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x 2 -4x+4>0 => (x-2)(x-2)>0. We can illustrate this line on a graph showing a quadratic whose vertex is at (2,0). Therefore, the answer to our inequality is x<2,x>2 (but x does not equal 2) fo...

This question tests fundamental understanding of integration and checks that the student is not simply memorizing the simple examples for the test. Most students will remember that the integral of 1/x is ln(...

As the coefficient of x^2 is not 1, we think of this equation as ax^2 +bx + c. When the coefficient of x^2 is not 1, then we need to firstly multiply the first and last numbers together (8 and -3) which give...

y = x x , by taking logs:ln(y) = ln(x x )By log laws:ln(y) = xln(x)From implicit differentiation; d/dx = y'*d/dy, so:d/dx[ln(y)] = y'*d/dy[ln(y)] = y' * 1/yFrom the product rule; d/dx[xln(x)] = ln(x) * d/dx(...

Algebra is fundamentally the way in which we can find out the value of some unknown element. So for example, if a salesman agrees to sell two apples for £10 algebra can help us find out how much one apple wo...