Year 8 synthesis
Objective. Solve mixed problems spanning the complete Year 8 programme.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Year 8 synthesis questions combine methods from across the whole year's topics, such as transformations, Pythagoras, statistics and probability, into single connected problems. Success relies on recognising which earlier technique applies to each part of a question, then applying it accurately alongside other methods in sequence. It is useful to annotate diagrams and label known values clearly before starting calculations, since mixed problems often hide the relevant information within wordy contexts. Example: a question might require finding a triangle's hypotenuse using Pythagoras, then using that length within a probability or statistics calculation.
Worked example
A ladder leans against a wall, reaching 12 m up the wall with its foot 5 m from the wall base. As part of this Year 8 synthesis question, find the length of the ladder.
- 1The ladder forms the hypotenuse of a right-angled triangle with sides 12 m and 5 m.
- 2Square both sides: 12² = 144 and 5² = 25.
- 3Add the squared values: 144 + 25 = 169.
- 4Take the square root: √169 = 13 m.
Answer: 13 m
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils often attempt only the topic they recognise first and ignore connected parts of a mixed question; always re-read the full question and check whether earlier answers are needed for later parts.
Your progress
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