Common Mistakes

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


Rearranging gives  

This is wrong. If something changes side it changes sign. We should have  


Every square root has two values. The solutions to  
\[x=3, -3\]

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

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