Mixed Problem-Solving Paper E
Mixed Problem-Solving Paper E is the final paper in this mixed-topic 11+ practice series, again combining arithmetic, fractions, percentages, ratio, measures, geometry and data in one timed sitting. It is intended as a full-difficulty checkpoint once Papers B, C and D are secure, since the mix of topics and time pressure closely matches a real GL or CEM maths paper.
Method
- Treat the paper as a complete timed exam: read the whole question before writing anything, and note the mark value before deciding how much detail to show.
- Identify the topic each question belongs to (arithmetic, fractions, percentage, ratio, measures, geometry or data) before choosing a method.
- Break every multi-step question into clearly separated steps, labelling what each one finds.
- Use estimation to sanity-check answers involving money, distance or large numbers.
- Show full working on questions worth more than one mark, so method marks are still available if the final answer is wrong.
- Use any remaining time at the end to revisit questions you were least confident about, rather than re-reading the whole paper equally.
Worked example
A theatre group prints 320 programmes for a show. They give away 1/8 of them free before the show and sell the rest for 3 pounds each. How much money do they take from programme sales?
- Find the programmes given away free: 1/8 x 320 = 40.
- Find the programmes sold: 320 - 40 = 280.
- Multiply by the price to find the total revenue: 280 x 3 = 840.
- Final answer: 840 pounds.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A factory produces 156 cars per day. How many cars does it produce in a 30-day month?Show answer
Answer: 4680 (156 x 30)
Q2An allotment has an area of 84 square metres. 7/12 of it is planted with vegetables. How many square metres are planted with vegetables?Show answer
Answer: 49 square metres (7/12 x 84)
Q3A laptop costs 480 pounds before VAT, which is charged at 20%. What is the total price including VAT?Show answer
Answer: 576 pounds (20% of 480 = 96, 480 + 96 = 576)
Q4Concrete is mixed from cement, sand and gravel in the ratio 1:2:3. If 15 kg of cement is used, how much gravel is needed?Show answer
Answer: 45 kg (1 part = 15 kg, so 3 parts = 45 kg)
Q5A runner covers 8 km every 40 minutes at a steady pace. At this rate, how long would it take to cover 20 km?Show answer
Answer: 100 minutes, or 1 hour 40 minutes (5 minutes per km, x 20)
Q6The median of five numbers arranged in order, 9, 14, x, 22, 27, is 18. What is x?Show answer
Answer: 18 (the middle value of five ordered numbers is the median)
Q7A parallelogram has a base of 14 cm and a height of 6 cm. What is its area?Show answer
Answer: 84 cm squared (14 x 6)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A stadium sells 5/6 of its 360 tickets for a match. Of the tickets sold, 25% are concession tickets priced at 6 pounds, and the rest are full-price tickets at 15 pounds. (a) How many full-price tickets are sold? (b) How much money is taken from full-price ticket sales?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
A charity fun run has 275 entrants. 2/5 of them complete the 10 km route, and the remaining entrants complete a shorter 5 km route. Every entrant who completes the 10 km route raises 12 pounds for charity, and every entrant who completes the 5 km route raises 7 pounds. (a) How many entrants complete the 5 km route? (b) How much money does the fun run raise in total?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 6 available
Free printable worksheet
Want more practice on paper? Download the mixed problem-solving paper e 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 16 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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