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Pythagoras’ Theorem is a staple of GCSE Maths, especially at Higher level, but students often lose marks through avoidable errors. Whether it’s mixing up sides, misapplying the formula, or forgetting to square root, these mistakes can be costly. Below, we highlight some of the most frequent errors and show the correct approach in a handy table.
| Common Error | Incorrect Technique | Correct Technique |
|---|---|---|
| Mixing up hypotenuse and shorter sides | Adding the two shorter sides without squaring: c = a + b | Use the correct formula: c^2 = a^2 + b^2 then c = \sqrt{a^2 + b^2} |
| Forgetting to square root | Leaving the answer as c^2: c^2 = 25 c = 25 | Take the square root: c^2 = 25 c = 5 |
| Using the wrong formula for shorter side | Adding instead of subtracting: a^2 = b^2 + c^2 | Subtract to find a shorter side: a^2 = c^2 - b^2 |
| Applying to non-right-angled triangles | Using Pythagoras for any triangle | Only use Pythagoras for right-angled triangles |
| Rounding too early | Rounding intermediate answers before the final step | Keep full accuracy until the final answer, then round |
| Ignoring units | Giving a numerical answer without units | Always include correct units (e.g., cm, m) in your answer |
Quick Tips:
- Always identify the hypotenuse (the side opposite the right angle).
- Double-check that the triangle is right-angled before applying the theorem.
- Write out the full formula and substitute values carefully.
- Only round your answer at the very end.
If you want to practise more Pythagoras questions and avoid these common pitfalls, Maths Tuition for GCSE Higher Students can provide expert guidance and targeted practice.
Conclusion
By being aware of these common errors and following the correct techniques, you’ll improve your accuracy and confidence when tackling Pythagoras’ Theorem in exams. Careful working and attention to detail are key to securing those all-important marks.
