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Function machines Quiz

Grade 2 • 2H • 10 Questions (28 Marks)

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Function machines — Notes & Worked Examples Show / Hide

Explanation:

To find the output of a function machine, start with the input and apply each operation in order from left to right. To find the input when given the output, work backwards from right to left using the inverse (opposite) operations (+ becomes −, × becomes ÷).

When the input is a letter x, write the algebraic result after each box to form an expression or equation.

Input × 4 − 7 Output

Example 1: Using the machine above:
(a) Find the output when the input is 6.
(b) Find the input when the output is 29.

(a) Forward: 6 × 4 = 24, then 24 − 7 = 17
(b) Reverse with inverse operations (+ 7, then ÷ 4):
• 29 + 7 = 36, then 36 ÷ 4 = 9

Example 2: Using the machine above:
(a) Write the output when the input is x.
(b) Find x when the output is equal to x + 20.

(a) x → 4x → 4x − 7
(b) Solve 4x − 7 = x + 20 → 3x = 27 → x = 9
Question 1
[1 mark]
Solve
5x + 7 = 37
x =
Worked Solution & Answer
5x = 30 ⇒ x = 6 B1
Answer: x = x = 6
Question 2
[2 marks]
Input× 5+ 8Output
Find the output when the input is 9
Worked Solution & Answer
(9 × 5) + 8 = 53 B1
Answer: 53
Question 3 AQA Nov 2022 3F Q13
[1 mark]
Luke wants to make a number machine so that y = 5x + 3
Here is his attempt.
Inputx+ 3× 5Outputy
What mistake has he made?
Worked Solution & Answer
His machine gives (x + 3) × 5 = 5x + 15
To get 5x + 3, the machine must do × 5 first, then + 3. B1
Inputx+ 3× 5OutputyGives 5(x + 3) = 5x + 15; should multiply by 5 then add 3
Answer: Mistake He added 3 before multiplying by 5 instead of multiplying by 5 then adding 3
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 AQA Nov 2024 3F Q8
[2 marks]
Here is a number machine.
InputOutput× 2+ 3
(a) Work out the **output** when the input is 10 [1 mark]
Answer
(b) Work out the **input** when the output is 17 [1 mark]
Answer
Worked Solution & Answer
(a)
10 × 2 + 3 = 23 B1
Answer (a): Answer 23
(b)
(17 - 3) ÷ 2 = 7 B1
Answer (b): Answer 7
Question Paper (PDF) • Mark Scheme (PDF)
Question 5
[2 marks]
Here is a number machine.
input× 8– 5output
(a) Work out the output when the input is 6 [1 mark]
(b) Complete the number machine. [1 mark]
input+ 13output
Worked Solution & Answer
(a)
6 × 8 – 5 = 48 – 5 = 43 B1
Answer (a): 43
(b)
17 + 13 = 30
30 – 20 = 10 or 30 ÷ 3 = 10 B1
Answer (b): – 20 or ÷ 3
Question Paper (PDF) • Mark Scheme (PDF)
Question 6
[3 marks]
Here is a number machine.
input× 3– 8output
(a) Find the output when the input is 6 [1 mark]
(b) Find the input when the output is –11 [2 marks]
Worked Solution & Answer
(a)
6 × 3 – 8 = 18 – 8 = 10 B1
Answer (a): 10
(b)
(–11 + 8) ÷ 3 = –3 ÷ 3 = –1 M1 A1
Answer (b): –1
Question Paper (PDF) • Mark Scheme (PDF)
Question 7
[4 marks]
Here is a number machine.
input+ 5÷ 2output
(a) Find the output when the input is 11 [2 marks]
(b) When the input is 10, the output is 28
Complete this number machine. [2 marks]
input× 4output
Worked Solution & Answer
(a)
(11 + 5) ÷ 2 = 8 M1 A1
Answer (a): 8
(b)
28 ÷ 4 = 7 M1
10 – 3 = 7 A1
Answer (b): – 3 (or × 0.7)
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 AQA Jun 2023 1H Q13
[4 marks]
(a) Number machine: x → ×a → +b → y. Show that when the input increases by 2 the output increases by 2a. [2 marks]
13 (b) f(x) = kx². Kai says f(6)/f(2) = f(3) because 6/2 = 3. Is he correct? [2 marks]
(a) Here is a number machine. [2 marks]
Inputx× a+ bOutputy
Show that when the input increases by 2 the output increases by 2a.
(b) f(x) = kx2 where k is a constant.
Kai says that f(6)f(2) is equal to f(3) because 62 = 3
Is he correct?
Show working to support your answer. [2 marks]
Worked Solution & Answer
(a)
Output for x is ax + b M1
Output for x + 2 is a(x + 2) + b = ax + 2a + b
Difference = 2a C1
Answer (a): y₁ = ax + b; y₂ = a(x + 2) + b = ax + 2a + b, which is 2a more than ax + b
(b)
f(6)/f(2) = (36k)/(4k) = 9, whereas f(3) = 9k, so he is not correct (unless k = 1) M1 C1
Answer (b): No — f(6)/f(2) = 36k / 4k = 9, whereas f(3) = 9k (only equal if k = 1)
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 AQA Jun 2025 3F Q4
[4 marks]
Here is a number machine.
Input× 3– 5Output
(a) Work out the output when the input is 4 [1 mark]
Answer
(b) Work out the input when the output is 19 [2 marks]
Answer
(c) Complete this number machine. [1 mark]
Input16+ 2Output3
Worked Solution & Answer
(a)
4 × 3 – 5 = 12 – 5 = 7 B1
Answer (a): Answer 7
(b)
Reverse machine: (19 + 5) ÷ 3 = 24 ÷ 3 = 8 M1 A1
Answer (b): Answer 8
(c)
16 + 2 = 18
To get 3 from 18: 18 ÷ 6 = 3 (or 18 – 15 = 3) B1
Input16+ 2÷ 6Output3
Answer (c): ÷ 6 (or – 15)
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[5 marks]
Here is a number machine.
input× 2– 10output
(a) Work out the output when the input is 13 [1 mark]
(b) Work out the input when the output is 28 [2 marks]
(c) Show that there is a number for which the output is the same as the input. [2 marks]
Worked Solution & Answer
(a)
13 × 2 – 10 = 26 – 10 = 16 B1
Answer (a): 16
(b)
(28 + 10) ÷ 2 = 38 ÷ 2 = 19 M1 A1
Answer (b): 19
(c)
2x – 10 = x M1
⇒ x = 10 (10 × 2 – 10 = 10) C1
Answer (c): Input = 10: 10 × 2 – 10 = 10
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 28 marks)
Function machines Worksheets Next: Solving one step equations →

Grade 2 Quizzes

19 Topics
2A - Calculation problems2B - Using a calculator
2C - Systematic listing2D - Fraction of an amount
2E - FDP2F - Simplifying algebra
2G - Writing an expression2H - Function machines
2J - Solving one step equations2K - Angles
2L - Area and perimeter2M - Reading scales
2N - Probability & Probability Scale2P - Frequency polygons
2Q - Unitary method2R - Bar charts
2S - Pie charts2T - Averages
2U - Stem and leaf diagrams