Mixed Problem-Solving Paper C
Mixed Problem-Solving Paper C is the next step up in the mixed-topic 11+ practice series, combining arithmetic, fractions, percentages, ratio, measures, geometry and data questions in one timed sitting. As with Paper B, the main challenge is not any single calculation but recognising, question by question, which topic and method each problem needs before the clock runs out.
Method
- Read every question fully before calculating anything, since some sentences change the required operation halfway through (for example, adding a discount after a total has already been found).
- Sort each question mentally into a topic (arithmetic, fractions, percentage, ratio, measures, geometry or data) before choosing your method.
- Break multi-step questions into separate, clearly labelled steps rather than one long calculation.
- Use estimation to sanity-check answers that involve money, distance or time, since a misplaced decimal point is the most common paper-wide error.
- Show working for every question worth more than one mark, so a small slip does not cost the whole question.
- Leave time at the end to revisit any question you were unsure of rather than only checking the ones you found easy.
Worked example
A stationery shop has 350 pens. It sells 2/5 of them in the morning and 30% of what remains in the afternoon. How many pens are left unsold at the end of the day?
- Find the pens sold in the morning: 2/5 x 350 = 140.
- Find the remainder after the morning: 350 - 140 = 210.
- Find the pens sold in the afternoon: 30% of 210 = 63.
- Subtract to find the pens left unsold: 210 - 63 = 147.
Practice questions
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Q1A factory packs eggs into boxes of 6. It has 925 eggs. How many complete boxes can it fill, and how many eggs are left over?Show answer
Answer: 154 boxes, 1 egg left over (925 = 6 x 154 + 1)
Q2A fuel tank has a capacity of 60 litres and is 5/6 full. How many litres of fuel are in the tank?Show answer
Answer: 50 litres (5/6 x 60)
Q3A book priced at 12 pounds is increased by 15%. What is the new price?Show answer
Answer: 13.80 pounds (12 x 1.15)
Q4Paint is mixed in the ratio blue:white = 2:7. If 18 litres of blue paint are used, how many litres of white paint are needed?Show answer
Answer: 63 litres (2 parts = 18, so 1 part = 9, and 7 parts = 63)
Q5A recipe needs 750 g of flour and makes 5 loaves. How much flour is needed for 8 loaves?Show answer
Answer: 1.2 kg (150 g per loaf, x 8 = 1200 g)
Q6Five numbers have a range of 18. The smallest number is 7. What is the largest number?Show answer
Answer: 25 (7 + 18)
Q7A square has an area of 81 cm squared. What is the length of one side?Show answer
Answer: 9 cm (the square root of 81)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A football club sells tickets for a charity match. Adult tickets cost 8 pounds and child tickets cost 5 pounds. The club sells 140 adult tickets and 95 child tickets. (a) How much money is raised in total? (b) The club donates 3/5 of this total to charity. How much money is donated?
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A cyclist rides 3/8 of a 64 km route before lunch, then rides the rest of the route at an average speed of 16 km/h. (a) How many kilometres does the cyclist ride after lunch? (b) How long does the ride after lunch take, giving your answer in hours and minutes?
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Free printable worksheet
Want more practice on paper? Download the mixed problem-solving paper c worksheet pack - 11 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 11 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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