Sequences, Patterns and Early Algebra: Practice Set 3
Sequences, Patterns and Early Algebra: Practice Set 3 is a practice set combining number sequences, both term-to-term and position-to-term rules, pattern recognition, and early algebra, including function machines and simple one-step and two-step equations, as tested in the reasoning sections of 11+ maths papers.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a sequence, find the term-to-term rule first by working out the difference, or ratio, between consecutive terms.
- Check the rule is consistent across the whole sequence, not just the first pair of terms, before using it to extend the sequence.
- For a position-to-term rule, test it against at least two terms with known positions to confirm it works before applying it to a term far along the sequence.
- For a function machine, apply each operation in the order shown to go forwards, and apply the inverse operations in reverse order to work backwards from an output.
- For a simple equation, such as 3x + 4 = 19, undo each operation in reverse order, subtract then divide, to isolate the unknown.
- Check any algebra answer by substituting it back into the original equation or rule to confirm both sides balance.
Worked example
The position-to-term rule for a sequence is: term = 4 x position + 3. Find the 6th term of the sequence, and find which position has a term equal to 39.
- Substitute position = 6 into the rule: term = 4 x 6 + 3.
- Calculate: 4 x 6 = 24, then 24 + 3 = 27, so the 6th term is 27.
- To find the position of the term 39, set up the equation 4 x position + 3 = 39.
- Undo the plus 3 by subtracting 3 from both sides: 4 x position = 36.
- Undo the times 4 by dividing both sides by 4: position = 9.
- Final answer: the 6th term is 27, and the term 39 is in position 9.
Practice questions
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Q1Find the next two terms in the sequence: 5, 9, 13, 17, ...Show answer
Answer: 21, 25
Q2The term-to-term rule of a sequence is 'subtract 6', starting at 100. Find the first four terms.Show answer
Answer: 100, 94, 88, 82
Q3A function machine takes a number, multiplies it by 3, then adds 5. What is the output when the input is 8?Show answer
Answer: 29 (8 x 3 = 24, 24 + 5 = 29)
Q4Solve: x + 7 = 15.Show answer
Answer: x = 8
Q5Solve: 5x = 45.Show answer
Answer: x = 9
Q6Find the position-to-term rule for the sequence 2, 5, 8, 11, ...Show answer
Answer: term = 3 x position - 1 (position 1 gives 3 - 1 = 2, position 2 gives 6 - 1 = 5)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A function machine takes a number, subtracts 4, then multiplies the result by 3. If the output is 27, what was the input number?
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The position-to-term rule for a sequence is term = 5 x position - 2. A pupil claims the number 48 is a term in this sequence. Is the pupil correct? Show your working and explain your reasoning.
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Free printable worksheet
Want more practice on paper? Download the sequences, patterns and early algebra: practice set 3 worksheet pack - 10 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.
This topic is chapter 15 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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