Numbers & Estimation · Mr Chan
Directed numbers: add, subtract, multiply and divide
Use number-line sense and sign rules so directed-number calculations stay accurate under exam pressure.
(+a)+(+b)=+(a+b)
MCQPracticeWorked example
Solid Number
Number & Algebra lessons for Hong Kong Secondary 2–3
Directed numbers, percentages, indices, factorisation and equations — each lesson packs formulas, a worked example, written practice and MCQ drills.
Indices
Square
Difference of squares
Percentage
Topics & sample lessons
Numbers & Estimation
Directed numbers, approximate values, primes and scientific notation.
- Directed numbers: add, subtract, multiply and divide(+a)+(+b)=+(a+b)
- Approximate values and sensible estimationNearest 10: look at units digit
- Rational numbers: fractions, decimals and recurring decimalsa/b = terminating or recurring decimal
- Prime factorisation, HCF and LCMHCF: take lowest powers of common primes
Percentage, Rate & Ratio
Percentage change, successive %, rate, ratio and proportion.
- Percentage increase and decreaseNew = Original × (1 ± r/100)
- Successive percentage changesFinal = Original × m1 × m2 × …
- Rate, ratio and direct proportiona:b = (a÷k):(b÷k)
- Percentage applications: discount, profit and simple interestSelling price = Cost × (1 ± profit or loss %)
Algebraic Manipulation
Expressions, indices, identities, expansion and factorisation.
- Simplifying algebraic expressionsa + a = 2a
- Laws of integral indicesa^m × a^n = a^{m+n}
- Identities and algebraic expansion(a+b)^2 = a^2 + 2ab + b^2
- Factorisation: common factors and groupingax + ay = a(x + y)
Equations & Inequalities
Linear equations, inequalities and changing the subject.
- Linear equations in one unknownIf a = b then a + c = b + c
- Linear equations in two unknownsSubstitution: solve for one variable, then replace
- Linear inequalities in one unknownIf a < b then a + c < b + c
- Changing the subject of a formulaInverse steps undo the formula
Exam & Challenge
TSA-style mixed drills and harder Number & Algebra problems.
- Mixed Number & Algebra drill (TSA style)Use the method of the topic asked
- Challenge: indices + factorisation comboSimplify indices before expanding when helpful
- Exam mix: directed numbers and percentagesReset method each question
- Exam mix: indices and expansionPositive indices at the end
Key formulas
Drill with quizIndices
Square
Difference of squares
Percentage
Negative index
Direct proportion
Featured lessons
All lessonsPercentage, Rate & Ratio · Ms Lam
Percentage increase and decrease
Convert between percentages and multipliers so increase and decrease problems stay consistent.
New = Original × (1 ± r/100)
MCQPracticeWorked example
Algebraic Manipulation · Mr Ng
Laws of integral indices
Master product, quotient, power and zero-index laws for Secondary 3 integral indices.
a^m × a^n = a^{m+n}
MCQPracticeWorked example
Algebraic Manipulation · Mr Ng
Factorising quadratics (cross method)
Factorise x² + bx + c and ax² + bx + c — a known weak area in S3 assessments.
x^2 + (p+q)x + pq = (x+p)(x+q)
MCQPracticeWorked example
Percentage, Rate & Ratio · Ms Lam
Reverse percentage problems
Recover the original value after a percentage change — classic exam reverse-percentage items.
Original = New ÷ (1 ± r/100)
MCQPracticeWorked example
Equations & Inequalities · Mr Yip
Linear equations in two unknowns
Solve simultaneous linear equations by substitution and elimination — core Secondary 3 skills.
Substitution: solve for one variable, then replace
MCQPracticeWorked example
Percentage, Rate & Ratio · Ms Lam
Successive percentage changes
Combine successive percentage changes by multiplying multipliers — never by adding the percentages.
Final = Original × m1 × m2 × …
MCQPracticeWorked example
Exam & Challenge · Mr Chan
Mixed Number & Algebra drill (TSA style)
A timed-style mixed set: primes, percentage change, expansion, factorisation and a linear equation.
Use the method of the topic asked
MCQPracticeWorked example
All lessons
Page 1/51Directed numbers: add, subtract, multiply and divideUse number-line sense and sign rules so directed-number calculations stay accurate under exam pressure.Numbers & Estimation· Mr Chan(+a)+(+b)=+(a+b)MCQPractice2Approximate values and sensible estimationRound to a required accuracy, estimate products and quotients, and check whether an answer is reasonable.Numbers & Estimation· Mr ChanNearest 10: look at units digitMCQPractice3Rational numbers: fractions, decimals and recurring decimalsConvert between fractions and decimals, recognise recurring decimals, and keep rational arithmetic organised.Numbers & Estimation· Ms Lama/b = terminating or recurring decimalMCQPractice4Percentage increase and decreaseConvert between percentages and multipliers so increase and decrease problems stay consistent.Percentage, Rate & Ratio· Ms LamNew = Original × (1 ± r/100)MCQPractice5Successive percentage changesCombine successive percentage changes by multiplying multipliers — never by adding the percentages.Percentage, Rate & Ratio· Ms LamFinal = Original × m1 × m2 × …MCQPractice6Rate, ratio and direct proportionExpress ratios in simplest form, share quantities, and solve direct proportion problems with clear units.Percentage, Rate & Ratio· Ms Lama:b = (a÷k):(b÷k)MCQPractice7Percentage applications: discount, profit and simple interestApply percentage tools to discount, profit/loss and simple interest — standard Secondary 2–3 applications.Percentage, Rate & Ratio· Ms LamSelling price = Cost × (1 ± profit or loss %)MCQPractice8Simplifying algebraic expressionsCollect like terms, apply the distributive law, and keep algebra tidy for later equation work.Algebraic Manipulation· Mr Nga + a = 2aMCQPractice9Laws of integral indicesMaster product, quotient, power and zero-index laws for Secondary 3 integral indices.Algebraic Manipulation· Mr Nga^m × a^n = a^{m+n}MCQPractice10Identities and algebraic expansionUse standard identities to expand quickly and to recognise structure in reverse for factorisation.Algebraic Manipulation· Ms Chu(a+b)^2 = a^2 + 2ab + b^2MCQPractice11Factorisation: common factors and groupingTake out the highest common factor and factor by grouping before attempting harder patterns.Algebraic Manipulation· Ms Chuax + ay = a(x + y)MCQPractice12Factorising difference of squaresRecognise a² − b² instantly and factor as (a − b)(a + b), including with coefficients.Algebraic Manipulation· Ms Chua^2 − b^2 = (a − b)(a + b)MCQPractice13Linear equations in one unknownSolve linear equations with brackets and fractions using balanced steps and clear checking.Equations & Inequalities· Mr YipIf a = b then a + c = b + cMCQPractice14Linear equations in two unknownsSolve simultaneous linear equations by substitution and elimination — core Secondary 3 skills.Equations & Inequalities· Mr YipSubstitution: solve for one variable, then replaceMCQPractice15Linear inequalities in one unknownSolve and represent linear inequalities, remembering to flip the inequality sign when multiplying or dividing by a negative.Equations & Inequalities· Mr YipIf a < b then a + c < b + cMCQPractice16Changing the subject of a formulaRearrange formulae with roots, fractions and products so a chosen variable becomes the subject.Equations & Inequalities· Mr YipInverse steps undo the formulaMCQPractice17Prime factorisation, HCF and LCMWrite numbers as products of primes, then read off HCF and LCM — a frequent TSA-style opener.Numbers & Estimation· Mr ChanHCF: take lowest powers of common primesMCQPractice18Scientific notation and large/small numbersConvert between ordinary form and a × 10ⁿ with 1 ≤ |a| < 10 — standard S3 index work.Numbers & Estimation· Mr Chana × 10^n with 1 ≤ |a| < 10MCQPractice19Directed numbers with brackets (challenge)Mixed operations with multiple brackets — the step that trips many S2–S3 students in timed papers.Numbers & Estimation· Ms LamWork innermost brackets firstMCQPractice20Reverse percentage problemsRecover the original value after a percentage change — classic exam reverse-percentage items.Percentage, Rate & Ratio· Ms LamOriginal = New ÷ (1 ± r/100)MCQPractice