Sequences, Patterns and Early Algebra: Practice Set 3 - Worksheets, Questions and Revision

24 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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11+ · GL ASSESSMENT

EP.M56 Sequences, Patterns and Early Algebra: Practice Set 3

GL ASSESSMENT EP.M56 · Calculators not allowed · about 58 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Sequences, Patterns and Early Algebra: Practice Set 3

Revision Library

A third 11+ sequences, patterns and early-algebra practice set, complementing EP.M13/EP.M13B (Sequences and Patterns), EP.M14/EP.M14B (Early Algebra) and EP.M28/EP.M39 (Algebra, Sequences and Patterns Depth). It covers term-to-term and position-to-term sequences, linear nth-term rules, function machines, forming and simplifying expressions, and one-step and two-step equations, with an entirely fresh set of numbers, contexts and names. Questions are ramped from straightforward warm-up items to demanding multi-step and reverse-reasoning problems.

1
Here is a number sequence:
11, 16, 21, 26, ...

What is the next term in the sequence?
  • A) 29
  • B) 30
  • C) 31
  • D) 32
  • E) 21
(Total for Question 1 is 1 mark)
2
Here is a number sequence:
90, 79, 68, 57, ...

What is the next term in the sequence?
  • A) 44
  • B) 45
  • C) 46
  • D) 47
  • E) 68
(Total for Question 2 is 1 mark)
3
Find the missing term in this number sequence.

14, 22, __, 38, 46
(Total for Question 3 is 1 mark)
4
A number sequence begins 100, 93, 86, 79, ...
(a)Describe, in words, the term-to-term rule for this sequence.(1)
(b)Write down the next two terms of the sequence.(1)
(Total for Question 4 is 2 marks)
5
A function machine works like this: input, then multiply by 7, to give the output.

What is the output when the input is 6?
  • A) 13
  • B) 36
  • C) 42
  • D) 48
  • E) 49
(Total for Question 5 is 1 mark)
6
A function machine works like this: input, then add 17, to give the output.

The output is 31. Work out the input.
(Total for Question 6 is 1 mark)
7
A jeweller threads beads onto a bracelet in a repeating pattern. Design 1 uses 9 beads, design 2 uses 13 beads, design 3 uses 17 beads.

How many beads are needed for design 4?
  • A) 19
  • B) 20
  • C) 21
  • D) 25
  • E) 17
(Total for Question 7 is 1 mark)
8
A jeweller's bracelet pattern begins 9, 13, 17, 21, ..., with each design using 4 more beads than the design before it.
(a)Describe, in words, the term-to-term rule for the number of beads.(1)
(b)How many beads are needed for design 7?(1)
(Total for Question 8 is 2 marks)
9
A number sequence begins 13, 15, 17, 19, ...
(a)Find an expression, in terms of n, for the nth term of the sequence.(1)
(b)Use your expression to find the 30th term of the sequence.(2)
(Total for Question 9 is 3 marks)
10
The nth term of a sequence is 5n - 6.

Work out the 14th term of the sequence.
(Total for Question 10 is 1 mark)
11
The nth term of a sequence is 7n + 4.
(a)Write down the first three terms of the sequence.(1)
(b)Is 100 a term in this sequence? Show your working to explain your answer.(2)
(Total for Question 11 is 3 marks)
12
A function machine works like this: input, then multiply by 5, then subtract 8, to give the output.
(a)Find the output when the input is 9.(1)
(b)Find the input when the output is 52. Show your working.(2)
(Total for Question 12 is 3 marks)
13
Write an expression for each statement. Use the letter given for the unknown number.
(a)7 less than a number w(1)
(b)a number t is trebled, then 5 is added(1)
(c)the cost, in pounds, of h headphones at 60p each(1)
(Total for Question 13 is 3 marks)
14
Simplify fully.
(a)9x - 4x + 2x(1)
(b)5p + 6q - 2p - q(1)
(Total for Question 14 is 2 marks)
15
m = 5 and k = -2. Work out the value of each expression.
(a)3m + k(1)
(b)4k - m(1)
(Total for Question 15 is 2 marks)
16
Solve x + 13 = 21.
  • A) 7
  • B) 8
  • C) 9
  • D) 34
  • E) -8
(Total for Question 16 is 1 mark)
17
Solve y + 18 = 5.
(Total for Question 17 is 1 mark)
18
Solve 4x - 9 = 23. Show your working.
(Total for Question 18 is 2 marks)
19
Solve 25 - 3x = 4. Show your working.
(Total for Question 19 is 2 marks)
20
A garden designer borders a circular flower bed with pebbles. Border 1 uses 6 pebbles, border 2 uses 15 pebbles, border 3 uses 24 pebbles, border 4 uses 33 pebbles, with each new border using 9 more pebbles than the one before.
(a)Find an expression, in terms of n, for the number of pebbles needed for border n.(1)
(b)Nadia says that border 10 will need fewer than 90 pebbles. Is Nadia correct? Show working to justify your answer.(2)
(c)A large display border uses exactly 168 pebbles. Work out which border number this is. Show your working.(2)
(Total for Question 20 is 5 marks)
21
A function machine has the rule: input, then multiply by 4, then subtract 11, to give the output. The output is 25.

Form an equation and solve it to find the input. Show your working.
(Total for Question 21 is 2 marks)
22
Aoife builds up a collection of stamps for a school project. In week 1 she has 9 stamps. Each week after that, she collects 13 more stamps than the week before, so her total is 9, 22, 35, 48, ...
(a)Find an expression, in terms of n, for the total number of stamps Aoife has after n weeks.(1)
(b)Work out how many stamps Aoife has after 12 weeks.(1)
(c)Aoife wants to know after how many whole weeks her collection will first contain more than 300 stamps. Work out this week number. Show your working.(2)
(Total for Question 22 is 4 marks)
23
Sequence E has nth term 4n + 9. Sequence F has nth term 6n - 7.

Find the value of n for which the nth term of Sequence E equals the nth term of Sequence F. Show your working.
(Total for Question 23 is 3 marks)
24
A number sequence has first term 15 and decreases by 3 each time, so it begins 15, 12, 9, 6, ...
(a)Find an expression, in terms of n, for the nth term of this sequence.(1)
(b)A second sequence has nth term 2n + 3. Find the value of n for which the two sequences give the same term. Show your working.(2)
(Total for Question 24 is 3 marks)
Mark scheme · EP.M56 Sequences, Patterns and Early Algebra: Practice Set 3

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24