## 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

\[\frac{2}{3} + \frac{4}{5} = \frac{2 \times 5}{3 \times 5} + \frac{3 \times 4}{3 \times 5} = \frac{10}{15} + \frac{12}{15} = \frac{22}{15}\]