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Prove that the square of an odd number is always 1 more than a multiple of 4

This is a nice little question off the 2018 Edexcel Higher Maths paper! When we heard the word 'prove' in a question at this level, automatically we should be thinking about using algebra to help us out! Fir...
TR
Answered by Thomas R. • Maths tutor
3860 Views

Let f(x)=xln(x)-x. Find f'(x). Hence or otherwise, evaluate the integral of ln(x^3) between 1 and e.

We use the product rule with u=x and v=ln(x) (so u'=1 andv'=1/x) to differentiate xln(x) to ln(x)+1, and -x just differentiates to -1, hence we have. f'(x)=ln(x). Now note that ln(x^3)=3ln(x) using propertie...
MJ
Answered by Matthew J. • Maths tutor
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Solve the simultaneous equations: 3x-y=1, x^2+y^2=5

x=1, y=2 x=-2/5, y=-11/5
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Answered by Chloe W. • Maths tutor
4400 Views

Work out the value of the following:

36 1/2 = 6(The square root of 36 is 6) 2) 23 0 = 1(Anything to the power of 0 is 1) 3) 27 -2/3 = 3 -2 = 1/3 2 = 1/9
HA
Answered by Hafsah A. • Maths tutor
3356 Views

How do you find a missing side length in a right-angled triangle?

Use Pythagoras' theorem. a 2 + b 2 = c 2 . The longest side of the triangle is the hypotenuse, and it is the side opposite the right angle. We use the length of this side as 'c' if we have it. 'a' and 'b' ar...
JD
Answered by James D. • Maths tutor
13005 Views