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Variables and Expressions

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Variables and Expressions

Work through each section. Show your substitution steps where asked, and use brackets when they help make your meaning clear.

Recognising parts of expressions

Identify variables, constants and algebraic expressions.

1.For each expression, write down every variable: 6p + 4; 2r − 9; 3m + 5n; 11 + q.

2.For each expression, identify the constant term: 8x + 13; 6 − 4y; 5a + 2b − 7; t − 18.

3.Which options are algebraic expressions? Select all that apply.

4z − 3
12
a ÷ 5
y = 9
2m + n
−6

4.Match each algebra term on the left with its description on the right.

Variable
Constant term
Coefficient
Expression
Term
Substitution

A number in an expression with no variable attached
The numerical factor multiplying a variable
Replacing a variable with a given value
A letter representing a value that can change
Numbers, variables and operations combined, without an equals sign
A single part of an expression separated by + or −

Writing expressions

Translate descriptions and situations into algebra.

5.Write an algebraic expression for each description: a number h increased by 11; seven times the number d; 15 less than a number t; twice x, then add 9; the sum of numbers u and v.

6.Kai has c collectible cards. A friend gives Kai 9 more cards. Write an expression for the new total.

7.A rectangle has length 13 cm and width w cm. Write a simplified expression for its perimeter.

8.A streaming service charges a fixed fee of $8 per month plus $3 for each movie rental. If r is the number of rentals, write an expression for the monthly cost in dollars.

Substituting values

Replace variables with the given values and evaluate using the correct order of operations.

9.Evaluate each expression when x = 6: x + 8; 4x; 3x − 5; 2x + 7.

10.Evaluate each expression when y = 9: y − 4; 3y + 2; 5y − 12; 2(y + 3).

11.When a = 4 and b = 7, calculate a + b, 2a + b, 3a + 2b, and a + 3b.

12.Given p = 3 and q = 2, evaluate 2p² + 5q.

Check your understanding

Choose, explain and apply your knowledge of variables and expressions.

13.Which expression means “a number m multiplied by 8, then decreased by 3”?

8 + m − 3
8m − 3
8(m − 3)
m ÷ 8 − 3

14.If n = 5, what is the value of 4n + 6?

15.In the expression 9k − 14, what is the constant term?

9
k
−14
9k

16.A bike hire shop charges $6 to unlock a bike and $4 for each hour of use. Let h represent the number of hours. Write an expression for the total cost, then calculate the cost for 5 hours.

17.Convert a temperature of 20°C to Fahrenheit using F = (9c ÷ 5) + 32, where c is the temperature in degrees Celsius.

18.In your own words, describe what a variable is and give one example of a variable used in an expression.

19.Explain how a variable differs from a constant. Use the expression 5x + 12 in your explanation.