# 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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.