Mixed Problem-Solving Paper B
Mixed Problem-Solving Paper B is a timed 11+ maths practice paper that mixes short problems from across the whole syllabus, arithmetic, fractions, percentages, ratio, measures, geometry and data, in a single sitting rather than testing one skill at a time. It mirrors the mixed-topic sections used by GL Assessment and CEM, where pupils must first work out which skill a question needs before they can start calculating, all under strict time pressure.
Before you start
Make sure you're comfortable with these topics first:
Method
- Skim the whole paper first so you know roughly how many questions there are and how the marks are spread, then start working through in order.
- For each question, identify which topic it belongs to (fractions, percentages, ratio, measures, and so on) before choosing a method, since the wording rarely says which skill is needed.
- For multi-step questions, write down each step separately rather than trying to do the whole problem in one calculation.
- Show enough working to earn method marks even if your final answer is wrong, especially on questions worth more than one or two marks.
- If a question is taking too long, mark it and move on, then return to it once you have banked the marks from easier questions.
- In the last few minutes, check your answers make sense for the context (money, time, number of people) rather than just re-reading your working.
Worked example
A school printed 480 raffle tickets. It sold 3/4 of them on the first day and 60% of the remainder on the second day. How many raffle tickets are still unsold after the second day?
- Find the tickets sold on the first day: 3/4 x 480 = 360.
- Find the remainder after day one: 480 - 360 = 120.
- Find the tickets sold on day two: 60% of 120 = 0.6 x 120 = 72.
- Subtract to find the tickets still unsold: 120 - 72 = 48.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A crate holds 24 bottles. A shop orders 37 crates. How many bottles is that in total?Show answer
Answer: 888 (24 x 37)
Q2A stall has 96 magnets and sells 2/3 of them. How many magnets are left?Show answer
Answer: 32 (96 x 2/3 = 64 sold, 96 - 64 = 32 left)
Q3A jacket costs 45 pounds and is reduced by 20% in a sale. What is the sale price?Show answer
Answer: 36 pounds (20% of 45 = 9, 45 - 9 = 36)
Q4Sweets are shared between Amir and Priya in the ratio 3:5. Priya gets 25 sweets. How many does Amir get?Show answer
Answer: 15 (5 parts = 25, so 1 part = 5, and Amir's 3 parts = 15)
Q5A train leaves at 14:35 and takes 1 hour 50 minutes to arrive. What time does it arrive?Show answer
Answer: 16:25
Q6The mean of four numbers is 9. Three of the numbers are 6, 11 and 8. What is the fourth number?Show answer
Answer: 11 (total needed = 36, sum of the three known numbers = 25, so 36 - 25 = 11)
Q7A rectangle has a length of 12 cm and a width of 5 cm. What is its perimeter?Show answer
Answer: 34 cm (2 x (12 + 5))
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A charity bake sale raises 240 pounds on Saturday. 3/8 of this comes from cake sales and the rest from raffle tickets. On Sunday, the total raised is 25% more than Saturday's total. (a) How much was raised from raffle tickets on Saturday? (b) How much was raised in total on Sunday? Show your working.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
A minibus travels at an average speed of 48 km/h for 2 hours 15 minutes, then stops for a break, then travels a further 90 km at an average speed of 60 km/h. (a) How far does the minibus travel before its break? (b) What is the total journey time, including a 20-minute break, giving your answer in hours and minutes?
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 b worksheet pack - 10 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 10 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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