Common mistakes made in A-Level exams

We all make silly mistakes when in comes to Maths, so here are some common mistakes to help you out. 1. Partial Fractions: Many students think x+2/(x+1)^2 becomes A/(x+1) + B/(x+1) This is however incorrect, as if we were to re-combine the fraction we would not get (x+1)^2 inn the denominator Therefore, the correct method would be x+2/(x+1)^2 = A/(x+1) + B/(x+1)^2 2. Fractions Many students infer a/b+c to become a/b + a/c This is not the case however, as we can only split a fraction numerators apart For example: a+b/c = a/c + b/c 3. Dividing by zero Take the following, where we assume a=b: 1) a = b 2) ab = a^2 3) ab - a^2 = a^2 - b^2 4) b(a-b) = (a+b)(a-b) 5) b = a + b 6) b = 2b 7) 1 = 2 Do you see the mistake? The problem lies in the step 5. Since we assumed a = b, then a-b=0, and hence when we divided by a-b we were really dividing by zero!