## Common Mistakes

Many students make the same mistakes again and again. Here are some of the most common mistakes.

$9x+3=5x+6$

Rearranging gives
$9x+5x=6+3$

This is wrong. If something changes side it changes sign. We should have
$9x-5x=6-3$

If
$x^2=9$
then
$x=3$

Every square root has two values. The solutions to
$x^2=9$
are
$x=3, -3$

The Cosine Rule gives particular trouble. We have to solve
$36=9+16-12cos A$

Many students simplify this to get
$9=13cos A$

In fact it it should be simplified to
$12 cos A = 9 +16-36$

Every student should know how to add fractions, Still I see students writing something like
$\frac{2}{3} + \frac{4}{5} = \frac{6}{8}$

To add fractions make a common denominator (bottom number) by multiplying the denominators. Add fractions like this
$\frac{2}{3} + \frac{4}{5} = \frac{2 \times 5}{3 \times 5} + \frac{3 \times 4}{3 \times 5} = \frac{10}{15} + \frac{12}{15} = \frac{22}{15}$