"Mathematics is easier without tricks."
Dr Duncan James
A complete relaunch is tentatively planned for September 2019. Bookmark this page and come back to see the exciting developments!
"Understanding through Practice".
Each question has at least one worked solution. With different vocabulary, situations and types of unknown for a complete learning experience.
UPmaths is changing! I taught my last private maths tutorial on Sunday 11th June 2017! My intention is to take a minimum of a 2 year sabbatical from tutoring. All the time I used to spend tutoring will be put into creating videos and other content for UPmaths. I am not messing around! You can contact me directly to request content.
I love maths tutoring. Seeing someone's confidence, learning skills and retention improve gives me such a buzz. I want to start reaching out to more people, including those that cannot afford a good private maths tutor.
I think the experience of learning with a maths tutor can be recreated with videos. This is based on extensive testing over approximately 7 years with my tutoring students: I have been developing this idea for a long time.
Free Maths Tutoring With UPmaths
Videos that recreate the unique experience of maths tutoring. Fast learning with clear explanations that are designed to compliment your other maths learning.
A maths tutor typically helps with confidence, basic skills (picking up on things that have been missed by your school), difficult-to-understand topics, revision and exam technique. You can also expect to learn at a much faster rate than at school; partly because the school has done the ground-work and partly because the learning can be more tailored to your specific needs. UPmaths is designed to do all this.
You can subscribe to my newsletter for quarterly-ish emails that will keep you up to date with the latest UPmaths content.
These topic guides are old! They are from when I occasionally uploaded videos for my students. Additionally, all the old Vimeo videos are no longer available. There are still some useful YouTube videos linked from these articles. This will be tidied up at some point after September 2017.
- Numbers: Arithmetic, Bidmas, Fractions, Decimals, Prime Numbers, Percentages, Ratios, Surds, Units and Conversions, etc.
- Algebra: Simplifying, Solving, Factorising, Expanding, Binomial Expansion, Fractions, Quadratic Equations, Inequalities, Simultaneous Equations, Functions, Factor Theorem, Algebraic Trigonometry, Logarithms, etc.
- Indices: Simplifying, Calculating, Numbers, Algebra, etc.
- Geometry: Transformations, Coordinates, Lines (Parallel, Perpendicular, etc.), Intersections, Triangles, Pythagoras, Trigonometry, Exact Trigonometry, Circles, Regular Polygons, Areas, Volumes, Density, Nets, Loci, etc.
- Graphs: Sketching, y=mx+c, Describing, Transforming, etc.
- Vectors: Addition, Mid-Points, Ratios, Dot-Product, Intersections, etc.
- Calculus: Differentiation, Integration, Trapezium Rule, Rate-of-Change, Chain Rule, Product Rule, Quotient Rule, Integration by Substitution, Integration by Parts, Parametrics, Implicit Differentiation, etc.
- Sequences and Series: Algebraic, Geometric, etc.
- Sets: Set Notation, Logic, etc.
- Logic: Notation, Even and Odd Numbers, etc.
- Probability: Tree Diagrams, Venn Diagrams, etc.
- Statistics: Mean, Median, Mode, Histograms, Interpolation, Skewness, etc.
- Mechanics: Resolving Forces, Centre of Gravity, etc.
All YouTube videos currently available and not yet organised into a topic page
The videos shown here have not yet found a comfy home on a topic page.
Partial Fractions Overview (UP4) (YouTube)
How to get Started with Different Triangle Questions (UP3) (YouTube)
Dot Product Written Different Ways (UP4) (YouTube)
Universal Factorise Approach (UP4) (YouTube)
Inequalities Universal Solve Approach (UP4) (YouTube)
Dr Duncan James
"A teaching technique I recommend is showing an incorrect solution and encouraging your students to find the mistake. I find this develops important skills including error-checking, team-work, communication and intuitive understanding."
Dr Duncan James (can be done from the earliest stages, for example by counting and using a number twice)
UPmaths is organised into four levels
- UP1 (basic skills to give everyone a foundation in mathematics from the earliest age, also important for revision whatever level you are studying)
- UP2 (moving on through school and leaving with a good grade, for example grade C Foundation GCSE in Britain)
- UP3 (leaving school with a higher grade for example GCSE Higher and AS-Level in Britain)
- UP4 (final preparations for university study, for example A-Level in Britain).
- See the levels page for more details.
"There is a moment when advanced techniques start to take longer. You need to accept this drop in speed so that you can gain the ability to deal with more complex questions."
based on the ideas of Ian Thompson
"Mathematics can be very difficult to teach. I find that the 'right/wrong issue' overshadows this subject. I try to praise method, including attention to detail and double-checking instead of the correct answer."
Dr Duncan James
- I sometimes help my students with other subjects. I have a few online resources for studying science.
- If, like me, you are trying to produce mathematics resources TTH is a useful Tex to html conversion method.
- I have a page called Exam Questions Worked Solutions which has a small selection of worked solutions to exam questions. Sometimes my students ask for help with a particular exam question and sometimes the best way I find to help is to make a video. If you have a request (after checking it is not already on this page) please let me know.
"I like to think of maths as a written language. I often avoid talking with my students and communicate just by writing to save time and cut straight to core of the subject."
Dr Duncan James (on the topic of more advanced mathematics) (also true for mental maths where it is possible to see an answer intuitively without a good reason)