Methodology for Checking for Careless Mistakes

Checking for careless mistakes using the Substitution Method

  • Normal method of checking (i.e. check your working from front to back again), may or may not find the error
  • Using Substitution Method of checking guarantees that your answer is correct, and will find an error if there is one.
  • Use  Substitution Method of checking for all algebra/solving/simplify questions worth 2 marks or more. You will be able to save many many marks using this method!
  • Only takes 10 seconds with practice. (use calculator)

Example (using substitution method)

Express \displaystyle\frac{2x-3}{x^2+4x+3}-\frac{1}{x+3} as a single fraction in its simplest form. [2 marks]

After getting your answer (\displaystyle\frac{x-4}{(x+3)(x+1)}), you can substitute in the value \boxed{x=9}.

When, x=9, \displaystyle\frac{2x-3}{x^2+4x+3}-\frac{1}{x+3}=\frac{1}{24}, and \displaystyle\frac{x-4}{(x+3)(x+1)}=\frac{1}{24}

Since both expressions give the same value, you have just checked that your answer is correct!

Humorous cartoon featuring Jackie Chan.
Sincerely wishing all students to reduce their careless mistakes to as low as possible!