This video is all about tangent proof - where a line touches a circle, and is aimed at GCSE maths grade 8. The whole idea is that it can be treated in a similar way to solving quadratic simultaneous equations, by substitution, but in this case there is only a single point. Prove algebraically that the straight line with the equation x - 2y = 10 is a tangent to the circle … [Read more...]

## Quadratic simultaneous equations – solving by substitution

These questions are fairly challenging and aimed at around grade 8 GCSE maths. They deal with solving quadratic simultaneous equations by substitution, and you'll need good 'algebra confidence.' Please do stop the video, try the questions and compare your solution. Video one - solve: x - 2x = 3 x² + y² = 18 Video two - solve: x - 2y = 1 x² + y² = … [Read more...]

## Solving simultaneous equations by substitution – circles & straight line question

This video is a fairly popular example of solving simultaneous equations, by substitution, in circles and straight lines. The question asks you to calculate the intersects (where the perimeter and straight line cross each other): The question is aimed at around grade 7+ GCSE maths: Find the coordinates of the points where line y + 5 = 3x intersects the circle x² + y² … [Read more...]

## nth term of a quadratic sequence – GCSE maths level 6 onwards

nth term of a quadratic sequence questions ... can seem extremely difficult, although in this video, I've tried to give you a fairly straightforward method to use. If you apply the same idea each time, you should be able to calculate an expression for the nth term with most of the questions in GCSE maths. The whole idea is that you are creating an expression with the … [Read more...]

## Completing the square and solving in surd form – advanced

Completing the square questions are becoming more popular with GCSE maths, as the technique can be useful if you're intending to study at a higher level. The main use is factorising and finding out the maximum and minimum values of a quadratic equation. Once you're familiar with the method, completing the square becomes quite straightforward. Top Tips! ● It’s just another … [Read more...]