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Misconceptions Of Mathematics Techniques 2008 Paper 1. Many students wrote xe x dx x dx e x dx . This is a question on integrating by parts and you cannot carry out the above operation: x x xe dx x dx e dx Not Equal Some students did not carry out the second integration. Although you get the same answer, that is x x x xe dx xe e C should be xe x dx xe x e x dx and then evaluate integral of e x . 2. Another misconception on integration was the following: dx 1 1 x 1 x 2 x 1 x 2 dx and then they use integration by parts with u x 1 1 and dv x 2 . This is a question on integration by partial fractions. You need to 1 convert the integrand into partial fractions and then x 1 x 2 integrate. 3. The main misconception on second order differential equations was when students try to find the complementary function and some students carried out the following derivation: m2 2 0 Step 1 m 2 2 m , m Step 2 Step 3 Step 3 in wrong because when we solve m2 2 we get m j . Remember we are taking the square root of a negative number. 4. Another error that students made was the following 1 1 sin x 1 dx sin x dx 0 x x 0 You cannot do the above operation unless x is a constant. 5. Some students also made some elementary arithmetic mistakes such as 182 6 12 324 36 1 2 They should know 6 36 not 36 . Some of them wrote 6 as 2 6 2 . 2 6. Most students managed to find the first derivative of the parametric equations. The correct answer for this part was cos 3t dy 3 but no one managed to get the correct answer for dx sin t d2y second derivative . They applied the quotient rule on dx 2 cos 3t dy d cos 3t 3 that is they found 3 . THIS IS dx sin t dt sin t INCORRECT because d dy d y dt dx dx 2 dx / dt 2 7. Many students forgot to add the constant C in the evaluation of indefinite integrals. 8. Another common error was the following: 2 d2 4 d x 2 x 2 1 x 4 2 x 2 1 2 dx dx d2 Remember the notation means find the second derivative of the dx 2 function and not square it.