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Algebra Basics Introduction
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Algebra Basics Introduction
Answer each question. Show working for calculations and equations.
Algebraic terms
1.Match each item to its description: 6m; 11; p; 2p + 9. Descriptions: variable, constant, product of a number and a variable, expression.
- 6m
- 11
- p
- 2p + 9
- Expression
- Variable
- Product of a number and a variable
- Constant
2.Which set contains only like terms?
- 4a, 9a, −a
- 4a, 9b, −a
- 4a, 9, −a
- 4a, 4a², −a
3.In 8q − 5, name the number multiplying q and the constant.
Simplifying and expanding
4.Simplify 7x + 3x.
5.Simplify 6y + 4 − 2y.
6.Simplify 3a + 8 + 2a − 5.
7.Expand 3(n + 4).
8.Expand 5(2r − 3).
9.Simplify 2(3x + 1) + 4x.
Solving equations
10.Solve x + 9 = 17.
11.Solve 4y = 28.
12.Solve 5a − 6 = 24. Show the inverse operations you use.
13.Check the solution x = 6 for 5x + 2 = 32 by substituting it into the left-hand side.
Algebra in context
14.Mele buys c movie tickets costing $12 each. Write an expression for the total cost in dollars.
15.Mele spends $60 on tickets that cost $12 each. Use an equation to find how many tickets she buys.
16.Which statement about algebra is true?
- A variable must always be x.
- Like terms have the same variable part, including the same powers.
- Terms with different variables can always be combined.
- An expression must contain an equals sign.
17.True or false: To keep an equation balanced, whatever operation you perform on one side must also be performed on the other side.
TrueFalse
18.Complete the statement: In 9m + 4, the number multiplying m is the .
19.Explain what it means to collect like terms. Include an example using 2p + 5p.
4 printable pages
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Page 3
Page 4
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