Expressions and equations topic check · G1 Mathematics

Practise

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Algebra and equations

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Algebra and equations

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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

Multiply and divide algebraic fractions with domain restrictions · 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 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

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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

Multiply and divide algebraic fractions with domain restrictions · 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 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

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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

Multiply and divide algebraic fractions with domain restrictions · 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 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

Practise questions on the skills you are learning.

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Algebra and equations

Practise: Multiply and divide algebraic fractions with domain restrictions

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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 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

Simplify expressions, interpret sequences and rearrange formulae, then solve linear, simultaneous and quadratic equations with domain checks.

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.
Algebraic fraction products and domains
Cancel factors rather than terms and preserve exclusions when multiplying or dividing algebraic fractions.
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.
Quadratic formula and models
Identify coefficients, retain both possible roots and reject values only for a stated domain reason.

Common mistakes

Mistake Any matching terms above and below a fraction bar can be cancelled.
Correct idea You can cancel only a factor that multiplies the whole numerator and the whole denominator. In (x + 3)/(x + 5), x is part of a sum, so it cannot be cancelled; in (3x)/(5x), x is a factor of both, so the fraction simplifies to 3/5.
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 G1 Mathematics 2027 syllabus

Show all 19 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 number sequences, including nth term for simple cases such as n + 3, 2n + 1
Addition and subtraction of linear expressions
Simplification of linear expressions such as −2(3x − 5) + 4x and 2x/3 − 3(x − 5)/2
Expansion of the product of two linear expressions
Multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10)
Changing the subject of a simple formula
Finding the value of an unknown quantity in a given formula
Factorisation of linear expressions ax + kay
Factorisation of quadratic expressions x² + px + q. Exclude (a ± b)² = a² ± 2ab + b² and a² − b² = (a + b)(a − b), and addition/subtraction of algebraic fractions such as 1/x + 1/(x − 1).
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
Graphs of linear equations in two variables ax + by = c
Solving simultaneous linear equations in two variables by substitution and elimination or graphically
Solving quadratic equations in one variable by formula
Formulating a linear or quadratic equation in one variable or a pair of linear equations in two variables to solve problems

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Revise algebra and equations

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What the syllabus asks