Expressions, equations and inequalities topic check · G2 Mathematics

Practise

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Algebra and equations

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Algebra and equations

Check your progress

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Algebra and equations

Simplify linear expressions by combining like terms · Check your progress

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Algebra and equations

Expand and factorise algebraic expressions · Check your progress

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Algebra and equations

Change the subject of a formula · Check your progress

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Algebra and equations

Evaluate an algebraic expression by substitution · Check your progress

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Algebra and equations

Represent a situation with algebraic expressions · Check your progress

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Algebra and equations

Express and use the general term of a sequence · Check your progress

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Algebra and equations

Calculate and simplify algebraic fractions with restrictions · Check your progress

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Algebra and equations

Solve quadratic equations by suitable methods · Check your progress

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Algebra and equations

Solve a system of linear equations completely, including systems with no or infinitely many solutions · Check your progress

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Algebra and equations

Solve linear inequalities and show the solution set on a number line · Check your progress

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Algebra and equations

Solve a first-degree equation by a specified expansion or denominator-clearing step, preserving original exclusions · Check your progress

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Algebra and equations

Apply the quadratic formula with signed coefficients, both branches and the complete real solution set · Check your progress

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Algebra and equations

Check again

After practising what your progress check showed, check those skills again.

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Algebra and equations

Simplify linear expressions by combining like terms · Check again

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Algebra and equations

Expand and factorise algebraic expressions · Check again

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Algebra and equations

Change the subject of a formula · Check again

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Algebra and equations

Evaluate an algebraic expression by substitution · Check again

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Algebra and equations

Represent a situation with algebraic expressions · Check again

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Algebra and equations

Express and use the general term of a sequence · Check again

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Algebra and equations

Calculate and simplify algebraic fractions with restrictions · Check again

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Algebra and equations

Solve quadratic equations by suitable methods · Check again

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Algebra and equations

Solve a system of linear equations completely, including systems with no or infinitely many solutions · Check again

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Algebra and equations

Solve linear inequalities and show the solution set on a number line · Check again

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Algebra and equations

Solve a first-degree equation by a specified expansion or denominator-clearing step, preserving original exclusions · Check again

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Algebra and equations

Apply the quadratic formula with signed coefficients, both branches and the complete real solution set · Check again

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Algebra and equations

Retention check

Come back later to see whether your learning has lasted.

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Algebra and equations

Simplify linear expressions by combining like terms · Retention check

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Algebra and equations

Expand and factorise algebraic expressions · Retention check

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Algebra and equations

Change the subject of a formula · Retention check

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Algebra and equations

Evaluate an algebraic expression by substitution · Retention check

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Algebra and equations

Represent a situation with algebraic expressions · Retention check

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Algebra and equations

Express and use the general term of a sequence · Retention check

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Algebra and equations

Calculate and simplify algebraic fractions with restrictions · Retention check

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Algebra and equations

Solve quadratic equations by suitable methods · Retention check

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Algebra and equations

Solve a system of linear equations completely, including systems with no or infinitely many solutions · Retention check

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Algebra and equations

Solve linear inequalities and show the solution set on a number line · Retention check

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Algebra and equations

Solve a first-degree equation by a specified expansion or denominator-clearing step, preserving original exclusions · Retention check

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Algebra and equations

Apply the quadratic formula with signed coefficients, both branches and the complete real solution set · Retention check

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Algebra and equations

Practise: Simplify linear expressions by combining like terms

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Algebra and equations

Practise: Expand and factorise algebraic expressions

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Algebra and equations

Practise: Change the subject of a formula

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Algebra and equations

Practise: Evaluate an algebraic expression by substitution

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Algebra and equations

Practise: Represent a situation with algebraic expressions

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Algebra and equations

Practise: Express and use the general term of a sequence

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Algebra and equations

Practise: Calculate and simplify algebraic fractions with restrictions

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Algebra and equations

Practise: Solve quadratic equations by suitable methods

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Algebra and equations

Practise: Solve a system of linear equations completely, including systems with no or infinitely many solutions

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Algebra and equations

Practise: Solve linear inequalities and show the solution set on a number line

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Algebra and equations

Practise: Solve a first-degree equation by a specified expansion or denominator-clearing step, preserving original exclusions

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Algebra and equations

Practise: Apply the quadratic formula with signed coefficients, both branches and the complete real solution set

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Algebra and equations

Revision notes

Revise algebra and equations

Transform algebraic expressions and fractions, factor quadratics, rearrange formulae and solve equations and linear inequalities.

Key ideas

Notation, evaluation and algebraic models
Interpret grouped algebraic notation and define a letter before substituting a value.
Read a sequence rule
Use the given position in a stated rule without confusing the term value with its index.
Linear expressions with integer coefficients
Distribute every sign through a bracket and combine only like terms.
Linear expressions with fractional coefficients
Use common denominators to combine fractional linear coefficients without losing bracket signs.
Linear equations with integer coefficients
Apply the same reversible operation on both sides and check the answer in the original equation.
Equations as balanced relationships
Preserve equality through each solution step and test a candidate solution in the original equation.
Sequences and nth terms
Relate a position to its term and distinguish a matching rule from evidence of a unique pattern.
Common factors and formula subjects
Reverse distribution, change a formula's subject and find an unknown value from the given quantities.
Products and simple quadratic factors
Distribute two linear factors and reverse the product for monic quadratics.
Identities and general quadratic factors
Derive useful identities by distribution and verify every factorisation by expansion.
Four-term common factors
Group terms to expose a matching complete factor and verify it by expansion.
Algebraic fraction products and domains
Cancel factors rather than terms and preserve exclusions when multiplying or dividing algebraic fractions.
Algebraic fraction sums
Choose a common denominator, retain excluded values and simplify only complete factors.
Fractional linear equations
Clear every denominator and check both the original domain and the solution.
Simultaneous linear equations
Construct two linear graphs, solve for their common pair and check graphical readings with algebra.
Zero products and quadratic equations
Set a factored quadratic equal to zero and retain every factor alternative.
Quadratic formula and models
Identify coefficients, retain both possible roots and reject values only for a stated domain reason.
Completing the square and fractional quadratics
Choose an exact quadratic method and distinguish solving from rewriting a function.
Linear inequalities
Reverse the order relation when multiplying or dividing by a negative number.

Common mistakes

Mistake An equals sign tells me to write the next calculation.
Correct idea An equals sign means that the two sides have the same value. It is not a signal to write the next step, so 3 + 5 = 8 × 2 = 16 is wrong, because 3 + 5 is not equal to 16.

What the syllabus asks

From the G2 Mathematics 2027 syllabus

Show all 23 syllabus statements

Using letters to represent numbers
Interpreting notations: ab as a × b; a/b as a ÷ b or a × (1/b); a² as a × a, a³ as a × a × a, a²b as a × a × b, …; 3y as y + y + y or 3 × y; 3(x + y) as 3 × (x + y); (3 + y)/5 as (3 + y) ÷ 5 or (1/5) × (3 + y)
Evaluation of algebraic expressions and formulae
Translation of simple real-world situations into algebraic expressions
Recognising and representing patterns/relationships by finding an algebraic expression for the nth term
Addition and subtraction of linear expressions
Simplification of linear expressions such as −2(3x − 5) + 4x and 2x/3 − 3(x − 5)/2
Use brackets and extract common factors
Factorisation of linear expressions ax + bx + kay + kby
Expansion of the product of algebraic expressions
Changing the subject of a formula
Finding the value of an unknown quantity in a given formula
Use of (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², a² − b² = (a + b)(a − b)
Factorisation of quadratic expressions ax² + bx + c
Multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10)
Addition and subtraction of algebraic fractions with linear or quadratic denominator such as 1/(x − 2) + 2/(x − 3); 1/(x² − 9) + 2/(x − 3); 1/(x − 3) + 2/(x − 3)²
Solving linear equations in one variable
Solving simple fractional equations that reduce to linear equations, such as x/3 + (x − 2)/4 = 3 and 3/(x − 2) = 6
Solving simultaneous linear equations in two variables by substitution and elimination or graphically
Solving quadratic equations in one variable by factorisation, formula, completing the square for y = x² + px + q, or graphically
Solving fractional equations that reduce to quadratics, such as 6/(x + 4) = x + 3 and 1/(x − 2) + 2/(x − 3) = 5
Formulating equations to solve problems
Solving simple inequalities ax ≤ b, ax ≥ b, ax < b, ax > b where a and b are integers

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Revise algebra and equations

Key ideas

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What the syllabus asks