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GCSE · Functions

2.8D Function Machines: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculator allowed · about 40 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A function machine multiplies the input by 6. The input is 7. Work out the output.

(Total for Question 1 is 1 mark)

A function machine subtracts 9 from the input. The input is 15. Work out the output.

(Total for Question 2 is 1 mark)

A function machine multiplies the input by 3, then adds 5. The input is 4. Work out the output.

(Total for Question 3 is 2 marks)

A function machine adds 8 to the input, then divides the result by 2. The input is 10. Work out the output.

(Total for Question 4 is 2 marks)

A function machine multiplies the input by 8. The output is 72. Write down the input.

(Total for Question 5 is 1 mark)

A function machine adds 15 to the input then divides by 5. The output is 14. Work out the input.

(Total for Question 6 is 2 marks)

A function machine doubles the input then subtracts 3. The output is 19. Work out the input.

(Total for Question 7 is 2 marks)

A number enters Machine A which adds 4. The result goes into Machine B which multiplies by 5. The starting input is 6. Work out the final output.

(Total for Question 8 is 2 marks)

A function machine multiplies the input by 7 then subtracts 2. Write an expression in terms of x for the output.

(Total for Question 9 is 1 mark)

Given f(x) = 3x + 5. Work out f(4).

(Total for Question 10 is 1 mark)

Let f(x) = 2x - 7 and g(x) = x + 3. Work out g(f(2)).

(Total for Question 11 is 2 marks)

A machine applies f(x) = 3x + 2 then a second machine applies g(x) = x - 5. Work out all values of x such that g(f(x)) = 22.

(Total for Question 12 is 3 marks)

A function f is linear: f(x) = ax + b. Given f(2) = 11 and f(5) = 20, work out a and b, then find the input that gives output 38.

(Total for Question 13 is 4 marks)

A machine multiplies the input by 3/2 then subtracts 4. The output is 8. Work out the input.

(Total for Question 14 is 3 marks)

A machine applies f(x) = kx + 4. Applying the machine twice to the input 1 gives 49, i.e. f(f(1)) = 49. Find all possible values of k.

(Total for Question 15 is 4 marks)

Mark scheme · 2.8D Function Machines: Fluency and Exam Drill

Question 1

B1 42 cao
Answer: 42 (because 6 x 7 = 42).

Question 2

B1 6 cao
Answer: 6 (because 15 - 9 = 6).

Question 3

M1 correct method shown, e.g. 3 x 4 = 12 and then 12 + 5
A1 17 cao
Answer: 17 (3 x 4 + 5 = 17).

Question 4

M1 attempt to add 8 then divide by 2, e.g. (10 + 8) / 2
A1 9 cao
Answer: 9 (because (10 + 8) / 2 = 9).

Question 5

B1 9 cao
Answer: 9 (because input = 72 ÷ 8).

Question 6

M1 reverse method applied, e.g. 14 x 5 = 70
A1 55 cao (70 - 15)
Answer: 55 (because input = 14 x 5 - 15 = 70 - 15 = 55).

Question 7

M1 reverse method or simple algebra, e.g. 2x - 3 = 19 -> 2x = 22
A1 11 cao
Answer: 11 (because 2x - 3 = 19 -> x = 11).

Question 8

M1 apply A then B correctly, e.g. (6 + 4) x 5
A1 50 cao
Answer: 50 (because (6 + 4) x 5 = 50).

Question 9

B1 7x - 2 cao
Answer: 7x - 2.

Question 10

B1 17 cao
Answer: 17 (3 x 4 + 5 = 17).

Question 11

M1 substitute 2 into f, e.g. f(2) = 2 x 2 - 7 = -3
A1 0 cao (g(-3) = -3 + 3 = 0)
Answer: 0 (f(2) = -3, g(-3) = 0).

Question 12

M1 substitute and form equation: g(f(x)) = (3x + 2) - 5 = 3x - 3
M1 solve 3x - 3 = 22 -> 3x = 25
A1 x = 25/3 cao
Answer: 25/3.

Question 13

M1 form two equations: 2a + b = 11 and 5a + b = 20
M1 subtract to find a = 3
M1 substitute a to find b = 5
A1 input 11 cao (solve 3x + 5 = 38 -> x = 11)
Answer: a = 3, b = 5, input = 11.

Question 14

M1 form equation (3/2)x - 4 = 8 or equivalent
M1 isolate x: (3/2)x = 12 -> x = 12 x 2/3
A1 8 cao
Answer: 8.

Question 15

M1 substitute: f(1) = k + 4, then f(f(1)) = k(k + 4) + 4
M1 form quadratic: k² + 4k + 4 = 49 -> k² + 4k - 45 = 0
M1 factor or use formula, e.g. (k + 9)(k - 5) = 0
A1 k = 5 or k = -9 cao
Answer: k = 5 or k = -9.

Function Machines: Fluency and Exam Drill - Worksheets, Questions and Revision