These are the course materials from my Preparing for A-level Maths course, covering the aspects of GCSE Maths that are expected prior knowledge for the A-level course.
Also useful as a resource for home learning for Higher GCSE students, especially if lack of time means that some of the top-end topics will have to be glossed over in school. Lots of practice questions are built in.
There are seven PowerPoints:
Fractions, surds, indices and vectors
5-1) Handling data
5-3) Mechanics (includes some GCSE Physics/Science as well as Maths)
… and accompanying supporting materials.
You can see an introduction to the course and couple of sample videos at this YouTube playlist: https://www.youtube.com/watch?v=BwZIjac-ghM&list=PLBIKX8sbX4FflLEqX7mch4vMkYSIwr3l7
With this resource you’re getting the PowerPoints used in the videos, but not the actual videos themselves. If you have students who might be interested in subscribing to the whole video course then they can find it at https://b28mathstutor.co.uk/maths-help/#PFALM or on https://mathscourses.co.uk.
Animated PowerPoint taking the student through the construction of various loci:
fixed distance from a point
fixed distance from a line/rectangle
equidistant from two points
equidistant from a line
… and finishing with a challenge inspired by the Diamond Heist resource that can be found at https://www.tes.com/teaching-resource/loci-diamond-heist-laser-challenge-6328947.
Includes a set of printable slides at the end, so the students can construct the loci themselves.
I also have a Constructions PowerPoint that you might find helpful if the students need some guidance for the bits that require them to use compasses: https://www.tes.com/teaching-resource/constructions-using-ruler-and-compasses-11521910
There are lots of resources around for this topic at Higher but they usually start with deriving the formulae, which isn’t required at Foundation. I’ve therefore put this handout together to cover just what a Foundation student needs to know:
forms of equation for direct and inverse proportion
shapes of graph
using the graphs and formulae to find values
It doesn’t include squares or roots, but if you’ve seen Foundation questions that do use those forms of equation then please let me know and I’ll add them.
Worksheet of questions requiring the use of algebra skills to form and solve an equation relating to the area or perimeter of, or angles in, a triangle or quadrilateral. A couple of the later questions also require use of Pythagoras’ theorem.
Answers on page 2, and full worked solutions also provided.
A short PowerPoint to highlight the connection between formulae and units. Dimensional analysis isn’t explicitly on the GCSE or A-level specification these days, but grasping the basics can really help a student to to use the right units or spot mistakes in their formulae.
Deals with speed, density and pressure triangles and the associated units, then goes on to look at what constitutes suitable formulae for length, area and volume.
The second half of the file consists of handout versions of the slides that the students can fill in as you go along; I suggest printing four slides to an A4 page.
Inspired by another similar resource found on TES, I’ve done one of my own. This one uses the rules on angles in parallel lines, different kinds of triangles and polygons, with parallel and equal lines indicated on the diagram. Starts off pretty straightforward but gets trickier towards the end.
Second slide is animated with the solutions. A copy of the problem sheet is also provided in PDF form for ease of printing.
A worksheet covering the subtopic on discrete probability distributions for the first year of A-level Maths. Includes a general intro, tabulating a probability distribution and other forms in which it might be defined, cumulative distribution function, expected value of a distribution. You’ll have to look elsewhere for tricky questions but this covers the need-to-knows.
Answers are on page 3 but I’ve also included a set of detailed solutions.
An activity to revise all the types of percentage questions that come up in GCSE (suitable for either tier). I wrote this because I was struggling to find exercises where all the different types of percentage questions were mixed up.
There are 9 question types identified, with non-calc and calculator methods for each (though reverse compound percentage and “find n” type questions are unlikely to come up on a non-calculator paper). Then there are 26 mixed questions, which can be given as either cards or a handout. Once the types and methods have been matched (these are in the same order on the sheets so it’s easy to skip this step if desired), the questions can be matched by type and then answered. The answer section confirms question types as well as answers.
More accomplished students might prefer to jump straight in and start working through the questions immediately, but those who have difficulty identifying what a question is asking for should find the matching process helpful.
A possible extension for early finishers would be to have them write additional questions of their own to challenge their peers.
Revision questions covering the whole of the Quadratics topic for both GCSE and A-level - a single A4 page for each. The GCSE version includes indications of the approximate grade level for each question. There’s a lot of overlap between the versions, hence only one set of solutions; these match the numbering on the GCSE version but there’s only one question on the A-level sheet that isn’t on the GCSE one, and solutions to that are included.
Map activity where students identify the scale of the map and identify target towns using bearings and distances. For KS3/4.
Make sure you print it at full size so as not to mess the scaling up! Should be 1cm : 50km when printed.
This is based on a poster that AQA published but is much gentler on the print budget, as well as being (in my opinion) easier to read than the original white and purple text on an orange background. I’ve added a couple of bits (e.g. equation of a circle, product rule in terms of u and v as well as the original f and g) and indicated which formulae come up in each year of the course, but it’s mostly the same as the original.
As well as the A4 version I’ve included a “2-up” version with two A5 copies per A4 sheet.
New version uploaded 10/7/19 with a correction to the Integration section.
Year 1 PowerPoint explains where the formula for differentiation from first principles comes from, and demonstrates how it’s used for positive integer powers of x. Ends with some questions to practise the skills required (solutions provided in a separate PDF file as well as on the last two slides).
Year 2 PowerPoint covers differentiation of sin x and cos x from first principles.
I’ve put this together to help trainee teachers hone their skills for the QTS Numeracy test, but it’s full of little tricks that will help in everyday life too, so it’s relevant to everyone really.
Have uploaded both the editable PowerPoint file and a slideshow version suitable for upload to a VLE.
A PowerPoint covering the Proof section of the new A-level (both years). It includes disproof by counterexample, proof by deduction, proof by exhaustion and proof by contradiction, with examples for each. The proof by deduction section also includes a few practice questions, with solutions in a separate file. The final slide lists a few suggested sources of further examples and questions on this topic. PowerPoint slideshow version also included - suitable for upload to a VLE.
Latest version posted 2/12/19 with a small correction to proof of the infinity of primes.
A simple animated PowerPoint file demonstrating how to work out arc length and sector area by thinking of them as fractions of the circle, with questions to practise the basic techniques and then some more challenging questions building up to finding the area and perimeter of a segment. All suitable for both Foundation and Higher students except the very last question, which requires the use of the triangle area formula and the cosine rule and so is Higher only (and is labelled as such).
A selection of problems from various sources, most of them quite challenging, for use with Higher GCSE students. Some only require Foundation skills (indicated in top right-hand corner of question slide) so they could also be used with Foundation students at a pinch. Each one is over two slides, with the first slide giving hints and the second giving the solution. The hints and solutions are all animated so that they are only revealed a line/paragraph at a time. Could be used in class or uploaded onto a VLE for keen students to use for extra challenge.
A pair of PowerPoints covering all the Foundation and Higher content for GCSE trigonometry. (No 3D work though.)
Foundation PPt starts with a brief recap of labelling conventions and Pythagoras, then covers SOHCAHTOA in some detail, including exact trig values (for acute angles only), and gives a brief introduction to bearings and angles of elevation and depression.
Higher PPt starts with a brief recap of labelling conventions, Pythagoras (including distance between two points, linking to straight lines) and SOHCAHTOA, then goes on to cover exact trig values for special angles (including using the graphs to find different angles with the same sin/cos/tan), area of a triangle (from 2 sides & enclosed angle), sine rule and cosine rule.
The Higher PPt could also be useful for the early parts of trig at A-level.
Page/exercise references are to the Elmwood Higher GCSE Maths 4-9 book (which is about half the price of the better-known text books and in my opinion just as good), but can easily be replaced/removed.
Main PowerPoint covers all aspects of ratio and proportion for GCSE (but not direct and inverse proportion):
relationship between fractions and ratios
dividing an amount in a ratio - inc finding the total amount and solving problems from the difference between two shares
simplifying ratios by converting units
expressing as 1:n
working with map scales
proportion and recipes
expressing a ratio in algebraic form
latest version includes a few harder questions involving fractions of fractions, combining pairs of ratios, and change of ratio, with worked examples for each.
Includes handout versions of main question pages (i.e. black & white with no answers included) at end of presentation.
Also a second PowerPoint with starter/homework questions, most pages including answers (but again with handout versions at the end). Updated April 2020 with a correction and a few minor changes.