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Variables and Algebraic Expressions
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Variables and Algebraic Expressions
Answer each question. Use a letter to stand for an unknown or changing number.
Variables and notation
1.In algebra, what does a variable usually represent?
- A fixed operation such as addition
- A number that is unknown or can change
- The final answer to every calculation
- A number that must always be zero
2.Which expressions mean 4 multiplied by t? Select all that apply.
- 4t
- 4 × t
- 4 + t
- t ÷ 4
3.A sequence begins 6, 10, 14, 18, 22, … What is the increase from one term to the next, and what letter could represent the term's position?
Writing expressions and rules
4.A museum entry ticket costs $9. Write an expression for the cost of g tickets.
5.A sequence starts at 5 and increases by 3 each time. Find the values at positions 4 and 5, then write a rule for the value at position n.
6.Ari has $64 in a savings jar and takes out $7 each week. Write an expression for the amount left after w weeks.
7.Write an algebraic expression for each description: 1) k increased by 9; 2) 6 multiplied by r; 3) 15 less than d; 4) one third of q.
Using algebra to solve problems
8.A rectangular paddock is 8 metres longer than it is wide. If its width is x metres, write an expression for its length and an expression for its perimeter.
9.A growing tile pattern has 3 tiles in Pattern 1, and each new pattern adds 2 tiles. How many tiles are in Pattern 10, and what rule gives the number of tiles in Pattern n?
10.Explain how the starting tile count and the number added each time help you write the rule 2n + 1 for the growing pattern.
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