Algebra, Sequences and Patterns Depth Worksheet with Answers

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11+ · GL ASSESSMENT

EP.M28 Algebra, Sequences and Patterns Depth

GL ASSESSMENT EP.M28 · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Algebra, Sequences and Patterns Depth

Revision Library

An 11+ early-algebra and sequences paper for scholarship-level preparation, complementing EP.M13 (Sequences and Patterns) and EP.M14 (Early Algebra). It covers function machines, missing-number problems, simple equations, term-to-term and position-to-term sequences, pattern continuation and formulae expressed in words. 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 adds 6 to the input number. If the input is 9, what is the output?

A) 3
B) 6
C) 15
D) 45
E) 54

(Total for Question 1 is 1 mark)

2

Find the missing number: 9 + ___ = 17

A) 6
B) 7
C) 8
D) 9
E) 26

(Total for Question 2 is 1 mark)

3

A function machine multiplies the input by 2, then adds 5. Complete the table below.

(a)Input = 3. Find the output.(1)

(b)Input = 8. Find the output.(1)

(Total for Question 3 is 2 marks)

4

Continue the pattern: 2, 4, 6, 8, ___

A) 9
B) 10
C) 11
D) 12
E) 16

(Total for Question 4 is 1 mark)

5

A sequence begins 3, 7, 11, 15, ...

(a)Write down the next two terms of the sequence.(2)

(b)Describe, in words, the term-to-term rule for the sequence.(1)

(Total for Question 5 is 3 marks)

6

Solve: x + 6 = 13

A) 6
B) 7
C) 8
D) 13
E) 19

(Total for Question 6 is 1 mark)

7

A function machine works like this: input, then multiply by 3, then subtract 4, to give the output. The output is 20. Work out the input, showing your working.

(Total for Question 7 is 2 marks)

8

Priya makes a pattern from matchsticks. Pattern 1 uses 4 matchsticks, pattern 2 uses 7 matchsticks and pattern 3 uses 10 matchsticks. Each new pattern uses 3 more matchsticks than the last.

(a)How many matchsticks are needed for pattern 4?(1)

(b)How many matchsticks are needed for pattern 6?(1)

(Total for Question 8 is 2 marks)

9

A shop hires out bikes. To find the total cost, in pounds, of hiring a bike, multiply the number of hours by 3, then add 2.

(a)Find the cost of hiring a bike for 4 hours.(1)

(b)Find the cost of hiring a bike for 7 hours.(1)

(Total for Question 9 is 2 marks)

10

Find the missing number: 5, 10, 15, ___, 25

A) 18
B) 20
C) 22
D) 25
E) 30

(Total for Question 10 is 1 mark)

11

A function machine works like this: input, then subtract 5, then multiply by 2, to give the output.

(a)Find the output when the input is 9.(1)

(b)Find the input when the output is 18. Show your working.(2)

(Total for Question 11 is 3 marks)

12

Solve: 2x = 18

A) 7
B) 8
C) 9
D) 16
E) 36

(Total for Question 12 is 1 mark)

13

A pattern of dots is drawn. Pattern 1 has 2 dots, pattern 2 has 5 dots and pattern 3 has 8 dots. Each new pattern has 3 more dots than the last.

(a)How many dots are in pattern 5?(1)

(b)Which pattern number has exactly 29 dots?(2)

(Total for Question 13 is 3 marks)

14

The nth term of a sequence is 4n - 2.

(a)Find the 6th term of the sequence.(1)

(b)Find the 10th term of the sequence.(1)

(Total for Question 14 is 2 marks)

15

Continue the pattern: 20, 17, 14, ___

A) 10
B) 11
C) 12
D) 13
E) 17

(Total for Question 15 is 1 mark)

16

Solve 3x + 2 = 17. Show your working.

(Total for Question 16 is 2 marks)

17

A function machine works like this: input, then add 4, then multiply by 2, then subtract 3, to give the output.

(a)Find the output when the input is 5.(1)

(b)Find the output when the input is 10.(1)

(Total for Question 17 is 2 marks)

18

Find the missing number: 6, 12, 18, ___, 30

A) 20
B) 22
C) 24
D) 26
E) 28

(Total for Question 18 is 1 mark)

19

Priya is p years old. Her brother Arjun is 5 years younger than Priya. Their auntie Fatima is 3 times as old as Arjun.

(a)Write an expression, in terms of p, for Arjun's age.(1)

(b)Write an expression, in terms of p, for their auntie's age.(1)

(c)Priya is 13. How old is their auntie?(1)

(Total for Question 19 is 3 marks)

20

A sequence begins 4, 9, 14, 19, ...

(a)Describe, in words, the term-to-term rule for the sequence.(1)

(b)Find the 10th term of the sequence.(2)

(Total for Question 20 is 3 marks)

21

The nth term of a sequence is 6n - 4. Find the first term in the sequence that is greater than 50. Show your working.

(Total for Question 21 is 2 marks)

22

Which rule describes the sequence 7, 12, 17, 22, ...?

A) nth term = 5n + 2
B) nth term = 5n - 2
C) nth term = 5n + 7
D) nth term = 7n + 5
E) nth term = 2n + 5

(Total for Question 22 is 1 mark)

23

A function machine has two operations: first multiply the input by a number, then add another number. Input 2 gives output 9. Input 5 gives output 18.

(a)Find the two operations of the function machine.(2)

(b)Use your rule to find the output when the input is 10.(1)

(Total for Question 23 is 3 marks)

24

Two sequences are given. Sequence A: 3, 8, 13, 18, ... (nth term = 5n - 2). Sequence B: 6, 11, 16, 21, ... (nth term = 5n + 1).

(a)Find the 20th term of Sequence A.(1)

(b)Find the 20th term of Sequence B.(1)

(c)What is the difference between the 20th term of Sequence B and the 20th term of Sequence A? Explain why this difference is the same for every matching pair of terms in the two sequences.(1)

(Total for Question 24 is 3 marks)

Mark scheme · EP.M28 Algebra, Sequences and Patterns Depth

Question 1

B1 C (15) cao
Answer: C) 15

Question 2

B1 C (8) cao
Answer: C) 8

Question 3

(a) B1 11 cao
(a) Answer: 11
(b) B1 21 cao
(b) Answer: 21

Question 4

B1 B (10) cao
Answer: B) 10

Question 5

(a) B1 19 oe
(a) B1 23 oe
(a) Answer: 19, 23
(b) B1 add 4 to the previous term each time oe
(b) Answer: Add 4 to the previous term each time (starting at 3).

Question 6

B1 B (7) cao
Answer: B) 7

Question 7

M1 correct reverse method: add 4 then divide by 3 oe
A1 8 cao
Answer: 8

Question 8

(a) B1 13 cao
(a) Answer: 13
(b) B1 19 cao
(b) Answer: 19

Question 9

(a) B1 14 cao (accept £14)
(a) Answer: £14
(b) B1 23 cao (accept £23)
(b) Answer: £23

Question 10

B1 B (20) cao
Answer: B) 20

Question 11

(a) B1 8 cao
(a) Answer: 8
(b) M1 correct reverse method: halve then add 5 oe
(b) A1 14 cao
(b) Answer: 14

Question 12

B1 C (9) cao
Answer: C) 9

Question 13

(a) B1 14 cao
(a) Answer: 14
(b) M1 3n - 1 = 29 set up, or equivalent correct method
(b) A1 pattern 10 cao
(b) Answer: Pattern 10

Question 14

(a) B1 22 cao
(a) Answer: 22
(b) B1 38 cao
(b) Answer: 38

Question 15

B1 B (11) cao
Answer: B) 11

Question 16

M1 3x = 15 seen
A1 x = 5 cao
Answer: x = 5

Question 17

(a) B1 15 cao
(a) Answer: 15
(b) B1 25 cao
(b) Answer: 25

Question 18

B1 C (24) cao
Answer: C) 24

Question 19

(a) B1 p - 5 oe
(a) Answer: p - 5
(b) B1 3(p - 5) oe (accept 3p - 15)
(b) Answer: 3(p - 5), which is the same as 3p - 15
(c) B1 24 cao (ft their expression from part b)
(c) Answer: 24

Question 20

(a) B1 add 5 to the previous term each time oe
(a) Answer: Add 5 to the previous term each time (starting at 4).
(b) M1 valid method, e.g. nth term = 5n - 1, or systematic continuation to the 10th term
(b) A1 49 cao
(b) Answer: 49

Question 21

M1 correct method, e.g. 6n - 4 > 50 set up, or systematic trial of terms near 50
A1 56 cao (with n = 10 identified)
Answer: 56 (the 10th term)

Question 22

B1 A (nth term = 5n + 2) cao
Answer: A) nth term = 5n + 2

Question 23

(a) M1 two correct equations formed, e.g. 2a + b = 9 and 5a + b = 18 oe
(a) A1 multiply by 3, then add 3 (both correct) cao
(a) Answer: Multiply the input by 3, then add 3.
(b) B1 33 cao (ft their rule from part a)
(b) Answer: 33

Question 24

(a) B1 98 cao
(a) Answer: 98
(b) B1 101 cao
(b) Answer: 101
(c) B1 3 stated, with a correct explanation that both sequences share the same common difference (5), so the gap between matching terms stays constant oe (ft their terms from parts a and b)
(c) Answer: 3. Both sequences increase by 5 each time (the same common difference), and their starting terms differ by 3 (6 - 3 = 3), so every matching pair of terms will always differ by 3.

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EP.M28 Algebra, Sequences and Patterns Depth

Algebra, Sequences and Patterns Depth

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Question 2

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