Uncategorised Archives - Miranda The Maths Tutor

25th April 202025th April 2020

Vital Text Books

Head Start to A-Level Maths – a nice bridge to make sure your GCSE maths is up scratch for the challenges of A-level maths.

Head Start to A-Level Physics – a nice bridge for those who are looking to go from GCSE to A-Level Physics.

Head Start to A-Level Chemistry – a nice bridge for those going on to A-Level Chemistry.

Edexcel A-Level Mathematics Year 1 Pure Maths – exactly what it says on the tin.

Edexcel A-Level Mathematics Year 1 Mechanics and Statistics – the statistics and mechanics you need for year one.

Edexcel A-Level Mathematics Year 2 Pure Maths – the second year pure maths book.

Edexcel A-Level Mathematics Year 2 Mechanics and Statistics – the statistics and mechanics you need for year two.

AQA GCSE Physics – complete book for the AQA Physics course.

AQA GCSE Chemistry – complete book for the AQA Chemistry course.

Collins Edexcel GCSE Maths Higher student book – comprehensive GCSE maths book that explains everything.

Letts KS3 Maths Complete Coursebook – a complete book for Key Stage 3.

20th April 202029th April 2020

All that is needed for Online Tutoring is a computer, WiFi and a pointer. I recommend the Wacom Intuos S bluetooth and USB pointer device. I have used this for all of my online tutoring and rate it extremely highly.

You can buy a Wacom Intuos S for online tutoring for less than £60 here.

These pens are difficult to get during the pandemic, an alternative pen is the X-Pen.

27th June 201827th June 2018

Tangents Of A Parabola Problem

This is a problem from the excellent book ‘Pure Mathematics 2‘ by Backhouse, Houldsworth and Cooper, reviewed by Horril and originally published in 1963 although I’d recommend this and the companion volumes ‘Pure Mathematics 1‘ and ‘Applied Mathematics‘. All are well-explained, well-written books with many examples and practice questions.

Within this video I demonstrate how to find the equation of the two tangents to the parabola $y^2=4ax$ from a point $(16a,17a)$ . To do this, we first define the problem in terms we can work with mathematically, our tangent on the parabola is defined as $(x1,y1)$ and we equate the gradient of the tangent to the parabola (derived in terms of $y1$ through implicit differentiation) to the gradient of the line from $(16a,17a)$ .

The resultant equation is simplified with a key substitution so resolves to a quadratic in terms of $y1$ and $a$ , which is factorised to give two values of $y1$ . These are substituted into $y^2=4ax$ to give the matching values of $x1$ and then we use the values of $x1$ and $y1$ to derive the equations of both tangents to the parabola.

I hope you enjoy, and please leave comments and requests!