Questions: Exam problems
New numbers every time.
Number problems
- Compound or simple interest: which account?Justify, 5 marks, Plus, Higher tier
- Two packs, a deal on one: which is better value, and by how much? (F)Work out, 5 marks, Plus, Foundation
- How much will the paint cost? Area, coats, tins (F)Work out, 5 marks, Plus
- Cheaper at home or abroad? An exchange rate and a discountWork out, 5 marks, Plus
- Compound interest against simple interestWork out, 5 marks, Plus
- The price before a sale, then the percentage profit (H)Work out, 5 marks, Plus, Higher tier
- Upper bound of a speed against a limit (H)Decide, 5 marks, Plus, Higher tier
- Fractions of what is left: how much is saved? (F)Work out, 5 marks, Plus, Foundation
- A long journey in standard form, then in days (H)Work out, 4 marks, Plus, Higher tier
- Equal numbers from different pack sizes, then the cost (F)Work out, 4 marks, Plus
Algebra problems
- Sides in x, the perimeter given: find the area (F)Work out, 5 marks, Plus
- Angles in terms of x: find the largest (F)Work out, 4 marks, Plus
- Form and solve an equation from ages (F)Work out, 4 marks, Plus, Foundation
- Simultaneous equations from two groups' ticketsWork out, 5 marks, Plus
- An area gives a quadratic: solve it, then the perimeter (H)Work out, 6 marks, Plus, Higher tier
- The first term of a sequence over a value (F)Work out, 4 marks, Plus
- A square and a rectangle with equal areas (H)Work out, 5 marks, Plus, Higher tier
- The largest whole number from a perimeter inequalityWork out, 4 marks, Plus
- A faster journey takes less time: form and solve a quadratic (H)Work out, 6 marks, Plus, Higher tier
Ratio and rates problems
- A ratio changes after a gift: how much at the start? (H)Work out, 5 marks, Plus, Higher tier
- The most people a recipe can serve from what is in the cupboard (F)Work out, 4 marks, Plus, Foundation
- A three-part ratio by mass, bags and their costWork out, 4 marks, Plus
- The average speed of a journey in two partsWork out, 5 marks, Plus
- The density of an alloy from two metals (H)Work out, 5 marks, Plus, Higher tier
- Inverse proportion: more workers, fewer days, then the cost (F)Work out, 4 marks, Plus
- y is proportional to the square of x: a value each way (H)Work out, 5 marks, Plus, Higher tier
- Greatest and least pressure of a box on its faces (H)Work out, 5 marks, Plus, Higher tier
- Two ratios with a shared part, then one share (H)Work out, 4 marks, Plus, Higher tier
Geometry problems
- An L-shaped lawn: turf to buy and its cost (F)Work out, 4 marks, Plus
- How long to fill a cylindrical tank?Work out, 5 marks, Plus
- Two right-angled triangles: Pythagoras, then trigonometry (H)Work out, 5 marks, Plus, Higher tier
- A regular polygon from its angles, then a sum of anglesWork out, 5 marks, Plus
- Similar solids: from areas to volumes (H)Work out, 4 marks, Plus, Higher tier
- The perimeter and area of a sector (H)Work out, 5 marks, Plus, Higher tier
- A ladder against a wall, moved closer (F)Work out, 4 marks, Plus
- Cosine rule for a side, then sine rule for an angle (H)Work out, 6 marks, Plus, Higher tier
- Melt a sphere into cones: how many whole cones? (H)Work out, 5 marks, Plus, Higher tier
Statistics and probability problems
- Means of two groups, then the score needed to reach a target (F)Work out, 5 marks, Plus
- An estimated mean and a percentage from grouped dataWork out, 5 marks, Plus
- Probabilities in terms of x, then an expected number (F)Work out, 4 marks, Plus
- Two picks without replacement: the same colour (H)Work out, 5 marks, Plus, Higher tier
- A Venn diagram from counts, then a conditional probability (H)Work out, 5 marks, Plus, Higher tier
- From frequency densities to an estimate between two values (H)Work out, 5 marks, Plus, Higher tier
- A fairground game: expected profit for the stall (F)Work out, 4 marks, Plus, Foundation
- Two surveys, one a pie chart: which had more? (F)Compare, 4 marks, Plus, Foundation
- Two missing numbers from the mean and the range (H)Work out, 4 marks, Plus, Higher tier
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