# B28 Maths Tutor

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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.

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#### Probability for GCSE

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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.

#### Arcs and sectors for GCSE

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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).

#### Direct and inverse proportion for Foundation GCSE

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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.

#### Trig Basics Powerpoint: unit circle, trig curves, ASTC, simple eqns in degrees & rads, calculus

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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.

#### Constructions using ruler and compasses

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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.

#### Working with loci

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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

#### Trigonometry for Foundation GCSE

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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.

#### Y10/11 Trigonometry summary

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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.

#### Preparing for A-level Maths

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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. I’m not allowed to inlcude external links here but these PowerPoints are the basis of the Flying Start to A-level Maths course on my Mathscourses site.

#### Basic dimensional analysis OR Getting the units and formula right!

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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.

#### Straight line equations and graphs for Foundation and Higher GCSE

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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 &amp; 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.

#### Numerical integration handout: trapezium rule, mid-ordinate rule, Simpson's rule

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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.

#### Mental Maths tricks

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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.

#### Bearings and working with map scales

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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. Also a nice bit of cross-curricular work incorporating a geography lesson - though I don’t know why Devon is shown as a town!

#### Domain and range of composite functions

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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.

#### Proof for A-level Maths

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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.

#### Ratio and proportion for GCSE

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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 &amp; 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.

#### Differentiation from first principles - for new A-level Maths

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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.

#### How many lights for my tree?

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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.

#### Compound & reverse percentage questions

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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 &amp; reverse percentages.