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Algebra and Sequences: Practice Set 5 - Worksheets, Questions and Revision

24 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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11+ · GL ASSESSMENT

EP.M86 Algebra and Sequences: Practice Set 5

GL ASSESSMENT EP.M86 · Calculators not allowed · about 54 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Algebra and Sequences: Practice Set 5

Revision Library

A fifth 11+ sequences and early-algebra practice set, complementing EP.M13/EP.M13B (Sequences and Patterns), EP.M14/EP.M14B (Early Algebra), EP.M28 (Algebra, Sequences and Patterns Depth), EP.M56 (Sequences, Patterns and Early Algebra: Practice Set 3) and EP.M68 (Sequences and Early Algebra: Practice Set 4). It covers term-to-term and position-to-term sequences, linear nth-term rules, function machines (including reverse and equation-forming problems), forming and simplifying expressions, and one-step, two-step and both-sides 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:
12, 19, 26, 33, ...

What is the next term in the sequence?
  • A) 38
  • B) 39
  • C) 40
  • D) 41
  • E) 47
(Total for Question 1 is 1 mark)
2
Here is a number sequence:
91, 79, 67, 55, ...

What is the next term in the sequence?
  • A) 41
  • B) 42
  • C) 43
  • D) 44
  • E) 55
(Total for Question 2 is 1 mark)
3
Find the missing term in this number sequence.

6, 17, __, 39, 50
(Total for Question 3 is 1 mark)
4
A number sequence begins 175, 163, 151, 139, ...
(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 8, to give the output.

What is the output when the input is 7?
  • A) 15
  • B) 49
  • C) 56
  • D) 63
  • E) 64
(Total for Question 5 is 1 mark)
6
A function machine works like this: input, then add 27, to give the output.

The output is 35. Work out the input.
(Total for Question 6 is 1 mark)
7
A choir sets out chairs in rows for a concert. Row 1 has 9 chairs, row 2 has 15 chairs, row 3 has 21 chairs.

How many chairs are in row 4?
  • A) 25
  • B) 26
  • C) 27
  • D) 28
  • E) 33
(Total for Question 7 is 1 mark)
8
The choir's row pattern begins 9, 15, 21, 27, ..., with each row having 6 more chairs than the row before it.
(a)Describe, in words, the term-to-term rule for the number of chairs.(1)
(b)How many chairs are in row 9?(1)
(Total for Question 8 is 2 marks)
9
A number sequence begins 23, 30, 37, 44, ...
(a)Find an expression, in terms of n, for the nth term of the sequence.(1)
(b)Use your expression to find the 45th term of the sequence.(2)
(Total for Question 9 is 3 marks)
10
The nth term of a sequence is 9n - 7.

Work out the 14th term of the sequence.
(Total for Question 10 is 1 mark)
11
The nth term of a sequence is 6n + 5.
(a)Write down the first three terms of the sequence.(1)
(b)Is 200 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 add 12, then multiply by 3, to give the output.
(a)Find the output when the input is 9.(1)
(b)Find the input when the output is 45. 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)14 less than a number w(1)
(b)a number h is trebled, then 6 is subtracted(1)
(c)the cost, in pounds, of g garden chairs at 35p each(1)
(Total for Question 13 is 3 marks)
14
Simplify fully.
(a)15t - 8t + 2t(1)
(b)9p + 4q - 6p - 5q(1)
(Total for Question 14 is 2 marks)
15
c = 8 and d = -5. Work out the value of each expression.
(a)3c + d(1)
(b)4d - c(1)
(Total for Question 15 is 2 marks)
16
Solve x + 27 = 19.
  • A) -8
  • B) 8
  • C) 46
  • D) -46
  • E) 27
(Total for Question 16 is 1 mark)
17
Solve y - 24 = 11.
(Total for Question 17 is 1 mark)
18
Solve 7x - 9 = 40. Show your working.
(Total for Question 18 is 2 marks)
19
Solve 38 - 3x = 5. Show your working.
(Total for Question 19 is 2 marks)
20
A framer joins picture frames in a row for an exhibition wall. Arrangement 1 uses 14 pins, arrangement 2 uses 23 pins, arrangement 3 uses 32 pins, arrangement 4 uses 41 pins, with each new arrangement using 9 more pins than the one before.
(a)Find an expression, in terms of n, for the number of pins needed for arrangement n.(1)
(b)Declan says that arrangement 10 will need fewer than 90 pins. Is Declan correct? Show working to justify your answer.(2)
(c)A large exhibition order uses exactly 158 pins. Work out which arrangement 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 5, then add 14, to give the output. The output is 69.

Form an equation and solve it to find the input. Show your working.
(Total for Question 21 is 2 marks)
22
Zainab trains for a running race. In week 1 she runs 14 kilometres. Each week after that, she runs 6 kilometres more than the week before, so her weekly distance is 14, 20, 26, 32, ...
(a)Find an expression, in terms of n, for the distance, in kilometres, Zainab runs in week n.(1)
(b)Work out how far Zainab runs in week 12.(1)
(c)After how many whole weeks will Zainab's weekly distance first exceed 100 km? Show your working.(2)
(Total for Question 22 is 4 marks)
23
The nth term of a sequence is 5n + 11.

Find the first term in the sequence that is greater than 130. Show your working.
(Total for Question 23 is 2 marks)
24
A number sequence has first term 54 and decreases by 4 each time, so it begins 54, 50, 46, 42, ...
(a)Find an expression, in terms of n, for the nth term of this sequence.(1)
(b)A second sequence has nth term 2n + 10. 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.M86 Algebra and Sequences: Practice Set 5

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

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