Mixed Problem-Solving Paper A
Mixed Problem-Solving Paper A is a full-length timed practice paper that mixes questions from across the 11+ maths curriculum, number, fractions, measures, geometry, data and reasoning, in the style of a real GL Assessment or CEM maths paper. It is designed to build stamina and exam pacing rather than to teach a single skill.
Before you start
Make sure you're comfortable with these topics first:
Method
- Before starting, note the total time allowed and the number of questions, and work out roughly how many seconds or minutes each question should take on average.
- Scan quickly through the paper first, if the format allows it, to spot any unusually long or multi-part questions and plan to leave more time for those.
- Answer questions in order but do not get stuck: if a question is not solved within its rough time allowance, mark it and move on, returning at the end if time allows.
- Show brief working for every calculation in the space provided, since it is faster to check a written step than to recalculate a whole question from scratch.
- Keep track of time at fixed checkpoints, for example after every 10 questions, rather than only checking the clock once near the end.
- In the final few minutes, prioritise checking answers to questions you were unsure of over attempting a new, unstarted question, unless it looks very quick to solve.
- After finishing, in practice rather than in the real test, go through every wrong answer and identify whether the mistake was a misread question, a calculation slip, or a topic that needs more revision.
Worked example
Representative paper question: a cyclist travels 18km in 1 hour 30 minutes at a constant speed. At the same speed, how long would it take the cyclist to travel 30km? Give your answer in hours and minutes.
- Find the cyclist's speed in km per hour: 18km in 1.5 hours means 18 / 1.5 = 12km per hour.
- Find the time needed to travel 30km at this speed: 30 / 12 = 2.5 hours.
- Convert 2.5 hours into hours and minutes: 2.5 hours is 2 hours and 0.5 x 60 = 30 minutes.
- Final answer: it would take 2 hours 30 minutes to travel 30km.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A rectangle has a length of 9cm and a width of 4cm. Find its area.Show answer
Answer: 36 cm squared
Q2What is 3/5 of 45?Show answer
Answer: 27
Q3A number is multiplied by 4, then 7 is subtracted, giving 21. What was the original number?Show answer
Answer: 7 ((21 + 7) / 4 = 28 / 4 = 7)
Q4Find the mean of 6, 9, 12, 13.Show answer
Answer: 10 (40 / 4)
Q5Convert 0.65 to a percentage.Show answer
Answer: 65%
Q6A shape has 3 sides of equal length and all angles equal. What is this shape called, and what is the size of each interior angle?Show answer
Answer: An equilateral triangle; each interior angle is 60 degrees
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A garden is in the shape of a rectangle measuring 12m by 7m. A path 1m wide is built all the way around the inside edge of the garden. Find the area of the remaining lawn inside the path.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A shop has a mixed offer: buy 3 notebooks for 5 pounds 40, or buy them individually at 2 pounds each. Aisha needs 7 notebooks. Using the offer as many times as possible and buying any remaining notebooks individually, find the smallest amount she can spend.
Show mark scheme
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 a 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 9 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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