CEM Style Maths Mixed Section 2
Section 2 keeps the unpredictable, mixed-topic format of a CEM-style section but draws on a wider slice of the KS2 curriculum than Section 1: ratio and proportion, converting between fractions, decimals and percentages, and basic geometry facts such as angles and perimeter. The pupil now also has to recall which branch of maths a question belongs to, not just which operation to use, before starting a calculation.
Before you start
Make sure you're comfortable with these topics first:
Method
- Before calculating, decide which area of maths the question is testing: is it about sharing in a ratio, converting between fraction, decimal and percentage forms, or measuring shape properties?
- For a ratio or proportion question, find the value of 'one part' first, by dividing the total by the sum of the ratio parts, before scaling up to the amounts asked for.
- Learn the common fraction, decimal and percentage equivalents, such as halves, quarters, fifths and tenths, by heart so you can convert instantly rather than calculating from scratch.
- For a geometry question, recall the relevant fact first, such as angles on a straight line summing to 180 degrees, angles around a point summing to 360 degrees, or a rectangle's perimeter being 2 x (length + width), before substituting the numbers.
- Draw a quick sketch for any shape or angle question rather than trying to picture it, since a mixed section gives no diagram unless the question includes one.
- Keep unit conversions explicit in your working, for example writing '5cm = 50mm', so a mixed-topic switch does not cause you to compare numbers in different units by mistake.
- Move on if a single question is taking noticeably longer than the others around it, and return to it only once the rest of the section is answered.
Worked example
A garden is divided between vegetables and flowers in the ratio 3:2. The garden has a total area of 40 square metres. (a) How many square metres are used for vegetables? (b) What percentage of the garden is used for flowers?
- (a) Add the ratio parts: 3 + 2 = 5 parts in total.
- Find the value of one part: 40 / 5 = 8 square metres per part.
- Vegetables use 3 parts: 3 x 8 = 24 square metres.
- (b) Flowers use 2 parts: 2 x 8 = 16 square metres.
- As a percentage of the whole garden: 16 / 40 = 0.4 = 40%, so flowers use 40% of the garden.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Write 3/5 as a percentage.Show answer
Answer: 60%.
Q2Share 60 pounds in the ratio 1:3.Show answer
Answer: 15 pounds and 45 pounds.
Q3What is 0.75 written as a fraction in its simplest form?Show answer
Answer: 3/4.
Q4Two angles on a straight line are 65 degrees and x degrees. Find x.Show answer
Answer: 115 degrees (180 - 65).
Q5A rectangle has length 9cm and width 4cm. Find its perimeter.Show answer
Answer: 26cm (2 x (9 + 4)).
Q6Share 36 sweets in the ratio 2:1.Show answer
Answer: 24 sweets and 12 sweets.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A recipe mixture uses flour, sugar and butter in the ratio 5:2:1, making a mixture with a total mass of 800g. (a) Find the mass of flour in the mixture. (b) Find the mass of butter in the mixture.
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Four angles meet at a point. Three of the angles are 95 degrees, 80 degrees and 110 degrees. (a) Find the size of the fourth angle. (b) Express the fourth angle as a percentage of the full 360 degrees, to the nearest whole percent.
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Free printable worksheet
Want more practice on paper? Download the cem style maths mixed section 2 worksheet pack - 7 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.
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