Image of someone going up an escalatorLevel up your Maths and Stats Skills

After a break away from studying, you may be feeling a little rusty and be worried about the maths and stats you will encounter as part of your course. To help you get a head start we've created this page which contains everything you need to revise key topics. It will help you explore areas that you want to focus on and sharpen your skills.

MASH also provides additional 1-1 support with any maths or stats related to your course. These sessions are free to all University of Sheffield students.

And last, but by no means least, if the thought of maths and stats makes you feel anxious, you are not alone: over 80% of students have some form of maths anxiety. Why not take a look at our maths anxiety page. It contains an online resource for you to work through to help you address this. We also run workshops on maths anxiety and there is a link to the workshop page as well.

If there are other topics which you would like to see on these pages, or if you have any other feedback, please contact us here.

If you're like to work on your academic skills more generally, visit the Level up your Academic Skills Page

Level up your Academic Skills









How to Use this Page

Getting good at maths and stats is a matter of practising skills, like learning an instrument or a sport. Many people focus on the first step: learning the methods, without moving on to the next step: consolidation through practice. If this sounds familiar, or if you’ve had other problems learning maths in the past, don’t panic! We’re here to help!

Effective methods for learning mathematics follow the Cycle of Practice. Click on the buttons on the image below to find out how you can use the cycle of practice to get the most from this resource.




















This page is split into sections that broadly reflect key topics from GCSE and A level. Each section is divided by topic. Within each topic you will find quizzes so that you can test your knowledge (Stage 1 of the Cycle of Practice); resources to enable you to refresh your knowledge (Stage 2); and further quizzes for you to practise your knowledge (Stage3). The quizzes are designed to be done repeatedly, with different numbers, so that you can continue to practise until you feel confident to move on to a different topic. 

Don't forget that if you would like some additional support, you can always book an appointment to speak to one of our friendly advisers. We're here to help all students, on all courses, at all levels. 









Pie chart imageSection A: Key topics from GCSE Level Maths


Numbers
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Numbers: Practical estimation

Test your knowledge

MASH Video on Practical Estimation

Corbett maths worksheet on Estimation

Numbers: Rounding

Test your knowledge

MASH Video on Rounding

Corbett maths worksheet on rounding (decimals)

Corbett maths worksheet on rounding (significant figures) 

BIDMAS
Topic Test your knowledge Refresh your knowledge Practise, practise, practise

BIDMAS

Test your knowledge

University of Leeds video detailing the order of calculations (note that it calls this BODMAS; 3:19 minutes)

Corbett maths worksheet on order of operations

Fractions
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Equivalent and cancelling

Test your knowledge

University of Leeds video on equivalent fraction (1:23 minutes)

University of Leeds video on simplifying fractions (1:08 minutes)

Corbett maths worksheet on simplifying fractions

Corbett maths worksheet on equivalent fractions 

Mixed numbers converting to improper

Test your knowledge

MASH video on mixed numbers and improper fractions

Corbett maths worksheet on improper fractions and mixed numbers

Factions of an amount

Test your knowledge

University of Leeds video on how to calculate a fraction of a particular sum (1:33)

Corbett maths worksheet on fractions of an amount

Finding the original amount

Test your knowledge

MASH video on finding the original amount

Corbett maths worksheet on Fractions: finding the original

Adding, subtracting, multiplying and dividing fractions

Test your knowledge

University of Leeds video on adding and subtracting fractions (1:56 minutes)

University of Leeds video on multiply and dividing fractions (2:29 minutes)

MathCentre worksheet

Percentages
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Of amounts and change (calculator and non-calculator, as a multiplier

Test your knowledge

University of Leeds video on finding percentage amounts (2:36 minutes)

University of Leeds video on calculating percentage increase or decrease (1:31 minutes)

MathCentre worksheet

Reverse percentages

Test your knowledge

University of Leeds video on finding the original amount before percentage change (1:23 minutes)

Corbett maths worksheet on reverse percentages

Compound interest/repeated proportional change

Test your knowledge

MASH video on repeated proportional change

MathCentre resource and worksheet

Converting between Fractions, Decimals and Percentages
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Converting Fractions, Decimals and Percentages

Test your knowledge

MASH Video on converting between Fractions, Decimals and Percentages

Corbett maths worksheet on converting between Fractions, Decimals and Percentages

Standard form
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Converting in and out of standard form

Test your knowledge

Engineering Maths First Aid Kit worksheet on standard form

MASH Video on Writing numbers in Standard Form

Corbett maths worksheet on the standard form

Calculations in standard form

Test your knowledge

MASH Video on Calculations in Standard Form

Corbett maths worksheet on standard form

Algebraic fractions
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Addition, subtraction, multiplication and division of algebraic fractions

Test your knowledge

HELM booklet on the arithmetic of algebraic fractions

Corbett Maths worksheet on adding algebraic fractions

Corbett Maths worksheet on dividing algebraic fractions

Corbett Maths worksheet on multiplying fractions

Simplifying algebra
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Collecting terms

Test your knowledge

University of Leeds video on simiplifying algebraic expressions (3:09 minutes) 

Corbett maths worksheet on collecting like terms

Expanding linear terms

Test your knowledge

MathCentre booklet on expanding and removing brackets

Corbett maths worksheet on expanding brackets

Factorising linear terms

Test your knowledge

Engineering Maths First Aid Kit worksheet on factorising simple expressions

Corbett maths worksheet on factorisation

Expanding double brackets

Test your knowledge

Coventry University's worksheet on brackets and quadratics

Corbett maths worksheet on expanding two brackets

Factorising double brackets

Test your knowledge

MathCentre worksheet on factorising quadratics

Corbett maths worksheet on factorising quadratics

Corbett maths worksheet on factorising harder quadratics

Solving linear equations
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Unknown on one side

Test your knowledge

MathCentre worksheet on solving linear equations

Corbett worksheet on solving equations

Unknown on both sides

Test your knowledge

MathCentre worksheet on solving linear equations

Corbett maths worksheet on solving equations with unknowns on both sides

Indices
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Rules: multiplying and dividing

Test your knowledge

University of Leeds video on rules of indices (4:26 minutes)

Corbett maths worksheet on laws of indices

MathCentre worksheet on rules of indices

Trigonometry
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Pythagoras' theorem

Test your knowledge

University of Leeds video on Pythagoras' Theorem (4:24 minutes)

Corbett maths worksheet on Pythagoras Theorem

Finding missing sides and angles in right angle triangles

Test your knowledge

University of Leeds resource on sine, cosine and tan (5:44 minutes)

Corbett maths worksheet on Trigonometry


Pie chart imageSection B: Key Topics from higher GCSE maths/easier A-level


Quadratics
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Solving by factorising

Test your knowledge

University of Leeds video on solving quadratic equations by factorising (3:42 minutes)

Corbett maths worksheet on solving quadratics by factorising 1

Corbett maths worksheet on solving quadratics by factorising 2

Solving with the formula

Test your knowledge

University of Leeds video on solving quadratic equations using the formula (3:24 minutes)

Corbett maths worksheet on solving quadratics using the formula

Completing the square

Test your knowledge

University of Leeds video on solving quadratic equations by completing the square (3:09 minutes)

Corbett maths worksheet on solving quadratics by completing the square

Quadratic graphs

Test your knowledge

MASH Video on Sketching Quadratic Graphs

Corbett maths worksheet on sketching quadratics

Simultaneous equations
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Linear by elimination

Test your knowledge

University of Leeds video on simultaneous linear equations (5:20 minutes)

Corbett maths worksheet on solving simultaneous linear equations by elimination

Linear by substitution

Test your knowledge

University of Leeds video on simultaneous linear equations (5:20 minutes)

Khan Academy quiz on solving simultaneous linear equations by substitution

Graphically

Test your knowledge

University of Leeds video on geometry: parallel, perpendicular and intersecting lines (9:23 minutes)

Corbett maths worksheet on solving simultaneous linear equations graphically

Algebraic and graphical when one non-linear

Test your knowledge

MASH Video on Substitution method for one linear and one non-linear equation

MASH Video on Simultaneous Equations and Graphs

Corbett maths worksheet on further simultaneous linear equations

Indices
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Fractional and negative indices

Test your knowledge

University of Leeds video on negative indices (2:55 minutes)

MASH video on Fractional Indices

Corbett maths worksheet on fractional indices

Corbett maths worksheet on negative indices

MathCentre worksheet on negative and fractional powers


Pie chart imageSection C: Key Topics from A-level Maths


Algebraic fractions
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Partial fractions

Test your knowledge

MathCentre booklet on partial fractions

MathCentre worksheet on partial fractions

Factor and remainder theorem
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Factor and remainder theorem

Test your knowledge

Coventry University worksheet on factor and remainder theorem

Maths Support Centre worksheet on Factor and remainder theorem

Logarithms
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Definition

Test your knowledge

MathCentre booklet on logarithms

MathCentre worksheet on logarithms

Multiplication, division, power rules

Test your knowledge

MathCentre worksheet on the laws of logarithms

MathCentre worksheet on the laws of logarithms

Trigonometry
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Graphs of sine, cosine and tan

Test your knowledge

MASH Video on Graphs of Sine, Cosine and Tangent

Engineering maths first aid kit: worksheet on graphs of trigonometric functions

Sine and cosine rules

Test your knowledge

University of Leeds video on the sine rule (11:16 minutes)

University of Leeds video on the cosine rule (9:31 minutes)

Engineering maths first aid kit: the sine rule and the cosine rule


Barchart imageProbability and Statistics refresher


Measures of average
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Mean, median and mode definitions and from lists

Test your knowledge

MathsCentre resource on mean, median and mode

Khan Academy video on calculating measures of average

Corbett Maths worksheet on averages and the range

Mean, median and mode from frequency tables (including grouped)

Test your knowledge

University of Leeds video on calculating the mean from a frequency table (2:10 minutes)

University of Leeds video on calculating the mean from grouped data (3:25 minutes)

University of Leeds video on calculating the median from a frequency table (2:14 minutes)

University of Leeds video on calculating the median from grouped data (2:37)

Corbett Maths worksheet on calculating the mean from a frequency table

Corbett Maths worksheet on estimating the mean

Corbett Maths worksheet on calculating the median from a frequency table

Corbett Maths worksheet on using linear interpolation to calculate the median

Spread
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Range, interquartile range, the idea of spread

Test your knowledge

Khan Academy video on the Interquartile range

Khan Academy video on the range and mid-range

Corbett Maths worksheet on averages and the range

Coventry University measures of spread worksheet

Variance and standard deviation

Test your knowledge

Khan Academy video on range, variance and standard deviation

Khan Academy video on sample variance

MathCentre worksheet on the variance and standard deviation of ungrouped data

MathCentre worksheet on the variance and standard deviation of grouped data

Displaying information
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Barcharts, pie charts, tally charts

Test your knowledge

University of Leeds video on barcharts (1:30 minutes)

University of Leeds video on piecharts (2:33 minutes)

MASH resource on displaying data in charts - some simple charts

Corbett Maths worksheet on reading barcharts

Corbett Maths worksheet on pie charts

Corbett Maths worksheet on tally charts

Box plots

Test your knowledge (Drawing)

Test your knowledge (Interpreting)

MASH resource on interpreting a box-plot

Khan Academy video on boxplots

Corbett Maths worksheet on box plots

Histograms

Test your knowledge

MASH video on Histograms

Corbett Maths worksheet on histograms

Collecting information
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Types of data

Test your knowledge

MASH resource on types of data

Corbett Maths resource on quantitative and qualitative data

Corbett Maths resource on continuous and discrete data

Corbett Maths resource on primary and secondary data

Probability
Topic Test your knowledge Refresh your knowledge Practise, practise, practise
Equally likely events

Test your knowledge

HELM workbook on elementary probability

Khan Academy video on probability

Coventry University resource on probability

Corbett Maths resource on probability

Conditional probability

Test your knowledge

Khan Academy video on conditional probabilities and combinations

Corbett Maths resource on conditional probability


Image of a computer keyboardJumpstart University

The Jumpstart University hub has been developed by The Open University in collaboration with the Russell Group to help students starting university this year to prepare for and settle into their studies. Below are links to the maths and stat resources.


Topics
Topic Description
Succeed with maths - Part 1

Does maths feel like a bit of a mystery to you? Are you looking to improve your confidence in using maths in a variety of everyday situations? If so, this course is for you. Beginning with the very foundations of maths,it will start by looking at how numbers are put together, before guiding you through how to use percentages, fractions and negative numbers. Taking real-life examples you will have the opportunity to practise your new skills and build your confidence in using maths to solve problems in everyday life and the wider world. This course will encourage you to not just mechanically follow the rules that are written to help with maths, but to also gain an understanding and appreciation of what lies behind these rules.

Succeed with maths - Part 2

Following on from Succeed with maths - Part 1, this course will continue to develop your mathematical knowledge and skills using everyday examples. It will guide you through measurement, scientific notation (based upon powers of 10) and roots of numbers, shapes and how to calculate their properties before finally turning to how to construct and read from tables, charts and graphs. It provides a solid foundation for you to continue with studies in any subject which requires some degree of mathematical knowledge.

Mathematics for science and technology

Maths is intimately entwined with science and technology, whether it is used to analyse data collected on plants in the Amazon rainforest, to calculate the trajectory of a comet or design a bridge to connect two countries. This means that science and technology go hand-in-hand with maths, and that a firm grasp of maths is crucial for studying any science and technology discipline. This course will help you build a stronger grip with the maths helping hand. You’ll learn about the power of algebra, get a sense of scientific notation, the beauty of basic trigonometry and why 70 db (decibels) is 10 times more powerful than 60 db. As well as this you will delve into scientific measurement, including the importance of units and the flexibility and practically of the SI – the internationally recognised system of units based on multiples of ten.

Medical statistics

This course is concerned with some of the statistical methods used in epidemiology and more widely in medical statistics. Section 1 introduces cohort studies in which individuals are classified according to their exposure and followed forward in time to evaluate disease outcomes. Section 2 looks at models for cohort studies. Section 3 introduces case-control studies in which individuals are selected according to their disease status and past exposures are then ascertained. Section 4 covers testing for no association in cohort studies and case-control studies.


Image of a question markIf there are topics that you would like to see added to this page, click here to let us know. In addition don't forget to the check our general resources pages for more things that can help you.