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SQA National 5 Maths Basic algebraic equations

Basic algebraic equations

This page covers the following topics:

For equations with multiple steps, operations must be performed in the following order: Brackets, Indices, Division and Multiplication, Addition and Subtraction. An acronym to remember this is BIDMAS. For the operations that rank equally, operations are performed from left to right.

Order of operations

An expression is a set of terms combined using mathematical operations. An equation is a mathematical statement which shows that two expressions are equal, ie. have the same value. A formula is a rule written in mathematical symbols, which is given as an equation made up of physical quantities. An identity is an equation which is true for any values chosen for the variables.

Vocabulary of equations

A term is either a single number or variable, or numbers and variables multiplied together. A factor is one part of a term which is a product.

Terms and factors

When writing algebraic equations or expression, letters are used to represent unknown values, most commonly x and y; these are known as variables. The rules of algebraic notation given in the table can be used to write and interpret algebraic expressions and equations.

Algebraic notation

The value of an expression can be calculated by putting known values into it in the place of variables and carrying out the operations using BIDMAS. This replacement of letters into values is called substitution.

Substituting values

1

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Calculate 7 + 2 Γ— 3Β² βˆ’ 6.

SQA National 5 Maths Basic algebraic equations Calculate 7 + 2 Γ— 3Β² βˆ’ 6.
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2

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Calculate 6Β² + 18/3 βˆ’ (4 Γ— 2Β³).

SQA National 5 Maths Basic algebraic equations Calculate 6Β² + 18/3 βˆ’ (4 Γ— 2Β³).
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3

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Give the definition of a mathematical expression.

SQA National 5 Maths Basic algebraic equations Give the definition of a mathematical expression.
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4

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Give the definition of a formula.

SQA National 5 Maths Basic algebraic equations Give the definition of a formula.
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5

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Separate the following into expressions and equations:
4x + 3y,
xΒ² = 9,
5z + 3 = 9,
xΒ³ + 5y.

SQA National 5 Maths Basic algebraic equations Separate the following into expressions and equations: 
4x + 3y, 
xΒ² = 9, 
5z + 3 = 9, 
xΒ³ + 5y.
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6

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Write the following definition in algebraic notation: x is added to x and 5 is taken away.

SQA National 5 Maths Basic algebraic equations Write the following definition in algebraic notation: x is added to x and 5 is taken away.
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7

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A stationary shop has a back to school offer. For every notebook sold, the buyer gets 5 pencils. Write an expression relating the number of notebooks (N) with the number of pencils (P).

SQA National 5 Maths Basic algebraic equations A stationary shop has a back to school offer. For every notebook sold, the buyer gets 5 pencils. Write an expression relating the number of notebooks (N) with the number of pencils (P).
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8

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The area of the first rectangle is three more than the area of the second rectangle. In algebraic notation, give an expression for the area of the second rectangle.

SQA National 5 Maths Basic algebraic equations The area of the first rectangle is three more than the area of the second rectangle. In algebraic notation, give an expression for the area of the second rectangle.
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9

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Calculate the value of xΒ² + 7xy + 3y when x = 2 and y = 9.

SQA National 5 Maths Basic algebraic equations Calculate the value of xΒ² + 7xy + 3y when x = 2 and y = 9.
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10

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Find an expression for the perimeter of the given shape and then, calculate the perimeter of the shape when x = 3 and y = 7.

SQA National 5 Maths Basic algebraic equations Find an expression for the perimeter of the given shape and then, calculate the perimeter of the shape when x = 3 and y = 7.
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