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Algebraic Concepts Introduction

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Algebraic Concepts Introduction

Read each question carefully. Show your working where helpful. Use algebraic notation in your answers.

Algebraic language

1.Match each algebra term to its meaning.

Variable
Coefficient
Constant
Expression
Equation

The number multiplying a variable
A mathematical statement that says two expressions are equal
A combination of numbers, variables and operations, without an equals sign
A letter or symbol whose value can vary
A number that has no variable attached

2.Which set contains only algebraic expressions?

4p − 9, 2q + 1, 6r
4p = 9, 2q + 1, 6r
12 − 5, 2q = 8, 6r
p + 3 = 10, q − 2 = 6, r

3.For the expression 7m − 12, state the variable, coefficient and constant.

4.Which algebraic expression means five times the sum of a number k and 4?

5k + 4
5(k + 4)
k + 20
5k − 4

5.Decide whether each statement is true or false: a) 3a is an expression. b) 3a = 12 is an expression. c) In 9x + 2, the constant is 2.

TrueFalse

Writing expressions

6.Write an expression for the total price of x notebooks costing $3.40 each, plus a $2 delivery charge.

7.Mere is y years old. Her cousin is 6 years younger. Write an expression for her cousin's age.

8.A cyclist rides at a steady speed of 18 kilometres per hour for h hours. Write an expression for the distance travelled in kilometres.

9.A music app charges $8 per month, plus $1.20 for each downloaded album. Write an expression for the monthly cost when a user downloads d albums.

10.Write an algebraic expression for: divide the difference between x and 11 by 3.

Substitution and patterns

11.Evaluate 4x + 7 when x = 3.

12.Evaluate 6p − 5 when p = 2.5.

13.A rectangle has length L and width W. Its perimeter is P = 2L + 2W. Find P when L = 12 cm and W = 7 cm.

14.A tile pattern has 4 tiles in pattern 1, 7 tiles in pattern 2 and 10 tiles in pattern 3. The number of tiles increases by the same amount each time. Write an expression for the number of tiles in pattern n.

15.Evaluate 2a² − 3b when a = 4 and b = 5.

16.A delivery service charges a fixed fee of $4.50 plus $1.80 per kilometre. Write an expression for a delivery of k kilometres, then calculate the charge for 6 kilometres.