printed by: Guest user
Date: Saturday, 22 September 2018, 6:50 AM

Improving your Numeracy

Do you feel you have forgotten your bookmaths since leaving school? Do you worry about numbers and whether you can cope with the university course you have chosen?

 Would you like to:

  • regain your numerical confidence? 
  • practice your basic skills?
If the answer is yes to all these questions, then it is time to refresh your basic skills. Take a look at the topic areas in this bookMaths and bookStatistics resource for help and advice.

You may also find the Numeracy Refresher booklet useful to refresh your knowledge on the following topics:

  • decimals
  • fractions
  • approximations
  • averages
  • percentages
  • ratios

The BBC Bitesize website is primarily aimed at school children but is also very useful as a revision tool for basic skills. Suitable for foundation and first year students transitioning into university, it provides you with a refresher on a range of numeracy topics including:

  • place value
  • distance, speed and time
  • rounding and estimating
  • ratio and proportion
  • prime numbers, factors and multiples
  • powers and roots
  • decimals
  • positive and negative numbers
  • operations (calculations/sums)
  • fractions
  • percentages
  • looking after your finances
  • standard index form
If these two resources are too basic for your needs, go to the Extra resources section at the end of this book for more relevant help. The pages in this bookMaths and bookStatistics resource will also provide more specific support.

Introductory Maths

There is currently a bewildering array of online support offering mathematical support. Some of this support is excellent; some of it not so helpful.

The BBC Skillswise website is a good starting point for foundation skills and revision. It offers "practical, commonsense bookmaths for adults":

If you prefer videos, the Everyday Maths Fundamentals video by explains essential bookmaths concepts using real-world problems. Topics include:

  • practising mental bookmaths
  • understanding decimals and fractions
  • working with percentages and ratios
  • solving equations
  • calculating area and volume
  • scaling recipes
  • estimating your running speed
  • calculating the area for home improvement projects
  • working with probability

Addition and subtraction

Straightforward addition and subtraction are foundation skills you will have mastered before coming to university. Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, offers you some useful tips around adding and subtracting positive and negative numbers, building on your basic skills.

One of the techniques she uses in the video (below) is number lines. For more information on this really useful bookmaths skill go to BBC Skillswise (bookMaths for adults):

A number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely. 

Watch Dee Greig-Dunn explain how you can add and subtract positive and negative numbers using number lines:

Multiplication and Division

There are a few basic rules to remember when multiplying and dividing positive and negative numbers. Take a look at the video (below) in which Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, explains these foundation skills and the basic rules you need to remember.

How to multiply and divide positive and negative numbers.

Rule 1

When both numbers are the same (two positive or two negative numbers) the answer will always be positive.

Rule 2

When both numbers are different (one positive number and one negative number), the answer will always be negative.

Remember: these rules apply when dividing numbers as well.


BIDMAS (also known as BODMAS) helps you to remember the order that you need to do your mathematical calculations where there is more than one mathematical operator (any combination of brackets, indices, division, multiplication, addition, subtraction).

This easily remembered acronym stands for:

B rackets
I ndices (powers of)
D ivision
M ultiplication
A ddition
S ubtraction

Take a look at the video (below) in which Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, explains how to apply BIDMAS (BODMAS)  to the following calculation:

(3 + 4)² - 7 + 4 × 3

Remember: numbers showing as ¹ or ² or ³ are know as Indices (or powers)

Rounding up

On your calculator you will often need to round up numbers with lots of decimal places to an appropriate level of accuracy.

In the video (below) Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, explains:

  • how to round up to one, two and three decimal places
  • how to round up to a specified number of significant figures

Remember: check the size of the next significant figure. If it's 5 or over, the number will round up. If it's less than 5, the number will stay exactly the same.


A ratio shows the relationship between two numbers and demonstrates how many times the first number contains the second. 

For example, if a shopping bag contains 8 bagels and 6 pints of milk, then the ratio of bagels to pints of milk is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

In the videos (below) Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, demonstrates:

  • what you need to do in order to share a sum of money or a weight in a particular ratio (video 1)
  • how to deal with problems where you are required to scale ratios (video 2)

Tip: before watching the second video see if you can work the problems out yourself (see below).

Problem 1
I would like to mix paint and white spirit in the ratio 5:2. 
How much white spirit is needed to thin 25 litres of paint?
How much white spirit (WS) will be required?

Problem 2

I would like to make cocktails by mixing whisky and vodka in the ratio 3:2. I only have 5 litres of each spirit.
How much cocktail can I make?

Substitution by integration

As a first year undergraduate student you may have come across substitution by integration (a part of calculus).

In the video (below), Dr Janet Bonar (Course Leader in the School of Maritime Science and Engineering) demonstrates a step by step approach to solving the following problem:

\( F( x )= \int_{} x^{2} \) cos(\( \chi \)3 + 1)  d\( \chi \), using the substitution u= \( \chi \)3 + 1

Try and solve the problem yourself by following the steps below, before watching the video.

Step 1 When two functions are multiplied and you want to integrate, you have two techniques you can use: integration by substitution, or integration by parts.  In general, try integration by substitution first to see if it will work, as it’s a bit tidier.

Step 2 Guess a likely substitution.   If there are brackets, this is often the bit inside the brackets.  Take the derivative of the substitution.  If the derivative term is in the original equation, then substitution is the right technique.  In particular, the variable should be in your derivative, and to the same power, as in the other part of your original equation.

Step 3  To do the substitution, solve your derivative term \( \frac{du}{dx} \) for d\( \chi \)

Step 4 Substitute your u term and your d\( \chi \) term into the original equation and cancel where you can.  

Have you changed all instances of your original variable to your new variable?
Now you can see why it's called 'substitution'!

Step 5 Integrate your new, simple equation.  It should be much easier!

Step 6 Write the solution, don’t forget to include the constant of integration.

Step 7 Substitute the original variable back in—and you’re done!

Now watch how Dr Janet Bonar works through the steps in this video:


For an introduction to everyday algebra fundamentals, go to:

Algebra topics include:

  • completing the square
  • expanding, or removing, brackets
  • factorising
  • logarithms
  • mathematical language
  • partial fractions
  • Pascal's triangle and the binomial expansion
  • polynomial division
  • powers or indices
  • simple linear equations
  • simplifying algebraic fractions
  • simultaneous linear equations
  • solution of linear and quadratic inequalities
  • solving cubic, polynomial and quadratic equations
  • substitution and formulae
  • symbols
  • transposition of formulae


To better understand the graphs topic, spend time refreshing your knowledge on key areas such as:

  • coordinates
  • plotting graphs
  • straight line graphs and gradients
  • travel graphs
  • conversion graphs
  • real-life graphs
  • quadratic graphs

Downloadable resources on the following topics include:

  • line graphs
  • histograms
  • double charts
  • tables
  • split tables
  • bar charts
  • composite bar charts
  • pie charts

Shapes and Area

To better understand the shapes and areas topics, spend time refreshing your knowledge on key areas such as:

  • the properties of 2D and 3D shapes
  • volumes and nets
  • perimeters and areas
  • circles
The BBC Bitesize website is suitable for foundation and first year students transitioning into university. It provides you with a refresher on a range of shapes and areas topics including:

  • transformations
  • symmetry
  • coordinates
  • perimeter, area, volume
  • measurement
  • trignometry
  • Pythagoras theorem
  • angles
  • shapes
  • time
  • loci

Angles and Geometry

To better understand the angles and geometry topics, spend time refreshing your knowledge on key areas such as:

  • lines and angles
  • measuring and drawing
  • polygons
  • transformations
  • triangles
  • Pythagoras's theorem

For an introduction to geometry take a look at:

Topics included are:

  • co-ordinate geometry of a circle
  • equation of a straight line including gradient and intercept
  • Euclidean geometry
  • other conic sections (ellipse, hyperbola, parabola)
  • polar co-ordinates
  • properties of straight line segments
  • the gradient of a straight line segment

The BBC Bitesize website is suitable for foundation and first year students transitioning into university. It also provides you with a refresher on a range of angles and geometry topics.


To better understand the measures topics, spend time refreshing your knowledge on key areas such as:

  • units and converting units
  • reading scales
  • rounding and estimating
  • reading timetables
  • compass directions and maps

If you are an engineering student, for example, you may have come across units that are not in the International System of Units (SI). 

The BBC Bitesize website is suitable for foundation and first year students transitioning into university. 

You will need to have Flash to play the video content.

Introductory Statistics

As you enter the world of work, you will find that most jobs use bookstatistics of some kind. 

bookStatistics help us to make decisions, plan ahead, discover trends and make predictions. We can use bookstatistics to deepen our understanding of any chosen topic. 

Once you understand the foundations, you will begin to understand how bookstatistics can not only be used, but also abused, in order to influence social policy

For example, the link below explores how foreign secretary, Boris Johnson, is accused of mis-using official bookstatistics for political gain, and considers whether the leader of the Labour Party, Jeremy Corbyn, is correct to say that there are fewer students from disadvantaged backgrounds going to university now.

But first of all, you need to be comfortable with the terms, formulas and techniques that are needed to use bookstatistics.

To better understand the bookstatistics and probability topics, spend time refreshing your knowledge on key areas such as:

  • collection data
  • mean, median and mode and range of data
  • charts and graphs
  • frequency tables
  • probability

The following websites are a useful source of further information:

Understanding the use of statistics-the law

Understanding how bookstatistics are used in your particular subject field is important too.

The Royal Statistical Society with the Inns of Court College of Advocacy have released a guide which helps understanding in the use of statistical evidence in courts and tribunals.

Whilst the guide is aimed at advocates it could also be of use to law students:


More detailed guides on criminal law and bookstatistics available from:

Statistics Foundations: Part 1

For an introduction to the foundations of bookstatistics, take a look at this video by Professor Eddie Davila covers the basics of bookstatistics including:

  • Why bookstatistics matter
  • Evaluating your data sets
  • Finding means, medians, and modes
  • Calculating standard deviation
  • Measuring distribution and relative position
  • Understanding probability and multiple-event probability
  • Describing permutations: the order of things
  • Calculating discrete and continuous probability distributions

Statistics Foundations: Part 2

As a follow on to bookStatistics Foundations: Part 1, Professor Eddie Davila reviews introductory concepts such as data and probability. If you are looking to work in data science, business, and business analytics—or just need a deeper understanding of how bookstatistics work in the real world- this video (below) is for you. 

Topics include: 

  • Data and distributions
  • Sample size considerations
  • Random sampling
  • Confidence intervals
  • Hypothesis testing

Statistics with Excel: Part 1

If you need help with understanding bookstatistics with Excel, then the video (below) is for you. In it, Joseph Schmuller explains the fundamental concepts of descriptive and inferential bookstatistics and shows you how to apply them using Microsoft Excel. 

Topics include:

  • Understanding data types and variables
  • Calculating probability
  • Understanding mean, median, and mode
  • Calculating variability
  • Organising and graphing distributions
  • Sampling distributions
  • Making estimations
  • Testing hypothesis: mean testing, z- and t-testing, and more
  • Analysing variance
  • Performing repeated measure testing
  • Understanding correlation and regression

Statistics with Excel: Part 2

This video shows you how to use statistical concepts and tools to perform analysis in Microsoft Excel. 

It would be useful to look at bookStatistics with Excel: Part 1 (on the previous page) if you are unsure of the basics. By watching both videos, you should have the necessary knowledge to perform basic analysis in workplace situations.

Topics include:

  • Using Excel's statistical functions and 3D charts
  • Visualising sampling distributions
  • Performing comparisions with ANOVA
  • Performing two-way analysis with ANOVA
  • Analysing linear regression
  • Performing multiple regression and non-linear regression analysis
  • Forecasting
  • Making advanced correlations
  • Testing variable frequencies
  • Running simulations

Introduction to SPSS

What is SPSS?

"SPSS is a comprehensive system for analyzing data. SPSS can take data from almost any type of file and use them
to generate tabulated reports, charts, and plots of distributions and trends, descriptive bookstatistics, and complex
statistical analysis." (SPSS Base User's Guide)

SPSS is the acronym of Statistical Package for the Social Sciences. It is a popular statistical package which can perform highly complex data manipulation and analysis with simple instructions. It is designed for both interactive and non-interactive (batch) uses.

SPSS has many statistical and mathematical functions. It can read data in almost any format (e.g., numeric, alphanumeric, binary, dollar, date, timeformats), and has useful data manipulation utilities.

Watch the SPSS bookStatistics essential training for more information.

SPSS Statistics Essential Training

If you want to make the most of the data you have collected for your academic assignments, then watch the video link below.The skills covered in the video are ideal for your research projects. 

The video will help you to:

  • build charts, scatterplots, and box plots
  • calculate descriptive bookstatistics such as means and standard deviations
  • use inferential bookstatistics such as t-tests and chi-squares
  • enter and read data
  • create new variables and crosstabulations
  • model associations with correlations, contingency tables, and multiple-regression analysis
  • format and export bookpresentations to share your data

You can also learn how to extend the power of SPSS with Python and R. 

More Help

If you'd like some more help with bookMaths and bookStatistics you can:

If you have any feedback about bookMaths and bookStatistics or additional material you'd like to see in the course, please email us at

Thank you to all staff and students at Southampton Solent University who contributed to this course.

Facts and formulae

This Functional Mathematics leaflet provides you with an at-a-glance list of facts and formulae to help you transition from school mathematics to university mathematics.

Have it beside you at all times!

Numerical reasoning support

The following leaflets (created for SIGMA by Dr E Lingham) will quickly and effectively refresh your knowledge on a range of topics that often arise in numerical reasoning tests including:

  • bar charts
  • shares and dividends
  • foreign exchange
Each leaflet is two pages long, and contains brief information and some worked examples. Where more space is needed, these bite-sized leaflets are aimed at particular skills (e.g. How to get X% of Y). 

While these leaflets may not contain enough detail and help for every student, they are a useful revision step for you.

Download leaflets on the following topics which arise in numerical reasoning tests:

Extra resources

Recommended websites

1. at Solent University (What is

The links below will take you directly to the course via Solent's institutional authentication on the SOL Lynda page:

2. bookMaths support centres will usually refer to these three resources banks for mathematics and bookstatistics at university level:

3. Graduate numerical assessment

4. Useful bookmaths support resources at other universities.

5. Online learning

There are a lot of online tools available to help you educate yourself. Khan Academy, FutureLearn and OpenLearn are useful starting points. For example, FutureLearn provides the following useful courses:


6. bookMaths anxiety 

7. Use of Software

8. Other