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