# 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 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).

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
best buys
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.

Latest version (19/10/18) covers both Foundation and Higher Tiers. For each tier there’s a PowerPoint, a set of practice questions and a PDF of model answers to these. In this latest version I’ve tweaked the Higher worksheet so the question order is a better match to the PowerPoint, and have also added a sheet of consolidation and extension questions for the stronger students (answers included on sheet).
Both PowerPoints include a recap of y = mx + c and introduce ax + by = c; plotting a graph; sketching a graph; formula for gradient; finding the equation of a line from its graph; mid-point of a line segment; and parallel lines. The Foundation one takes things a little slower, while the Higher one also includes distance between two points; use of y - y1 = m(x - x1) for the equation of a line given gradient & 1 point / given 2 points; perpendicular lines; perpendicular bisector; intersection of two lines (with a brief mention of inequalities); and tangent to a circle.
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.

Interactive PowerPoint for GCSE Maths: covers translation, reflection, rotation and enlargement. Works best when projected onto a whiteboard (not necessarily an interactive one) but can also be viewed/used on screen by individuals.
New improved version (Oct 2017) includes enlargement with negative scale factor, invariant points and an accompanying worksheet (in both Word and PDF format). There are two versions of the PowerPoint: the (editable) original and a slideshow version (identical in content) suitable for upload to your VLE for student use.
May 2018 - error on first diagram (a discrepancy from the slide it was supposed to match) on worksheet corrected.
Apr 2020 - added vertical and horizontal arrows to make angle of rotation easier to see.

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.

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.

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.

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.

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 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.

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.

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.

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 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

Map activity where students identify the scale of the map and identify target towns using bearings and distances. For KS3/4.
Answers provided.
Make sure you print it at full size so as not to mess the scaling up! Should be 1cm : 50km when printed.

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.

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.

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

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).

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.