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Introduction to Algebraic Concepts
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Introduction to Algebraic Concepts
Show your working for equations. Use n for the position number in each pattern question.
Algebra vocabulary
1.Match each algebra word to its meaning.
- Variable
- Constant
- Coefficient
- Expression
- D. Numbers, variables and operations combined without an equals sign
- C. A number with no variable attached
- A. A number multiplying a variable, as 6 does in 6p
- B. A letter or symbol that stands for a number
2.In 7a + 9, which symbol is the variable?
- 7
- a
- 9
3.In 4k − 3, which symbol is the variable?
- 4
- k
- 3
4.In 12 + 5r, which symbol is the variable?
- 12
- 5
- r
Writing expressions
5.A book costs $p. Write an expression for the cost of 6 books.
6.Write an expression for a number t increased by 11.
7.Write an expression for 8 times a number q, then subtract 5.
8.At a bookshop, each notebook costs $c. Write an expression for the cost of 3 notebooks plus a $4 gift-wrapping fee.
9.Complete the expression: 9 more than x is x + .
10.Complete both forms: 7 times m is × m, or m.
11.Complete the expression: y decreased by 12 is y − .
Solving equations
12.Solve: x + 9 = 23.
13.Solve: n − 7 = 16.
14.Solve: 4y = 36.
15.Solve: m ÷ 6 = 7.
16.Test x = 8 in the equation x + 5 = 13. Is this value a solution? Show the substitution.
17.Test n = 7 in the equation 3n = 24. Is this value a solution? Show the substitution.
Patterns and rules
Position n
1
2
3
Pattern A
3
6
9
Pattern B
4
9
14
18.Pattern A has values 3, 6, 9, 12, … at positions 1, 2, 3, 4, …. Write a rule for the value at position n.
19.Pattern B has values 4, 9, 14, 19, … at positions 1, 2, 3, 4, …. Write a rule for the value at position n.
20.A sequence begins 2, 5, 8, 11, …. Its first term is at position 1. Write a rule for its nth term.
21.Use the rule 3n to find the value of Pattern A at position 12.
22.Use the rule 3n to find the value of Pattern A at position 25.
23.Use the rule 3n to find the value of Pattern A at position 80.
Algebra in everyday situations
24.Zoe had some bookmarks. She gave 9 away and now has 17. Let b be the number she had first. Write an equation and find b.
25.Hana buys several pens at $5 each and spends $35 altogether. Let p be the number of pens. Write an equation and solve for p.
26.Which equation means that a number k, after being reduced by 8, equals 19?
- k + 8 = 19
- k − 8 = 19
- 8k = 19
- k ÷ 8 = 19
27.At a bookshop, Wiremu buys 4 identical reading journals. They cost $28 in total. Write an equation for the cost j of one journal, then solve it.
4 printable pages
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