CSSE-Style Maths Mock 6 (Essex)
CSSE-Style Maths Mock 6 (Essex) focuses on sequences, patterns and early algebra, a question family CSSE often places near the end of its paper in the form of a growing pattern, such as tiles, seats or trees, described in words rather than as a bare list of numbers. Working out the position-to-term rule, rather than extending a list by hand, is what separates a fast, confident answer from a slow one when the question asks for a term many steps further on.
Method
- For a number sequence, work out the term-to-term rule first, what is added, subtracted, multiplied or divided to get from one term to the next, using at least three consecutive terms, since two terms alone can sometimes fit more than one rule.
- For a growing pattern described in words or pictures, such as tiles, seats or trees added in a repeating way, work out how many are added at each new step, and whether that amount stays the same or itself changes.
- Where a question asks for a term far along the sequence, such as the 20th term, do not extend the list by hand; instead find the position-to-term rule, an expression such as 'multiply the term number by a fixed amount, then add or subtract a fixed amount', and substitute the term number into it.
- To find a position-to-term rule from a sequence, work out the term-to-term difference first, since this difference becomes the amount you multiply the term number by.
- Once you have a position-to-term rule, check it against at least two known terms in the sequence before using it to jump ahead, since a rule that fits only one term may still be wrong.
- For a function-machine or 'think of a number' style question, work backwards from the given output, undoing each operation in reverse order.
- Since this is the final mock in this run, use it as a check on your overall exam timing across a full CSSE-style paper: sequence and pattern questions are often placed near the end of a CSSE paper, so note how much time you have left when you reach them, since a slow start elsewhere can leave too little time for this question type.
Worked example
A gardener plants a row of trees, then surrounds them with a pattern of square paving slabs. With 1 tree, 4 slabs are needed. With 2 trees, 7 slabs are needed. With 3 trees, 10 slabs are needed. If this pattern continues, how many slabs are needed for 8 trees?
- Find the term-to-term rule: from 1 tree to 2 trees, slabs go from 4 to 7, an increase of 3, and from 2 trees to 3 trees, slabs go from 7 to 10, also an increase of 3, so each extra tree needs 3 more slabs.
- Since each term increases by 3, the position-to-term rule involves multiplying the number of trees by 3, then adjusting by a fixed amount.
- Test this with 1 tree: 3 x 1 = 3, but the actual number of slabs is 4, so add 1: 3 x 1 + 1 = 4, which matches.
- Check the rule against 3 trees: 3 x 3 + 1 = 10, which matches the given value, confirming the rule 'slabs = 3 x number of trees + 1'.
- Substitute 8 trees into the rule: 3 x 8 + 1 = 24 + 1 = 25.
- Final answer: 25 slabs are needed for 8 trees.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Find the next two terms in the sequence: 6, 11, 16, 21, ...Show answer
Answer: 26 and 31 (each term adds 5).
Q2A sequence has the position-to-term rule 'multiply the term number by 4, then subtract 2'. What is the 6th term?Show answer
Answer: 22 (4 x 6 - 2 = 22).
Q3The first term of a sequence is 3, and each term after that is found by doubling the previous term and adding 1. What is the third term?Show answer
Answer: 15 (the second term is 2 x 3 + 1 = 7, and the third term is 2 x 7 + 1 = 15).
Q4A pattern of tiles has 2 tiles in step 1, 5 tiles in step 2, and 8 tiles in step 3. How many tiles are needed for step 10?Show answer
Answer: 29 tiles (each step adds 3 tiles, and the rule is 3 x step number - 1, so 3 x 10 - 1 = 29).
Q5A number machine takes an input, doubles it, then adds 6, to give an output of 20. What was the input?Show answer
Answer: 7 (working backwards: 20 - 6 = 14, and 14 / 2 = 7).
Q6Row 1 of a theatre has 12 seats. Each row after that has 3 more seats than the row before it. How many seats are in row 6?Show answer
Answer: 27 seats (12 + 3 x 5 = 27, since row 6 is 5 steps on from row 1).
Q7A sequence begins at 8, and each term is found by adding 7 to the previous term: 8, 15, 22, 29, ... What is the first term in the sequence greater than 60?Show answer
Answer: 64 (the sequence continues 36, 43, 50, 57, 64, and 57 is not greater than 60 but 64 is).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A stack of chairs is arranged so that the bottom row has 15 chairs, and each row above has 2 fewer chairs than the row below it: 15, 13, 11, 9, and so on. (a) How many chairs are in the 6th row from the bottom? (b) Explain why the pattern cannot continue below a row of 1 chair.
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A mobile phone plan charges a fixed fee of 12 pounds a month, plus 3 pounds for every gigabyte of data used beyond the first free gigabyte. Priya's bill for a certain month is 27 pounds. How many gigabytes of data beyond the first free gigabyte did she use that month, and what was her total data use for the month, including the free gigabyte?
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Free printable worksheet
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