# B28 Maths Tutor

Former teacher now specialising in private tuition and offering online courses at https://mathscourses.co.uk. On TES I have a wide range of resources for GCSE and A-level Maths.

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Former teacher now specialising in private tuition and offering online courses at https://mathscourses.co.uk. On TES I have a wide range of resources for GCSE and A-level Maths.

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Former teacher now specialising in private tuition and offering online courses at https://mathscourses.co.uk. On TES I have a wide range of resources for GCSE and A-level Maths.

A PowerPoint covering probability up to Higher GCSE level. Assumes that the basics have already been covered, but includes:
- Venn diagrams and set notation
- addition law
- two-way tables
- frequency trees and probability trees (both with and without replacement)
- conditional probability using Venn diagrams and two-way tables
- multiplication law for both independent and non-independent events.
I’ve also included one Venn diagram problem (with solution) that involves solving a quadratic. There are a few signposts to exercises in the Elmwood “Higher GCSE Maths 4-9” text book but these are easily removed if not applicable to you.
The latter section of the presentation consists of handout/worksheet versions of some of the slides.
Update Jan 2018: small correction to set notation slide.

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
examples
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.

PowerPoint including triangle labelling conventions, SOHCAHTOA, exact trig values, bearings and angles of elevation/depression. A convenient set of key points that can be drip-fed to students as you progress through the topic, and printed (8 or 9 pages to a sheet works well) as a reference handout at end of topic.

Animated PowerPoint demonstrating how to use ruler and compasses to construct:
a 60-degree angle
an equilateral triangle
a triangle with sides of specified lengths
a perpendicular bisector
an angle bisector
a rhombus
the perpendicular from a point to a line
the perpendicular at a given point on a line.
Aimed at GCSE students.
I also now have a similar resource on working with loci, which can be found at https://www.tes.com/teaching-resource/working-with-loci-12221878.

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.

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
Algebra
Graphs
Trigonometry
5-1) Handling data
5-2) Probability
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.

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).

Powerpoint covering key points of this topic - including a Pythagoras and SOHCAHTOA recap, special angles, sine rule, cosine rule, area of a triangle, and which rule to use when. Can be used in lessons then printed out as a summary / revision aid for students at the end of the topic.

A single-page handout introducing and summarising the three numerical integration techniques required for The Level 3 BTEC in Engineering (Unit 7: Calculus). May also be useful for other courses.

Updated 2020 for new A-level spec.
Takes the student through the process of generating the sin, cos and tan curves from the unit circle; explains how to solve simple trig equations in both degrees and radians using the ASTC (CAST) grid as a mnemonic; and also shows how to use the same grid to help remember sign changes when differentiating/integrating sin and cos functions.
Suitable for classroom use (no IWB needed) or for uploading to a VLE for students to use independently as a support tool.

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.

A short animated PowerPoint showing the derivation of the Newton-Raphson formula and an illustrated example of its application.

A Christmas-themed problem for Year 10/11 (the last part of the extension task requires proportionality to have been covered). High-ability Y9s should also be able to have a bash at most of it.

Assorted percentages questions including reverse compound percentages, for the new (9-1) GCSE spec. Answers included - though be warned that these have not been fully checked. In Word format so easy to edit.
Also an end-of-topic homework sheet with a mixture of percentage questions, including percentage profit/loss as well as compound & reverse percentages.

Treasure hunt revision activities inspired by a similar Core 4 one that I downloaded some years ago from a TES contributor... but this one has the twist of two possible answers to choose from for each question, which prevents the students from getting the last two or three by process of elimination instead of actually working them out. Because they just put the appropriate letters in the boxes, it also makes it really easy to check answers. It does have to be explained quite carefully though!
Will typically take a team of 2-3 students about 45-60 minutes to complete, though some manage it in 20-25. Tell each team to start at a different question as this will reduce bottlenecks and copying!
Written for the AQA spec but should be fine to use for Edexcel or other boards for summer revision, once both C1 and C2 modules have been covered.

A worksheet that takes the student through most of the circle theorems they will need for GCSE. Includes opposite angles in a cyclic quadrilateral; angle in a semicircle; angles in the same segment; angles at centre vs at circumference; a tangents activity; and a few practice questions.
Doesn't include alternate segment theorem though, nor intersecting chords theorem (on Edexcel IGCSE 2009 spec).

This PowerPoint uses a golf club manufacturing analogy to introduce the idea of restricting the range of the nested function so that the “outer” function can use all of its outputs. Also covers range of composite functions.
Also included is a worksheet with a more basic exercise on composite functions followed by a few practice questions on domain and range of composite functions.
Written for A-level Maths. Requires prior knowledge of composite functions, domain and range.

Updated 28/3/18
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.

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.

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.