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Finding normals and tangents to curves is a very common question in A-level maths papers, especially core 3 modules, giving between 5-8 marks depending on complexity. In order to start this question, the ...

Firstly, lets name each equation A and B- this will help us later. If I told you what x was, you would be able to use either equation to find y- easy! so lets first find one unknown (x or y) then use that...

This problem requires using the quotient rule, product rule and the chain rule. The derivative of the entire thing is ((du/dx)v-(dv/dx)u)/v^2 where u=2x+xe^6x and v=9x-2x^2-lnx. dv/dx is relatively strait...

x=1, y=3; Firstly, rearranging for x in the first equation: x = (7-2y); Substitute this into the second equation: 3y - (7 -2y) = 8; Expand: 3y -7 +2y = 8 (watch negative) 3y +2y = 15 Therefore, 5y = 15 an...

Step 1: Draw a labelled diagram of the triangle, marking the side lengths. Step 2: Recall Pythagoras’ theorem equation ‘c2=a2+b2’ Step 3: Substitute the values of a and b into the equation. c2=8.652+10.15...