CEM Style Numerical Reasoning Paper 2
CEM-style numerical reasoning Paper 2 keeps the standard written-answer format of Paper 1, working from a shared data source before a run of questions, but shifts from tables towards bar charts and pictograms as the main data source. Reading the chart correctly, including working out what a partial bar or a part-symbol on a pictogram represents, matters as much as the calculation that follows.
Before you start
Make sure you're comfortable with these topics first:
Method
- Check the scale on a bar chart's axis carefully before reading any bar, including what each small gridline represents, since bars are often not drawn to obviously round numbers.
- On a pictogram, check the key first to see what one full symbol represents, and work out what a half or quarter symbol is worth before using it in a calculation.
- Read off the exact value for each bar or symbol needed for a question, writing it down before calculating, rather than trying to hold several values in your head.
- Where several questions share one chart, expect later questions to combine two or more bars or categories, such as finding a total or a difference.
- Keep your written working visible for every calculation, even though the paper is written-answer rather than multiple choice, since it helps you spot an error quickly.
- Manage your time across the whole mixed timed section the numerical reasoning questions sit within, not just the maths questions themselves.
Worked example
A pictogram shows the number of books read by four pupils in a month, where one full book symbol represents 4 books, and a half symbol represents 2 books. Ahmed has 3 full symbols, and Priya has 2 full symbols and one half symbol. (a) How many books did Ahmed read? (b) How many books did Priya read? (c) How many more books did Ahmed read than Priya?
- Find Ahmed's total: 3 full symbols x 4 books each = 12 books.
- Find Priya's total: 2 full symbols x 4 books = 8 books, plus the half symbol worth 2 books, giving 8 + 2 = 10 books.
- Find the difference: 12 - 10 = 2.
- Ahmed read 2 more books than Priya.
Practice questions
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Q1A bar chart shows a shop sold 35 umbrellas in April and 20 in May. How many more umbrellas were sold in April than May?Show answer
Answer: 15.
Q2A pictogram key shows one symbol = 5 pupils. A bar for Year 5 shows 6 full symbols. How many Year 5 pupils are represented?Show answer
Answer: 30.
Q3A bar chart shows votes for favourite colours: red 18, blue 24, green 12. How many votes were cast in total?Show answer
Answer: 54.
Q4A pictogram shows one symbol = 10 cars. A row shows 3 full symbols and one half symbol. How many cars does this represent?Show answer
Answer: 35.
Q5A bar chart shows rainfall of 45mm in June and 63mm in July. Find the total rainfall over the two months.Show answer
Answer: 108mm.
Q6A bar chart shows 4 classes with 28, 30, 26 and 32 pupils. Find the mean class size.Show answer
Answer: 29 (total = 116; 116 / 4 = 29).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A bar chart shows the number of goals scored by a football team over four matches: Match 1: 2 goals, Match 2: 5 goals, Match 3: 1 goal, Match 4: 4 goals. (a) Find the total number of goals scored over the four matches. (b) Find the mean number of goals per match. (c) Find the range of goals scored.
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A pictogram shows the number of trees planted by three schools, where one full tree symbol represents 8 trees, a half symbol represents 4 trees, and a quarter symbol represents 2 trees. Oakfield shows 4 full symbols, Elmwood shows 2 full symbols and one half symbol, and Birchgrove shows 3 full symbols and one quarter symbol. (a) Find the number of trees planted by each school. (b) Find the total number of trees planted by all three schools.
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Free printable worksheet
Want more practice on paper? Download the cem style numerical reasoning paper 2 worksheet pack - 8 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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