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Question: 5x² + 3x - 3y = 4, -4x - 6y + 5x² = -7.........Step 1: make the y-coefficient equal in both equarions: (y and not x because it has the lowest power so it is easier, but x w...

∫ u(dv/dx) dx = uv − ∫ v(du /dx)dx is the Integration by Parts formula. 

If you set u=lnx, differentiation (rememeber from tables) leads to du/dx= 1/x, and dv/dx=x and so v=x^2/2 (raise power by on...

This question is aimed at A-Level Pure Core 1 students. A circle with centre C(2, 3) passes through the point A(-4,-5).  Find the equation of the circle in the form (x-a)^2 + (y-b)^2 = k ...

i) Square both sides of the expression to make x^2=(a-y)/b 

Multiply by b to remove the fraction from the equation and then rearrange to make y the subject.

bx^2=a-y --> y=a-bx^2

i...

To differentiate, we bring the power down and decrease the power by 1. So x³ becomes 3x², -3x² becomes -6x, and -9x (which can be written as -9x¹ ) becomes -9. ...