AQA · Mathematics · 8300
GCSE Maths: Function Machines
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Function Machines (Corbettmaths Video 386), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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How do you find the input of a function machine when given the output?
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Work backwards: apply the inverse of each operation in reverse order (e.g. undo the last operation first).
A function machine multiplies by 3 then subtracts 12. Input equals output. Find the input.
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6. Solve 3x − 12 = x, so 2x = 12 and x = 6.
A function machine multiplies by 6 then subtracts 80. Input equals output. Find the input.
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16. Solve 6x − 80 = x, so 5x = 80 and x = 16.
A two-step machine maps 3 → 13 and 8 → 38. What are the two operations?
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Multiply by 5, then subtract 2. (3×5−2 = 13 and 8×5−2 = 38.)
Which function machine gives the output y = x/3 + 2?
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Divide by 3, then add 2.
If the output of a function machine is 120% of the input, what is the multiplier?
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1.2 (output = 1.2 × input).
If 16 km ≈ 10 miles, what single multiplier converts kilometres to miles?
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Multiply by 0.625 (i.e. 5/8), since 10 ÷ 16 = 0.625.
What is 30°C in degrees Fahrenheit?
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86°F. Multiply by 1.8 (or 9/5) and add 32: 30 × 1.8 + 32 = 86.
What is 59°F in degrees Celsius?
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15°C. Subtract 32 then divide by 1.8: (59 − 32) ÷ 1.8 = 15.
How do you write the output of a function machine as an expression when the input is x?
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Apply each operation to x in order, e.g. 'multiply by 2 then add 5' gives 2x + 5.
What is a number (function) machine?
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A diagram that applies one or more operations in order to an input number to produce an output.
Two number machines share the same input x and give equal outputs. How do you find x?
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Write each machine's output as an expression in x, set the two expressions equal, and solve the equation.
How do you complete a two-step number machine given two input–output pairs?
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Let the unknown operations be a and b, write an equation for each pair, and solve the two equations simultaneously.
A machine is '× a then + b'. Input 5 gives 14; input 10 gives 21. Find a.
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a = 1.4. Subtracting the equations 10a + b = 21 and 5a + b = 14 gives 5a = 7.
How do you find the inputs for which a number machine's input exceeds its output?
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Form the inequality x > (output expression in x) and solve it for x.
When solving an inequality, when must you reverse the inequality sign?
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When multiplying or dividing both sides by a negative number.
Outputs of machines A and B are in the ratio 9 : 2 for the same input. What equation do you form?
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2 × (output of A) = 9 × (output of B), with each output written as an expression in the input; then solve.
The inverse operation of multiplying by 3 is ?.
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dividing by 3
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