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A tricky question which is actually really simple if you know the technique and will save a lot of time during the exam. The method is to simply add 1 and minus one to the numerator. so the integral becom...

Using the formula for differentiation: if y=ax^N then dy/dx= Na*x^N-1 apply this to each term in the equation given; first term: dy/dx= 9x²second term: dy/dx= 14xth...

A needs to be multiplied up by x+3 to make the fraction have the same in denominator as the other expressions. Then you need to equate the numerators. 3 - 5x = A(x+3) + B
You can gain two simultaneou...

First, we must cross multiply to remove the fractions, to do this, we multiply each numerator by the opposite denominator: (x)(12x+31) = (6x+5)(4x-1). Then, we multiply out the brackets t...

We know the discriminant (b^2 - 4ac) must be equal to zero for an equation to have equal roots (think about the fact that the square root of this is taken in the quadratic equation). So we can form the eq...