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What marks do I need to achieve an A* grade in A-level Maths?

The A* grade in Maths is awarded to candidates who achieve an A (480 out of 600 UMS) in their overall A Level as well as achieving a combined score of 180 out of 200 UMS in modules Core 3 and Core 4 (i.e. an...
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Answered by Omar C. • Maths tutor
13280 Views

Integral between 0 and pi/2 of cos(x)sin^2(x)

The key point in here is noticing that the derivative of sin(x) is cos(x). That way, if we rename sin(x) as u , i.e u:=sin(x), the derivative will be du=cos(x)dx. So, inside the integral, instead of having c...
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Answered by Maria L. • Maths tutor
6320 Views

What is the derivative with respect to x of the function f(x)=1+x^3+ln(x), x>0 ?

Despite the hideous view, we can apply to this function the same methodology as all the other ones: break it down to pieces. What we mean is that we recognize three terms inside f(x): one is the number 1 alo...
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Answered by Maria L. • Maths tutor
3805 Views

Where does integration by parts come from?

The best way to do well in maths, is to learn where things come from. Mastering the basics makes everything else much easier! To start, consider the product rule with two functions u(x) and v(x) (using dashe...
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Answered by Tom M. • Maths tutor
3576 Views

Integrate (12x^5 - 8x^3 + 3)dx giving the terms of the answer in the simplest terms

Integration is essentially differentiation in reverse! So in the simpler cases instead of multiplying by the power of x and subtracting one from the power of x, you add one to the power of x and divide by th...
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Answered by Ellen S. • Maths tutor
6938 Views