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Find the area between the curve y = 8 + 2x - x^2 and the line y = 8 - 2x.

First sketch the curve and the line, noting down where they intersect each axis.area under y = 8 + 2x - x 2 is given by the integral between 0 and 4 of (8 + 2x - x 2 ) dx.area under line is given by the inte...
Answered by • Maths tutor
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Prove that the square of an odd number is always 1 more than a multiple of 4

First we need to find a general form for an odd number, so that we can prove that when we square it, it will be 1 more than a multiple of 4 regardless of which odd number it is. An even number can always be ...
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Answered by Isobel A. • Maths tutor
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Solve the simultaneous equations x^2+y^2=1 and x+2y=1

x=1,y=0 or x=-3/5,y=4/5
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Answered by Rosie P. • Maths tutor
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Before an exam, I always go through as many past papers as possible but I still don't know how to do the questions on an exam when they come up, why and what can I do?

Despite getting lots of practice being very important, maths is not really a memory based subject and you shouldn't be just going through the all the questions before you have tried to fully understand the c...
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Answered by Simone L. • Maths tutor
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The rate of growth of a population of micro-organisms is modelled by the equation: dP/dt = 3t^2+6t, where P is the population size at time t hours. Given that P=100 at t=1, find P in terms of t.

First, we integrate the equation with respect to t to find an equation for P. dP/dt = 3t 2 + 6t Then, P= integral (3t 2 + 6t) dt Integrating gives P= t 3 +3t 2 +c, c is the constant of integration. As we are...
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Answered by Claire B. • Maths tutor
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