IGCSE Mathematics: Pythagoras Theorem Practice Questions

Using a squared plus b squared equals c squared: c squared = 3 squared plus 4 squared = 9 plus 16 = 25. So c = the square root of 25 = 5 cm.

Mark schemeCorrect use of theorem, 9 + 16 = 25 (1). Answer 5 cm (1).

Common mistakeAdding the sides directly, giving 7 cm, instead of squaring first.

Exam tipSquare each side, add, then square root. Do not add the lengths before squaring.

Rearrange to find a shorter side: a squared = c squared minus b squared = 13 squared minus 5 squared = 169 minus 25 = 144. So a = the square root of 144 = 12 cm.

Mark schemeSubtract because finding a shorter side, 169 - 25 (1). = 144 (1). Answer 12 cm (1).

Common mistakeAdding instead of subtracting when the hypotenuse is already known.

Exam tipIf the hypotenuse is given, subtract the squares. Only add when finding the hypotenuse itself.

Check whether the two shorter sides squared add to the longest side squared: 6 squared plus 8 squared = 36 plus 64 = 100. And 10 squared = 100. Since they are equal, the triangle is right angled.

Mark schemeCalculate 36 + 64 = 100 and 10 squared = 100 (1). Conclude equal, so right angled (1).

Common mistakeNot stating the conclusion. The final statement that it is right angled is needed.

Exam tipFor a show that question, write a clear concluding sentence. The mark is for the reasoning.