Sequences and Early Algebra: Practice Set 4 Worksheet with Answers

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11+ · GL ASSESSMENT

EP.M68 Sequences and Early Algebra: Practice Set 4

GL ASSESSMENT EP.M68 · Calculators not allowed · about 56 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Sequences and Early Algebra: Practice Set 4

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A fourth 11+ sequences and early-algebra practice set, complementing EP.M13/EP.M13B (Sequences and Patterns), EP.M14/EP.M14B (Early Algebra), EP.M28/EP.M39 (Algebra, Sequences and Patterns Depth) and EP.M56 (Sequences, Patterns and Early Algebra: Practice Set 3). 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:
6, 14, 22, 30, ...

What is the next term in the sequence?

A) 36
B) 37
C) 38
D) 39
E) 46

(Total for Question 1 is 1 mark)

2

Here is a number sequence:
84, 71, 58, 45, ...

What is the next term in the sequence?

A) 30
B) 31
C) 32
D) 33
E) 58

(Total for Question 2 is 1 mark)

3

Find the missing term in this number sequence.

9, 20, __, 42, 53

(Total for Question 3 is 1 mark)

4

A number sequence begins 200, 188, 176, 164, ...

(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 9, to give the output.

What is the output when the input is 5?

A) 14
B) 40
C) 45
D) 50
E) 81

(Total for Question 5 is 1 mark)

6

A function machine works like this: input, then add 19, to give the output.

The output is 32. Work out the input.

(Total for Question 6 is 1 mark)

7

A landscaper lays a path from hexagonal tiles. Path 1 uses 8 tiles, path 2 uses 13 tiles, path 3 uses 18 tiles.

How many tiles are needed for path 4?

A) 20
B) 21
C) 22
D) 23
E) 28

(Total for Question 7 is 1 mark)

8

The landscaper's path pattern begins 8, 13, 18, 23, ..., with each path using 5 more tiles than the path before it.

(a)Describe, in words, the term-to-term rule for the number of tiles.(1)

(b)How many tiles are needed for path 8?(1)

(Total for Question 8 is 2 marks)

9

A number sequence begins 21, 25, 29, 33, ...

(a)Find an expression, in terms of n, for the nth term of the sequence.(1)

(b)Use your expression to find the 40th term of the sequence.(2)

(Total for Question 9 is 3 marks)

10

The nth term of a sequence is 6n - 9.

Work out the 15th term of the sequence.

(Total for Question 10 is 1 mark)

11

The nth term of a sequence is 8n + 3.

(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 subtract 6, then multiply by 4, to give the output.

(a)Find the output when the input is 11.(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)9 more than a number d(1)

(b)a number k is halved, then 4 is added(1)

(c)the cost, in pounds, of j jars of honey at 45p each(1)

(Total for Question 13 is 3 marks)

14

Simplify fully.

(a)12y - 5y + y(1)

(b)8m + 3n - 5m - n(1)

(Total for Question 14 is 2 marks)

15

r = 6 and s = -3. Work out the value of each expression.

(a)2r + s(1)

(b)5s - r(1)

(Total for Question 15 is 2 marks)

16

Solve x + 16 = 9.

A) -7
B) 7
C) 25
D) -25
E) 16

(Total for Question 16 is 1 mark)

17

Solve y - 21 = 8.

(Total for Question 17 is 1 mark)

18

Solve 6x - 7 = 41. Show your working.

(Total for Question 18 is 2 marks)

19

Solve 33 - 4x = 5. Show your working.

(Total for Question 19 is 2 marks)

20

A market trader stacks crates for a stall. Stack 1 uses 10 crates, stack 2 uses 17 crates, stack 3 uses 24 crates, stack 4 uses 31 crates, with each new stack using 7 more crates than the one before.

(a)Find an expression, in terms of n, for the number of crates needed for stack n.(1)

(b)Ronke says that stack 12 will need fewer than 90 crates. Is Ronke correct? Show working to justify your answer.(2)

(c)A large market-day order uses exactly 129 crates. Work out which stack 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 7, then subtract 19, to give the output. The output is 30.

Form an equation and solve it to find the input. Show your working.

(Total for Question 21 is 2 marks)

22

Kwame saves money for a bicycle. In week 1 he has saved 11 pounds sterling. Each week after that, he saves 9 pounds sterling more than the week before, so his total is 11, 20, 29, 38, ...

(a)Find an expression, in terms of n, for the total amount, in pounds, Kwame has saved after n weeks.(1)

(b)Work out how much Kwame has saved after 15 weeks.(1)

(c)After how many whole weeks will Kwame's savings first exceed 200 pounds? Show your working.(2)

(Total for Question 22 is 4 marks)

23

The nth term of a sequence is 4n + 7.

Find the first term in the sequence that is greater than 150. Show your working.

(Total for Question 23 is 2 marks)

24

A number sequence has first term 46 and decreases by 4 each time, so it begins 46, 42, 38, 34, ...

(a)Find an expression, in terms of n, for the nth term of this sequence.(1)

(b)A second sequence has nth term 2n + 8. 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)

25

Solve 5x + 9 = 2x + 33. Show your working.

(Total for Question 25 is 2 marks)

Mark scheme · EP.M68 Sequences and Early Algebra: Practice Set 4

Question 1

B1 C (38) cao
Answer: C) 38

Question 2

B1 C (32) cao
Answer: C) 32

Question 3

B1 31 cao
Answer: 31

Question 4

(a) B1 subtract 12 from the previous term oe
(a) Answer: Subtract 12 from the previous term
(b) B1 152 and 140 both correct cao
(b) Answer: 152, 140

Question 5

B1 C (45) cao
Answer: C) 45

Question 6

B1 13 cao
Answer: 13

Question 7

B1 D (23) cao
Answer: D) 23

Question 8

(a) B1 add 5 to the previous term each time oe
(a) Answer: Add 5 to the previous term each time (starting at 8)
(b) B1 43 cao
(b) Answer: 43

Question 9

(a) B1 4n + 17 oe
(a) Answer: 4n + 17
(b) M1 substitutes n = 40 into 4n + 17
(b) A1 177 cao
(b) Answer: 177

Question 10

B1 81 cao
Answer: 81

Question 11

(a) B1 11, 19, 27 all correct cao
(a) Answer: 11, 19, 27
(b) M1 sets 8n + 3 = 100 and attempts to solve for n
(b) A1 correct conclusion with valid reason: No, because n = 97/8 = 12.125, which is not a whole number
(b) Answer: No, because n is not a whole number (n = 97/8 = 12.125)

Question 12

(a) B1 20 cao
(a) Answer: 20
(b) M1 correct reverse method: divide by 4 then add 6 oe
(b) A1 19 cao
(b) Answer: 19

Question 13

(a) B1 d + 9 oe
(a) Answer: d + 9
(b) B1 k/2 + 4 oe
(b) Answer: k/2 + 4
(c) B1 0.45j oe (accept 9j/20)
(c) Answer: 0.45j (or 9j/20)

Question 14

(a) B1 8y cao
(a) Answer: 8y
(b) B1 3m + 2n oe cao
(b) Answer: 3m + 2n

Question 15

(a) B1 9 cao
(a) Answer: 9
(b) B1 -21 cao
(b) Answer: -21

Question 16

B1 A (-7) cao
Answer: A) -7

Question 17

B1 29 cao
Answer: 29

Question 18

M1 6x = 48 seen
A1 8 cao
Answer: 8

Question 19

M1 4x = 28 seen (correct rearrangement)
A1 7 cao
Answer: 7

Question 20

(a) B1 7n + 3 oe
(a) Answer: 7n + 3
(b) M1 substitutes n = 12 into 7n + 3
(b) A1 correct conclusion: Yes, correct, since 7 x 12 + 3 = 87 and 87 < 90
(b) Answer: Yes, Ronke is correct; stack 12 needs 87 crates, which is fewer than 90
(c) M1 sets 7n + 3 = 129 and attempts to solve
(c) A1 18 cao
(c) Answer: 18

Question 21

M1 7x - 19 = 30 formed, and rearranges to 7x = 49
A1 7 cao
Answer: 7

Question 22

(a) B1 9n + 2 oe
(a) Answer: 9n + 2
(b) B1 137 cao (accept £137)
(b) Answer: £137
(c) M1 sets up 9n + 2 > 200 and attempts to solve, or tests successive weeks
(c) A1 week 23 cao, with week 22 shown not to satisfy the condition
(c) Answer: Week 23

Question 23

M1 correct method, e.g. 4n + 7 > 150 set up, or systematic trial of terms near 150
A1 151 cao (with n = 36 identified)
Answer: 151 (the 36th term)

Question 24

(a) B1 50 - 4n oe (accept -4n + 50)
(a) Answer: 50 - 4n
(b) M1 sets 50 - 4n = 2n + 8 and rearranges, e.g. 42 = 6n
(b) A1 n = 7 cao
(b) Answer: n = 7

Question 25

M1 3x = 24 seen (correct collection of terms)
A1 x = 8 cao
Answer: x = 8

Sequences and Early Algebra: Practice Set 4 - Worksheets, Questions and Revision

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EP.M68 Sequences and Early Algebra: Practice Set 4

Sequences and Early Algebra: Practice Set 4

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

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Question 11

Question 12

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Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25