CSSE-Style Maths Mock 4 (Essex)
CSSE-Style Maths Mock 4 (Essex) gives further practice at the wordy, multi-step question style used in the Essex Consortium of Selective Schools' Maths paper, focusing on number properties: factors, multiples, primes, square and cube numbers, and negative numbers used in a real-life context such as temperature. CSSE questions of this kind often ask for a number that fits two or three conditions at once, buried inside a sentence about a real situation.
Method
- Learn the definitions precisely: a factor of a number divides into it exactly with no remainder; a multiple of a number appears in its times table; a prime number has exactly two factors, 1 and itself; a square number is a whole number multiplied by itself.
- For a 'multiple of A and a factor of B' style question, list the multiples of A up to B, then check which of those also divide exactly into B, rather than testing every number between A and B one at a time.
- Remember that 1 is not a prime number, that 2 is the only even prime number, and that you only need to test dividing a number by primes up to its square root to be sure whether it is prime.
- For negative numbers in context, such as temperature, elevation or a bank balance, picture a number line, and remember that moving to a colder, lower or more overdrawn value means moving further into the negative numbers.
- For a change that crosses through zero, such as a temperature rising from below zero to above it, it can help to find the distance to zero first, then the distance from zero to the final value, and add the two together.
- Memorise the square numbers up to at least 15 squared (225) and the cube numbers up to at least 5 cubed (125), since recalling these instantly saves time on a wordy question that only needs the fact, not the working.
- Since CSSE questions bury the actual number-property question inside a longer sentence, reread the final question sentence once you think you have solved it, to check you are answering exactly what was asked, such as the number itself or how many such numbers exist.
Worked example
A youth group leader is choosing a number of activity stations for a school fete. She wants the number of stations to be a factor of 60, and also an odd number greater than 5. List all the numbers that fit both of these conditions.
- List the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- From this list, pick out only the odd numbers: 1, 3, 5, 15.
- From those odd factors, keep only the ones greater than 5: 1, 3 and 5 are not greater than 5, so only 15 remains.
- Final answer: the only number of stations that fits both conditions is 15.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1List all the factors of 18.Show answer
Answer: 1, 2, 3, 6, 9, 18.
Q2Is 51 a prime number? Explain your answer.Show answer
Answer: No, because 51 = 3 x 17, so it has factors other than 1 and itself.
Q3What is the smallest common multiple of 4 and 6?Show answer
Answer: 12 (the multiples of 4 are 4, 8, 12, and the multiples of 6 are 6, 12, so the smallest one they share is 12).
Q4What is 11 squared?Show answer
Answer: 121.
Q5What is 3 cubed?Show answer
Answer: 27 (3 x 3 x 3 = 27).
Q6The temperature at the start of the day is -6 degrees Celsius. By midday it has risen by 11 degrees. What is the temperature at midday?Show answer
Answer: 5 degrees Celsius (-6 + 11 = 5).
Q7A submarine is at a depth of 45 metres below sea level. It rises by 60 metres. What is its new position, relative to sea level?Show answer
Answer: 15 metres above sea level (-45 + 60 = 15).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A number is a multiple of 7. It is also a factor of 84. It is greater than 10, less than 30, and it is an odd number. Find the number, showing how you checked it meets every condition.
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The temperature in a town was -4 degrees Celsius at 6am. By 2pm it had risen to 9 degrees Celsius. By 10pm it had fallen again by 15 degrees from its 2pm value. What was the temperature at 10pm?
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Free printable worksheet
Want more practice on paper? Download the csse-style maths mock 4 (essex) worksheet pack - 13 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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