Foundation - Algebraic Manipulation - GCSE Mathematics

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Foundation - Algebraic Manipulation

infoWhy this? Algebra gives us a language for representing situations, expressing general relationships, and constructing mathematical arguments. Simplifying, expanding, factorising, and substituting help us recognise equivalent expressions and choose useful forms for solving problems.

scheduleWhy now? Building on numerical factors and powers, we extend these ideas to algebraic expressions. Establishing manipulation and substitution here prepares us to work with sequence rules, solve equations, rearrange formulae, and construct graphs later in Year 10.

List all square, cube, and prime numbers up to a given value.
List all factors and multiples of a given number.
Identify the LCM and HCF of any two or more numbers, including using prime factorisation.
Round numbers to the nearest integer, 10, 100, 1000, decimal place, or significant figure as specified.
Estimate answers to calculations by rounding each number to one significant figure and performing the calculation.
Truncate numbers to a specified number of decimal places or significant figures.
Express any number as a product of its prime factors, using index notation where appropriate.
Use prime decomposition to find the LCM and HCF of two or more numbers.
Solve worded problems involving LCM and HCF in real-life contexts (e.g., finding when events coincide, grouping items).
Find upper and lower bounds for a value given a degree of accuracy (e.g., rounding or measurement).
Write error intervals for numbers rounded to a given degree of accuracy, using correct mathematical notation.

rocket_launchYou must be able to

Simplify algebraic expressions by collecting like terms.
Multiply and divide algebraic terms, using the laws of indices.
Expand single brackets and simplify the resulting expressions.
Expand and simplify expressions involving multiple single brackets.
Substitute positive and negative values into basic linear expressions.
Form algebraic expressions from worded problems or statements.
Use algebraic expressions to form and construct simple mathematical arguments or proofs.
Factorise basic linear expressions by taking out a common factor
Expand and simplify double brackets (e.g., (x + 2)(x + 3)).
Substitute values into non-linear expressions (e.g., quadratic or cubic expressions).
Factorise quadratic expressions into single brackets (when possible, e.g., x² + 2x = x(x + 2)).
Factorise quadratic expressions with a unitary coefficient of x² into double brackets (e.g., x² + 5x + 6 = (x + 2)(x + 3)), including the difference of two squares (e.g., x² - 9 = (x + 3)(x - 3)).

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