About this worksheet

This free Year 8 Pythagoras’ theorem problems worksheet is written for the Western Australian curriculum and mapped to SCSA content description WA8MMGTW3. It targets one skill so students can practise until it sticks: by the end, students can say “I can use Pythagoras’ theorem to solve practical problems, find distances on a grid and test for right angles.”

What’s inside

• Key idea box – a short explanation with worked examples to read before starting.
• A · Fluency (16 questions) – quick practice to build accuracy.
• B · Core (10 questions) – worded problems set in everyday Australian contexts.
• C · Reasoning (4 questions) – explain, justify and spot the error.
• D · Challenge (4 questions) – harder multi-step and problem-solving questions for students ready to stretch.
• Separate marking key – every answer with working, plus mark allocations and marking criteria for reasoning questions.

Skills covered

• Drawing diagrams for practical Pythagoras problems
• Finding distances between points on a grid
• Using the converse to test for right angles

How to use this worksheet

Start with the Key idea box, then complete Section A (use a calculator only where a question says so). Most students should attempt Sections B and C; Section D suits students aiming for the top of the class or preparing for accelerated or extension maths. The worksheet is marked out of 59, and the score box on the last page helps students see which section needs more practice.

Common mistakes to watch for

• Not drawing a diagram first
• Treating the ladder as a shorter side
• Assuming a triangle is right-angled without testing
• Mixing units within one problem

Where this fits in the WA Year 8 sequence

Pythagoras’ Theorem in Problems sits in the Two-dimensional space and structures sub-strand of Measurement and geometry. It is one of a set of short, single-skill EduLift worksheets that split each Year 8 content description into sub-skills. Use the previous and next links to work through the sequence in order.

Common errors we see in tutoring

• Not drawing a diagram first
• Treating the ladder as a shorter side
• Assuming a triangle is right-angled without testing
• Mixing units within one problem