Mixed Problem-Solving Paper D
Mixed Problem-Solving Paper D continues the mixed-topic 11+ practice series, combining arithmetic, fractions, percentages, ratio, measures, geometry and data questions in one timed sitting. As in Papers B and C, most of the difficulty comes from working out, question by question, which topic and method is needed before any calculation begins.
Method
- Read each question fully before starting, since the context (a shop, a journey, an event) often disguises which operation is actually needed.
- Sort each question into a topic (arithmetic, fractions, percentage, ratio, measures, geometry or data) before choosing a method.
- For multi-step problems, write each step out separately and label what each part of your working represents.
- Use an efficient written method for any calculation too large to do mentally, rather than guessing.
- Check money, time and quantity answers make sense in context, for example that a percentage answer is not larger than the whole amount.
- Return to any unfinished questions at the end of the paper rather than leaving them blank.
Worked example
A cinema sells 3/5 of its 150 seats for a matinee showing. Of the tickets sold, 40% are child tickets priced at 4 pounds and the rest are adult tickets priced at 7 pounds. How much money does the cinema take in total?
- Find the tickets sold: 3/5 x 150 = 90.
- Find the child tickets: 40% of 90 = 36.
- Find the adult tickets: 90 - 36 = 54.
- Find the money from child tickets: 36 x 4 = 144.
- Find the money from adult tickets: 54 x 7 = 378.
- Add the two amounts: 144 + 378 = 522 pounds.
Practice questions
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Q1A warehouse has 27 boxes, each containing 48 tins. How many tins in total?Show answer
Answer: 1296 (27 x 48)
Q2A water tank has a capacity of 240 litres and is 5/8 full. How many litres of water does it hold?Show answer
Answer: 150 litres (5/8 x 240)
Q3A washing machine costs 320 pounds and is reduced by 12.5% in a sale. What is the sale price?Show answer
Answer: 280 pounds (12.5% of 320 = 40, 320 - 40 = 280)
Q4A youth orchestra has string and wind players in the ratio 5:3. There are 24 wind players. How many string players are there?Show answer
Answer: 40 (3 parts = 24, so 1 part = 8, and 5 parts = 40)
Q5A recipe uses 300 ml of milk to make 4 pancakes. How much milk is needed for 10 pancakes?Show answer
Answer: 750 ml (75 ml per pancake, x 10)
Q6Six numbers have a mean of 14. Five of them are 9, 17, 12, 20 and 11. What is the sixth number?Show answer
Answer: 15 (total needed = 84, sum of the five known numbers = 69, so 84 - 69 = 15)
Q7A triangle has angles of 55 degrees and 68 degrees. What is the size of the third angle?Show answer
Answer: 57 degrees (180 - 55 - 68)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A bookshop has 3/4 of its 240 books on the fiction shelves and the rest on the non-fiction shelves. It then sells 30% of the non-fiction books. (a) How many non-fiction books are sold? (b) How many non-fiction books remain unsold?
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A delivery van travels the first 5/9 of a 108 km route at an average speed of 45 km/h, then covers the rest of the route at an average speed of 30 km/h. (a) How far does the van travel at 30 km/h? (b) What is the total time taken for the whole journey, 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 d 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 15 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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