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Ignition Learning — Activity Sheet

Introduction to algebra

Mathematics · Year 7

Name: ______________________Date: ____________

Algebra uses a letter, called a pronumeral or variable, to stand in for a number we don't know yet — often x or n. An expression like "3n + 2" means "3 lots of n, plus 2". You can substitute a number for the pronumeral to work out the value, and combine "like terms" (terms with the same letter) to simplify expressions.

Example

A takeaway charges $3 delivery plus $8 per pizza. If n is the number of pizzas, the total cost is 8n + 3. For 2 pizzas: 8(2) + 3 = $19.

Key terms

Pronumeral:: A letter used to represent an unknown number.
Expression:: A combination of numbers, pronumerals and operations, e.g. 3n + 2.
Substitute:: Replacing a pronumeral with a given number.

Questions

1. In the expression 3n + 2, what does n represent?
- A fixed number
- An unknown number
- A fraction always
- Nothing
2. If n = 4, what is n + 5?
- 9
- 20
- 1
- 45
3. If n = 3, what is 2n?
- 5
- 6
- 23
- 9
4. A pronumeral is:
- A letter standing for an unknown number
- A type of fraction
- A percentage
- A ratio
5. If n = 10, what is n − 4?
- 4
- 6
- 14
- 40
6. What does "5n" mean?
- 5 plus n
- 5 times n
- 5 minus n
- n divided by 5
7. If n = 2, what is 3n + 1?
- 5
- 6
- 7
- 9
8. If n = 5, what is 4n + 3?
- 20
- 23
- 17
- 35
9. Simplify: 3n + 2n
- 5n
- 6n
- 5n²
- 2n
10. A delivery costs $3 plus $8 per pizza (n pizzas). Write this as an expression.
- 8n + 3
- 3n + 8
- 8 + 3 + n
- n(8 + 3)
11. Using 8n + 3, what is the cost for 2 pizzas?
- $16
- $19
- $22
- $11
12. Simplify: 5n − 2n
- 3n
- 3
- 7n
- 10n
13. If a = 3 and b = 4, what is a + b?
- 1
- 7
- 12
- 34
14. Simplify: 4n + 3 + 2n
- 6n + 3
- 9n
- 6n + 3n
- 9n + 3
15. A phone plan costs $20 plus $2 per gigabyte (g). Write an expression for the total cost.
- 2g + 20
- 20g + 2
- 22g
- g + 22
16. Using 2g + 20, what is the cost for 6 gigabytes?
- $26
- $32
- $120
- $22
17. Simplify: 3n + 5 + 2n − 2
- 5n + 3
- 5n + 7
- 3n + 3
- 1n + 3
18. If x = 5, what is 2(x + 3)?
- 13
- 16
- 10
- 11
19. A theme park charges $15 entry plus $4 per ride (r). Write an expression for total cost.
- 4r + 15
- 15r + 4
- 19r
- r + 19
20. Using 4r + 15, how much would 5 rides cost in total?
- $19
- $20
- $35
- $75
21. Simplify: 6n + 4 − 2n − 1
- 4n + 3
- 4n + 5
- 8n + 3
- 4n − 3

Answer key (parent copy)

1. An unknown number
2. 9
3. 6
4. A letter standing for an unknown number
5. 6
6. 5 times n
7. 7
8. 23
9. 5n
10. 8n + 3
11. $19
12. 3n
13. 7
14. 6n + 3
15. 2g + 20
16. $32
17. 5n + 3
18. 16
19. 4r + 15
20. $35
21. 4n + 3