Mixed Problem-Solving Paper F
Mixed Problem-Solving Paper F is the sixth in a series of full mixed problem-solving papers, combining multi-step worded problems across number, fractions, percentages, ratio, measures and shape into one longer sitting. It is closer to the length and variety of a real GL Assessment or CEM-style exam than a single-topic practice set, so it also tests planning and pacing across a whole paper.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read every question fully before starting, since problem-solving papers often bury the actual question in the final sentence after several pieces of information.
- Break a multi-step problem into smaller, separate calculations, and write down what each one represents rather than trying to do it all in your head.
- Watch for units changing mid-question, such as metres to centimetres or pounds to pence, and convert at the point where it matters, not before.
- Where a question gives more information than seems needed, check whether it is a distractor or whether it is needed for a later part of the question.
- For a question with several parts (a), (b), (c), use your answer from an earlier part in a later part only if the question tells you to.
- Keep track of remaining time against remaining marks so no single long question eats time needed for several shorter ones later in the paper.
- Where a question asks you to show your working, write the calculation itself, not just narration, since that is what earns method marks.
Worked example
A cafe buyer orders 15kg of coffee beans at £18 per kg. She sells the coffee as 250g bags for £5.00 each. If she sells every bag, how much profit does she make?
- Find the total cost of the beans: 15 x 18 = 270, so the beans cost £270.
- Convert 15kg to grams: 15 x 1000 = 15000g.
- Find the number of 250g bags that can be made: 15000 / 250 = 60 bags.
- Find the total sales revenue: 60 x 5.00 = 300, so she takes £300 in sales.
- Find the profit: 300 - 270 = 30.
- State the answer: she makes a profit of £30.
Practice questions
Try each question, then tap to reveal the answer.
Q1A tank holds 80 litres and is 3/4 full. How many more litres are needed to fill it?Show answer
Answer: 3/4 of 80 = 60, so 80 - 60 = 20 litres are needed.
Q2A journey of 240km is completed at an average speed of 60km/h. How long does it take?Show answer
Answer: 240 / 60 = 4 hours.
Q3A rope 15m long is cut into 20cm pieces. How many pieces are made?Show answer
Answer: 15m = 1500cm, so 1500 / 20 = 75 pieces.
Q4A shop buys pens for 40p each and sells them for 65p each. Find the profit on selling 30 pens.Show answer
Answer: Profit per pen = 25p, so 30 x 25 = 750p = £7.50.
Q5A school trip costs £12 per student. 45 students go on the trip. How much is collected in total?Show answer
Answer: 12 x 45 = £540.
Q6A recipe for 4 people uses 320g of rice. How much rice is needed for 10 people?Show answer
Answer: 320 / 4 = 80g per person, so 80 x 10 = 800g.
Q7A car's fuel tank holds 50 litres. If it uses fuel at a rate of 1 litre per 8km, how far can it travel on a full tank?Show answer
Answer: 50 x 8 = 400km.
Q8A book has 240 pages. A student reads 15 pages a day. How many full days does it take to read the whole book?Show answer
Answer: 240 / 15 = 16 days.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A school buys 240 exercise books at £1.35 each. They are shared equally between 8 classes. (a) Find the total cost of the exercise books. (b) Find how many books each class receives. (c) If one class then loses 3 books, how many books are left in that class?
Show mark scheme
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A cyclist travels 18km in the first hour, then increases her speed by 25% for the second hour, travelling at that increased speed for the whole hour. (a) Find her speed in the second hour. (b) Find the total distance she travels in the two hours.
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Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the mixed problem-solving paper f 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 21 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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