Algebra Practice Test for Key Algebra Topics
Use these interactive algebra practice questions to revise linear equations, fraction equations, cross multiplication, word problems, brackets, variables on both sides and challenging algebra problem solving.
Basic Linear Equations Practice
Fraction Equations and Cross Multiplication Practice
Multi-Step Linear Equations Practice
Algebra Word Problems Practice
Advanced Fraction Equations Practice
Fractions with Variables on Both Sides Practice
Brackets and Fractions Practice
Challenging Algebra Word Problems Practice
What is Algebra? Why do we use it?
Algebra is a part of maths where we use letters, symbols and numbers to represent unknown values and solve problems. We use algebra because it helps us solve problems where we do not know the exact number yet. Instead of guessing, algebra gives us a clear method.
What are the topics covered in Algebra?
The topics covered in algebra are:
- Pronumerals, variables and constants
- Algebraic expressions and equations
- Algebraic notation, such as
4x,ab,x² - Writing algebra from everyday language
- Substitution of values into expressions
- Number patterns and algebraic rules
- Like and unlike terms
- Simplifying algebraic expressions
- Expanding brackets
- Factorising expressions
- Basic linear equations
- Fraction equations
- Word problems using algebra
- Properties of arithmetic: commutative, associative and distributive laws
Algebraic Techniques
- A pronumeral is a letter or symbol used to represent a number in algebra. For example, in x+5 the letter x is a pronumeral.
- When a pronumeral can take different values, it’s called a variable.
- If the value is fixed, it’s called a constant. Example : 5, 7, 12 etc.
- An algebraic expression is made up of numbers, pronumerals, and operations like addition, subtraction, multiplication, and division. Examples: 3x, 2a+5, x/2+4
- An expression does not have an equals sign — it’s different from an equation.
Algebra Notation
In algebra, algebraic notation is a shorter way to write multiplication, powers and division so expressions are easier to read and solve:
- ab means a × b
- xyz means x × y × z
- a2 means a × a
- y3 means y × y × y
- a/b means a÷b
- Write 4x, and not 4 × x
Writing Algebraic Expressions from Words
In algebra, We need to translate everyday language into algebraic expressions. Focus on the statements and what they mean to write the algebraic expression.
Examples:
- “Five more than a number” → x+5
- “A number divided by 3” → x/3
- “Double a number and subtract 7” → 2x−7
Algebra Substitution
In algebra substitution, the pronumeral is replaced with a number
Example:
If x=3 then: 4x+1 = 4(3)+1 = 12 +1= 13
Algebra can describe patterns in numbers
Example: Pattern: 3, 5, 7, 9, 11; Expression: 2n+1 (where n is the position in the pattern)
Like and Unlike Terms
Like terms have the same variable and power.
You can add or subtract them.
Examples: 3x+4x = 7x; 5a−2a = 3a
If terms are not like terms, you cannot combine them.
For example: 2x+3y; 4a + 2b; stays the same.
Properties of Arithmetic in Algebra
- Commutative Property: Order doesn’t matter for addition or multiplication
a+b = b+a & ab = ba - Associative Property: Grouping doesn’t change the result: (a+b)+c = a+(b+c)
- Distributive Property: You multiply the number outside the brackets by each term inside: a(b+c) = ab+ac
- Factorizing: You factor out the common factor and put it back into brackets:
- ab+ac = a(b+c)
