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The diagram shows the lamina shape.

To begin, divide the lamina into smaller sections and calculate the area. In this example, the lamina is best divided into sections A, B and C. Calculate the are...

The trick with this question is noticing the hidden quadratic as quartic equations are unsolvable at A-level.

Letting u=x^2 the question becomes u^2+2u-3=0 which most students would be able to solv...

Example.

" Solve the simultaneous equations

y + 4x + 1 = 0

y^2 + 5x^2 + 2x = 0 "

We can rearrange the first equation to something that we can substitute into the seco...

To find the integral of a function you must first incease the power of x by one then divide to coefficient by the new power. So, by increasing the powers first you get 3x^2 - x^(5/2) and then dividing by ...

9x^2 + 8x + 5y +5xdy/dx + 7dy/dx = 0

9x^2 + 8x + 5y = dy/dx(-5x - 7)

dy/dx = - (9x^2 + 8x +5y)/(5x + 7)