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.
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