Algebraic expressions · Ages 12–13

Substitution and input–output machines worksheet

Part of: Algebraic expressions & sequences

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Algebraic expressions · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

6.Put 2 into the machine. What is the output?
- A. 11
- B. 28
- C. 14
- D. 16
Choose the right answer
Answer:
7.Put 9 into the machine. What is the output?
- A. 54
- B. 55
- C. 60
- D. 16
Choose the right answer
Answer:
8.The machine's output is 55. What is the input?
- A. 178
- B. 42
- C. 18
- D. 14
Choose the right answer
Answer:
9.The table follows one rule. What number is the '?'?
- A. 34
- B. 45
- C. 30
- D. 39
Choose the right answer
Answer:
10.The machine's output is 82. What is the input?
- A. 63
- B. 757
- C. 9
- D. 7
Choose the right answer
Answer:
11.This table is a function: each input has just one output.
True or false?
Answer:
12.All the outputs in this table come from y = 6x + 9.
True or false?
Answer:

13.A water bill is 40 + 7x dollars for x cubic metres. Last month's was $313. How many cubic metres?
Working:
Answer:
14.A trapezium's area = (a + b)h2. With a = 11 cm, b = 20 cm and h = 4 cm, what is the area in cm²?
Working:
Answer:
15.C degrees Celsius is (9C5 + 32) Fahrenheit. What is 55 degrees Celsius in Fahrenheit?
Working:
Answer:
16.Minutes in, monthly bill in dollars out. What is the bill for 120 minutes?
- A. 240
- B. 270
- C. 210
- D. 600
Choose the right answer
Working:
Answer:
17.An input–output machine gives this table. What is its rule?
- A. y = x + 8
- B. y = 2x + 7
- C. y = 2x + 8
- D. y = 9x
Choose the right answer
Working:
Answer:
18.A machine's rule is 'times 4, add 10', and its output is 22. Backwards: 22 − 10 = , ÷ 4 = , the input.
Fill in each blank
Working:
Answer:

Show the answers and working

Substitution and input–output machines worksheet: Answers and working

6. D. 16
In order: 2 × 7 = 14, then 14 + 2 = 16.
7. B. 55
In order: 9 × 6 = 54, then 54 + 1 = 55.
8. D. 14
Backwards, doing the opposite: 55 − 13 = 42, 42 ÷ 3 = 14.
9. D. 39
Each 1 more in gives 27 − 21 = 6 more out. The rule is y = 6x + 9, so 6 × 5 + 9 = 39. Or simply 33 + 6 = 39.
10. D. 7
Backwards, doing the opposite: 82 − 19 = 63, 63 ÷ 9 = 7.
11. True
1 → 3, 8 → 21, 12 → 17. Only the same input with two different outputs stops it being a function.
12. False
Put each one in: 15, 21 and 27 fit; with x = 4, y = 6 × 4 + 9 = 33, and the table shows 34.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 39
Backwards: 313 − 40 = 273, 273 ÷ 7 = 39. Check with x = 39: 40 + 7 × 39 = 313.
14. 62
The bracket first: 11 + 20 = 31. Then 31 × 4 ÷ 2 = 62.
15. 131
55 × 9 ÷ 5 = 99, then 99 + 32 = 131. Times and divide first, plus last.
16. B. 270
10 more minutes add 20 dollars, so $2 a minute; beyond 2 × 10, 50 has 30 more, the fixed charge. 2 × 120 + 30 = 270.
17. B. y = 2x + 7
Every input must fit. Each 1 more in gives 2 more out; 2 × 1 + 7 = 9, 2 × 2 + 7 = 11, 2 × 3 + 7 = 13.
18. 12, 12, 3
The machine multiplies then adds, so going backwards subtracts then divides: 22 − 10 = 12, 12 ÷ 4 = 3.

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