Algebra, Sequences and Patterns Depth Set 2 - Worksheets, Questions and Revision

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

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11+ · GL ASSESSMENT

EP.M39 Algebra, Sequences and Patterns Depth Set 2

GL ASSESSMENT EP.M39 · Calculators not allowed · about 60 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Algebra, Sequences and Patterns Depth Set 2

Revision Library

A second 11+ early-algebra and sequences paper for scholarship-level preparation, complementing EP.M13 (Sequences and Patterns), EP.M14 (Early Algebra) and EP.M28 (Algebra, Sequences and Patterns Depth). It covers function machines, forming and simplifying expressions, one-step and two-step equations, term-to-term and position-to-term sequences, linear nth-term rules and pattern sequences, with an entirely fresh set of numbers and contexts. Questions are ramped from straightforward warm-up items to demanding multi-step and reverse-reasoning problems designed to stretch the strongest candidates.

1
A function machine multiplies the input number by 4. If the input is 7, what is the output?
  • A) 11
  • B) 21
  • C) 28
  • D) 33
  • E) 4
(Total for Question 1 is 1 mark)
2
A function machine works like this: input, then subtract 3, then multiply by 5, to give the output. Find the output when the input is 8.
(Total for Question 2 is 1 mark)
3
Simplify: 4a + 7a
  • A) 11
  • B) 11a
  • C) 28a
  • D) 3a
  • E) 11a2
(Total for Question 3 is 1 mark)
4
Simplify: 10c - 3c
(Total for Question 4 is 1 mark)
5
Leah has t trading cards. Her friend Yusuf has 9 more trading cards than Leah. Write an expression, in terms of t, for the number of trading cards Yusuf has.
(Total for Question 5 is 1 mark)
6
Solve: x + 11 = 19
  • A) 8
  • B) 30
  • C) 9
  • D) -8
  • E) 7
(Total for Question 6 is 1 mark)
7
Solve: 7y = 56
(Total for Question 7 is 1 mark)
8
Simplify fully: 6p + 4q - 3p + 2q
(Total for Question 8 is 2 marks)
9
A function machine works like this: input, then multiply by 6, then subtract 7, to give the output. The output is 29. Work out the input, showing your working.
(Total for Question 9 is 2 marks)
10
Zara puts 9 pounds sterling into a money box in week 1. Each week after that, she adds 8 pounds sterling more, following the term-to-term rule 'add 8'. Write down the amount of money she has at the end of each of the first five weeks.
(Total for Question 10 is 2 marks)
11
Mrs Boateng's class makes a pattern from hexagonal tiles for a wall display. Pattern 1 uses 6 tiles, pattern 2 uses 10 tiles and pattern 3 uses 14 tiles. Each new pattern uses 4 more tiles than the last.
(a)Describe, in words, the term-to-term rule for the number of tiles.(1)
(b)How many tiles are needed for pattern 5?(1)
(Total for Question 11 is 2 marks)
12
Continue the pattern: 3, 9, 15, 21, ___
  • A) 25
  • B) 26
  • C) 27
  • D) 28
  • E) 33
(Total for Question 12 is 1 mark)
13
A sequence begins 2, 8, 14, 20, ... Find the 10th term of the sequence. Show your working.
(Total for Question 13 is 2 marks)
14
Solve 4x + 3 = 27. Show your working.
(Total for Question 14 is 2 marks)
15
Solve 5y - 6 = 19. Show your working.
(Total for Question 15 is 2 marks)
16
Expand and simplify 3(x + 5) + 2
(Total for Question 16 is 2 marks)
17
The nth term of a sequence is 5n + 3.
(a)Write down the first three terms of the sequence.(1)
(b)Find the 20th term of the sequence.(2)
(Total for Question 17 is 3 marks)
18
A sequence begins 7, 13, 19, 25, ... Find an expression for the nth term of the sequence. Show your working.
(Total for Question 18 is 2 marks)
19
A function machine has two operations: first multiply the input by a number, then add another number, using the same rule each time. Input 3 gives output 13. Input 6 gives output 25. Input 9 gives output 37.
(a)Find the two operations of the function machine.(2)
(b)Use your rule to find the output when the input is 15.(1)
(Total for Question 19 is 3 marks)
20
Chidinma thinks of a number. She adds 9 to it, then multiplies the result by 2. Her answer is 38. Form an equation and solve it to find Chidinma's number. Show your working.
(Total for Question 20 is 2 marks)
21
A garden centre lays an L-shaped path from square slabs. Pattern 1 uses 8 slabs, pattern 2 uses 11 slabs, pattern 3 uses 14 slabs and pattern 4 uses 17 slabs.
(a)Describe, in words, the term-to-term rule for the number of slabs.(1)
(b)Find an expression for the nth term of the sequence.(2)
(c)A pattern in this sequence uses 47 slabs. Work out which pattern number this is. Show your working.(2)
(Total for Question 21 is 5 marks)
22
Solve 6(x - 4) = 18. Show your working.
(Total for Question 22 is 2 marks)
23
The nth term of a sequence is 3n - 8. Which term of the sequence is equal to 40? Show your working.
(Total for Question 23 is 3 marks)
24
Which rule describes the sequence 10, 17, 24, 31, ...?
  • A) nth term = 7n + 3
  • B) nth term = 7n - 3
  • C) nth term = 7n + 10
  • D) nth term = 3n + 7
  • E) nth term = 10n - 7
(Total for Question 24 is 1 mark)
25
A sequence begins 31, 27, 23, 19, ...
(a)Describe, in words, the term-to-term rule for the sequence.(1)
(b)Find an expression for the nth term of the sequence.(2)
(c)Find the first term in the sequence that is negative. Show your working.(2)
(Total for Question 25 is 5 marks)
26
Sequence P has nth term 4n + 7. Sequence Q has nth term 6n - 5.
(a)Find the 8th term of Sequence P.(1)
(b)Find the 8th term of Sequence Q.(1)
(c)Show that there is a value of n for which Sequence P and Sequence Q give the same term, and find that term.(3)
(Total for Question 26 is 5 marks)
Mark scheme · EP.M39 Algebra, Sequences and Patterns Depth Set 2

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

Question 25

Question 26