Wirral-Style Maths and Reasoning Mock
The Wirral-Style Maths and Reasoning Mock is modelled on the 11+ test used by grammar schools on the Wirral, including Wirral Grammar School for Boys and Girls and Calday Grange, which has combined maths with a reasoning paper in various forms across recent admissions cycles. It covers number, calculation and worded-problem questions from maths alongside numerical and logical reasoning items such as sequences, missing numbers and simple deduction puzzles.
Before you start
Make sure you're comfortable with these topics first:
Method
- Separate the paper mentally into its maths questions and its reasoning questions as you work through, since they need different approaches even when mixed together on the same page.
- For maths questions, show your working in the space provided even on short questions, since method marks can be awarded even if your final answer is wrong.
- For numerical reasoning and missing-number puzzles, write down what you know as an equation before trying values, rather than guessing numbers at random.
- For sequence questions, work out the rule using at least three consecutive terms before applying it, since two terms alone can sometimes fit more than one rule.
- Keep track of the time per question: with a large number of short items, spending too long on any one question risks losing marks on ones further down the paper.
- Use any time left at the end to check maths questions with a rough estimate (for example, rounding numbers) rather than only rereading the question.
Worked example
In the equation 4 x [ ] + 7 = 39, what number goes in the box?
- Treat the box as an unknown value and rearrange the equation to isolate it: subtract 7 from both sides.
- Calculate: 39 - 7 = 32.
- Now divide both sides by 4 to find the value of the box: 32 / 4.
- Calculate: 32 / 4 = 8.
- Check the answer by substituting it back in: 4 x 8 + 7 = 32 + 7 = 39, which matches.
- Final answer: 8.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1What number comes next in the sequence: 3, 7, 11, 15, ...?Show answer
Answer: 19 (the rule is add 4 each time).
Q2Work out the missing number: 56 / [ ] = 8.Show answer
Answer: 7 (56 / 7 = 8).
Q3A number is doubled and then 5 is added, giving a result of 27. What was the original number?Show answer
Answer: 11 (27 - 5 = 22, 22 / 2 = 11).
Q4What is 7 squared minus 3 cubed?Show answer
Answer: 22 (7 squared = 49, 3 cubed = 27, 49 - 27 = 22).
Q5A bus timetable shows buses leaving every 12 minutes starting at 9:00am. What is the fourth departure time?Show answer
Answer: 9:36am (9:00, 9:12, 9:24, 9:36).
Q6If 3 books cost the same as 2 games, and one game costs 9 pounds, how much does one book cost?Show answer
Answer: 6 pounds (2 games = 18 pounds, so 3 books = 18 pounds, 18 / 3 = 6 pounds per book).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Find the missing number in the sequence: 2, 6, 18, [ ], 162. Explain the rule you used. (3 marks)
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A number machine takes an input, multiplies it by 3, then subtracts 4 to give an output of 23. What was the input number? Show your working. (3 marks)
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Free printable worksheet
Want more practice on paper? Download the wirral-style maths and reasoning mock worksheet pack - 17 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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