Questions: Problem solving and proof
New numbers every time.
Number and money problems
- Which pack is better value?Justify, 4 marks, Plus
- Which phone plan is cheaper?Justify, 5 marks, Plus
- An electricity bill with VATWork out, 5 marks, Plus
- Will she be on time? A bus timetableGive reasons, 4 marks, Plus
- Sharing a cost in the ratio of nights stayedWork out, 4 marks, Plus
- Scaling a recipe and buying enoughWork out, 6 marks, Plus
- Cheaper at home or abroad?Justify, 5 marks, Plus
- A percentage off or three for two?Justify, 4 marks, Plus
- Estimate first, then checkCircle, 4 marks, Plus
Angle reasoning with reasons
- An exterior angle of a triangle, with reasonsGive reasons, 4 marks, Plus
- Parallel lines: two angles, two reasonsGive reasons, 4 marks, Plus
- A quadrilateral with one side extendedGive reasons, 4 marks, Plus
- Regular polygons: exterior and interior anglesGive reasons, 5 marks, Plus
- Crossing lines and an isosceles triangleGive reasons, 4 marks, Plus
- Angles with algebra on parallel linesGive reasons, 5 marks, Plus
- An isosceles triangle under a parallel lineGive reasons, 4 marks, Plus
- Describe the mistake in an angle argumentDescribe, 3 marks, Plus
- A rectangle and a square with the same perimeterWork out, 5 marks, Plus
Interpret, justify and show that
- Is the claim about the bar chart right?Interpret, 4 marks, Plus
- Pick a player: mean and rangeJustify, 5 marks, Plus
- Two pie charts with different totalsInterpret, 4 marks, Plus
- Describe and use a scatter graphDescribe, 4 marks, Plus
- Estimate from a sample and judge itJustify, 4 marks, Plus
- Interpret a distance-time graphInterpret, 4 marks, Plus
- Compare two teams from frequency tablesJustify, 5 marks, Plus
- Show that a mean rounds to a given valueShow that, 4 marks, Plus
- Draw a fare graph and interpret itDraw, 5 marks, Plus
Proof and show that
- Three consecutive even numbersProve, 5 marks, Plus, Higher tier
- The difference of two odd squaresProve, 5 marks, Plus, Higher tier
- Differences in an n² sequenceShow that, 6 marks, Plus, Higher tier
- Show an identity and find kShow that, 4 marks, Plus, Higher tier
- The sum of squares of consecutive odd numbersProve, 5 marks, Plus, Higher tier
- The product of consecutive even numbersProve, 4 marks, Plus, Higher tier
- Checking examples is not a proofDescribe, 3 marks, Plus, Higher tier
- Show a sum of squares is evenShow that, 5 marks, Plus, Higher tier
- Three consecutive multiplesProve, 5 marks, Plus, Higher tier
Mixed exam problems
- Painting a wall: area, tins and costWork out, 5 marks, Plus, Foundation
- Fencing a garden: panels and postsWork out, 4 marks, Plus, Foundation
- Will he arrive in time? Speed and timeJustify, 4 marks, Plus, Foundation
- A diagonal path: Pythagoras and costWork out, 6 marks, Plus, Higher tier
- A ratio that changesWork out, 5 marks, Plus, Higher tier
- A spinner: missing probabilities and expected resultsWork out, 4 marks, Plus, Foundation
- Filling a cylindrical tankWork out, 5 marks, Plus, Higher tier
- Seats in rows: a linear sequenceWork out, 5 marks, Plus, Foundation
AQA, Pearson Edexcel and OCR are registered trade marks of their owners. Brainlag Learn is independent: it is not affiliated with or endorsed by any exam board, and every question on it is original.