Algebraic Manipulation
Expressions, indices, identities, expansion and factorisation.
Simplifying algebraic expressionsCollect like terms, apply the distributive law, and keep algebra tidy for later equation work.Algebraic Manipulation· Mr NgMCQ2
Laws of integral indicesMaster product, quotient, power and zero-index laws for Secondary 3 integral indices.Algebraic Manipulation· Mr NgMCQ3
Identities and algebraic expansionUse standard identities to expand quickly and to recognise structure in reverse for factorisation.Algebraic Manipulation· Ms ChuMCQ4
Factorisation: common factors and groupingTake out the highest common factor and factor by grouping before attempting harder patterns.Algebraic Manipulation· Ms ChuMCQ5
Factorising difference of squaresRecognise a² − b² instantly and factor as (a − b)(a + b), including with coefficients.Algebraic Manipulation· Ms ChuMCQ6
Negative indices and positive-index answersSimplify products and quotients with negative indices, then rewrite with positive indices as papers usually demand.Algebraic Manipulation· Mr NgMCQ7
Expanding binomials (exam practice)Expand products such as (x−1)(x+5) and arrange polynomials in descending powers of x.Algebraic Manipulation· Mr NgMCQ8
Factorising quadratics (cross method)Factorise x² + bx + c and ax² + bx + c — a known weak area in S3 assessments.Algebraic Manipulation· Mr NgMCQ9
Factorisation by grouping and common binomialsFactor expressions such as 5(x+y) − a(x+y) and four-term groupings.Algebraic Manipulation· Ms ChuMCQ10
Adding and multiplying polynomialsAdd, subtract and multiply polynomials, then arrange in descending powers of x.Algebraic Manipulation· Ms ChuMCQ11
Substituting values into algebraic expressionsReplace letters carefully with brackets, especially for negatives.Algebraic Manipulation· Mr ChanMCQ12
Collecting like terms with several variablesSort x, y and constant terms before combining coefficients.Algebraic Manipulation· Ms LamMCQ13
Expanding single bracketsDistribute positive and negative factors across sums and differences.Algebraic Manipulation· Mr NgMCQ14
Expanding two brackets with FOILProduce four products then collect like terms reliably.Algebraic Manipulation· Ms ChuMCQ15
Using perfect square identitiesRecognise and expand (a±b)² without missing the middle term.Algebraic Manipulation· Mr YipMCQ16
Recognising a³ − b³ patterns (intro)Spot cubes and quote a³ − b³ = (a−b)(a²+ab+b²) at junior challenge level.Algebraic Manipulation· Mr ChanMCQ17
Factorising ax² + bx + c when a ≠ 1Split the middle term or use cross method for leading coefficient not 1.Algebraic Manipulation· Ms LamMCQ18
Mixed laws of indices practiceCombine product, quotient and power laws in one simplification.Algebraic Manipulation· Mr NgMCQ19
Zero and negative indices drillEvaluate and rewrite expressions that include a⁰ and a^{−n}.Algebraic Manipulation· Ms ChuMCQ20
Linking indices to scientific notationMove between ordinary form and a×10ⁿ using index laws.Algebraic Manipulation· Mr YipMCQ