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KS2 · Algebra

KS2.M-ALG2 Pre-Algebra and Sequences

NATIONAL CURRICULUM National Curriculum (2014) Mathematics - KS2 Algebra (missing numbers, formulae, sequences) · Calculators not allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Find the missing number: 6 + ___ = 13

(1)

Find the missing number: ___ - 8 = 13

(1)

Find the missing number: 9 x ___ = 63

(1)

Find the missing number: ___ / 6 = 8

(1)

Find the missing number in each sentence.

(a)14 + ___ = 22(1)

(b)___ - 15 = 9(1)

A function machine adds 9 to the input.

Figure (to be drawn): input -> +9 -> output

(a)Find the output when the input is 3.(1)

(b)Find the output when the input is 8.(1)

(c)Find the output when the input is 15.(1)

A function machine multiplies the input by 4.

Figure (to be drawn): input -> x4 -> output

(a)The output is 12. Find the input.(1)

(b)The output is 28. Find the input.(1)

(c)The output is 40. Find the input.(1)

A function machine multiplies the input by 3, then adds 2.

Figure (to be drawn): input -> x3 -> +2 -> output

(a)Find the output when the input is 2.(1)

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

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

A function machine multiplies the input by 2, then subtracts 5. The output is 27. Find the input.

Figure (to be drawn): input -> x2 -> -5 -> output

(2)

Find the next two terms in this sequence: 3, 8, 13, 18, ___, ___

(2)

Find the two missing terms in this sequence: 45, ___, 33, ___, 21

(2)

Look at this sequence: 2, 6, 18, 54, ___

(a)Find the next term.(1)

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

At a school fair, raffle tickets cost £5 each. The total cost, C (in pounds), for n tickets is given by the formula C = 5 x n.

(a)Find C when n = 7.(1)

(b)Amara paid £45 for raffle tickets. Find n, the number of tickets she bought.(2)

For a rectangular vegetable patch with length l metres and width w metres, the perimeter P (in metres) is given by the formula P = 2 x (l + w).

(a)A patch has l = 9 m and w = 6 m. Find P.(1)

(b)Another patch has perimeter P = 42 m and length l = 13 m. Find w.(2)

Find the missing number: 3 x ___ + 4 = 25

(2)

Find the missing number: (___ + 5) x 3 = 27

(2)

Rhys programmes a function machine. Input 2 gives output 9. Input 5 gives output 18. Input 8 gives output 27.

Figure (to be drawn): input -> ? -> ? -> output (rule unknown - work it out from the given pairs)

(a)Find the two-step rule connecting the input and the output.(2)

(b)Use your rule to find the output when the input is 12.(1)

Freya makes patterns from matchsticks by joining squares in a row. Pattern 1 has 1 square (4 matchsticks). Pattern 2 has 2 squares (7 matchsticks). Pattern 3 has 3 squares (10 matchsticks).

Figure (to be drawn): Pattern 1: 4 matchsticks -> Pattern 2: 7 matchsticks -> Pattern 3: 10 matchsticks

(a)Find the number of matchsticks in Pattern 4.(1)

(b)Find the number of matchsticks in Pattern 12.(2)

Jack is a plumber. He charges a £25 callout fee plus £30 for each hour he works. The total cost, C (in pounds), for h hours is given by the formula C = 25 + 30h.

(a)Find C when h = 5.(1)

(b)Chidi paid £145 for a job. Find h, the number of hours Jack worked.(2)

Olivia writes a number sequence. It begins at 5, and the term-to-term rule is 'add 7 to the previous term'.

(a)Write the first five terms of the sequence.(1)

(b)Without writing out all the terms, explain how you could find the 25th term of the sequence, and use your method to find its value.(3)

Mark scheme · KS2.M-ALG2 Pre-Algebra and Sequences

Question 1

B1 7 cao
Answer: 7

Question 2

B1 21 cao
Answer: 21

Question 3

B1 7 cao
Answer: 7

Question 4

B1 48 cao
Answer: 48

Question 5

(a) B1 8 cao
(a) Answer: 8
(b) B1 24 cao
(b) Answer: 24

Question 6

(a) B1 12 cao
(a) Answer: 12
(b) B1 17 cao
(b) Answer: 17
(c) B1 24 cao
(c) Answer: 24

Question 7

(a) B1 3 cao
(a) Answer: 3
(b) B1 7 cao
(b) Answer: 7
(c) B1 10 cao
(c) Answer: 10

Question 8

(a) B1 8 cao
(a) Answer: 8
(b) B1 17 cao
(b) Answer: 17
(c) B1 32 cao
(c) Answer: 32

Question 9

M1 27 + 5 (= 32) seen, using the inverse operations in reverse order
A1 16 cao
Answer: 16

Question 10

B1 23 cao
B1 28 cao
Answer: 23, 28

Question 11

B1 39 cao
B1 27 cao
Answer: 39, 27

Question 12

(a) B1 162 cao
(a) Answer: 162
(b) B1 'multiply the previous term by 3' oe
(b) Answer: Multiply the previous term by 3.

Question 13

(a) B1 35 (pounds) cao
(a) Answer: £35
(b) M1 45 / 5 seen or implied
(b) A1 9 cao
(b) Answer: 9

Question 14

(a) B1 30 (m) cao
(a) Answer: 30 m
(b) M1 42 / 2 (= 21) seen, or an equivalent correct method
(b) A1 8 (m) cao
(b) Answer: 8 m

Question 15

M1 25 - 4 (= 21) seen or implied
A1 7 cao
Answer: 7

Question 16

M1 27 / 3 (= 9) seen or implied
A1 4 cao
Answer: 4

Question 17

(a) M1 correctly identifies the first operation, x3 (oe)
(a) A1 correctly identifies the full rule, x3 then +3 (oe) cao
(a) Answer: Multiply by 3, then add 3 (input x 3 + 3)
(b) B1 39 cao, ft their rule from part (a)
(b) Answer: 39

Question 18

(a) B1 13 cao
(a) Answer: 13
(b) M1 4 + 11 x 3 seen, or an equivalent correct method
(b) A1 37 cao
(b) Answer: 37

Question 19

(a) B1 175 (pounds) cao
(a) Answer: £175
(b) M1 145 - 25 (= 120) seen or implied
(b) A1 4 (hours) cao
(b) Answer: 4 hours

Question 20

(a) B1 5, 12, 19, 26, 33 all five correct cao
(a) Answer: 5, 12, 19, 26, 33
(b) M1 correct method shown, e.g. 5 + 24 x 7 (oe)
(b) A1 173 cao
(b) B1 clear explanation that the number of 'add 7' steps needed is one fewer than the term number (oe)
(b) Answer: 173

Pre-Algebra and Sequences - Worksheets, Questions and Revision