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Numbers & Estimation
  • Directed numbers: add, subtract, multiply and divide
  • Approximate values and sensible estimation
  • Rational numbers: fractions, decimals and recurring decimals
  • Prime factorisation, HCF and LCM
  • Scientific notation and large/small numbers
  • Directed numbers with brackets (challenge)
  • Ordering directed numbers on the number line
  • Absolute value of directed numbers
  • Four operations mixed with directed numbers
  • Rounding to decimal places
  • Significant figures in calculations
  • Converting fractions and decimals
  • View all →
Percentage, Rate & Ratio
  • Percentage increase and decrease
  • Successive percentage changes
  • Rate, ratio and direct proportion
  • Percentage applications: discount, profit and simple interest
  • Reverse percentage problems
  • Direct and inverse proportion
  • Percentage word problems (exam style)
  • Finding a percentage of a quantity
  • Expressing one quantity as a percentage of another
  • Percentage error and approximate values
  • Profit, loss and markup percentage
  • Discount and sale price
  • View all →
Algebraic Manipulation
  • Simplifying algebraic expressions
  • Laws of integral indices
  • Identities and algebraic expansion
  • Factorisation: common factors and grouping
  • Factorising difference of squares
  • Negative indices and positive-index answers
  • Expanding binomials (exam practice)
  • Factorising quadratics (cross method)
  • Factorisation by grouping and common binomials
  • Adding and multiplying polynomials
  • Substituting values into algebraic expressions
  • Collecting like terms with several variables
  • View all →
Equations & Inequalities
  • Linear equations in one unknown
  • Linear equations in two unknowns
  • Linear inequalities in one unknown
  • Changing the subject of a formula
  • Simultaneous equations from word problems
  • Linear inequalities (exam drills)
  • Changing the subject with roots and products
  • Linear equations with brackets
  • Linear equations with fractions
  • Forming equations from word problems
  • Elimination with multiplied equations
  • Substitution with rearranged subjects
  • View all →
Exam & Challenge
  • Mixed Number & Algebra drill (TSA style)
  • Challenge: indices + factorisation combo
  • Exam mix: directed numbers and percentages
  • Exam mix: indices and expansion
  • Exam mix: factorise then solve
  • Exam mix: ratio and proportion
  • Exam mix: simultaneous equations and inequalities
  • Challenge: nested brackets with indices
  • Challenge: multi-step percentage reasoning
  • Challenge: full quadratic factorisation set

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81Challenge: multi-step percentage reasoningReverse percentages chained with successive changes.Exam & Challenge· Ms ChuMCQ82Challenge: full quadratic factorisation setFactorise several quadratics including a≠1 and perfect squares.Exam & Challenge· Mr YipMCQ
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Number Quiz

Timed MCQs on percentages, indices, factorisation and equations.

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Quick formulas
  • % change
    (change/original)×100%(change/original)\times 100\%(change/original)×100%
  • Inverse
    xy=kxy = kxy=k
  • Factor
    x2−9=(x−3)(x+3)x^{2}-9=(x-3)(x+3)x2−9=(x−3)(x+3)
For you
  • All number lessons
  • Exam & challenge
  • Percentage & ratio
  • Algebra set
  • Equations set
  • Study FAQ
Teachers
  • Mr Chan
    Mr Chan leads Number and Algebra classes in a Kowloon secondary school. He writes clear notes on directed numbers, estimation and exam pacing for Secondary 2–3.
  • Ms Lam
    Ms Lam specialises in percentages, ratio and reverse-percentage problems. Her drills mirror the wording students meet in school tests and TSA-style papers.
  • Mr Ng
    Mr Ng focuses on indices, scientific notation and algebraic structure. He trains students to keep positive indices and check expansions by substitution.
  • Ms Chu
    Ms Chu teaches factorisation and quadratic cross-method work. She emphasises complete factorisation and linking every factor pair back to expansion.
  • Mr Yip
    Mr Yip writes equations, inequalities and formula-rearrangement lessons. He likes short checks: substitute the answer and confirm both sides.
Latest lessons
  • Directed numbers: add, subtract, multiply and divide
    Numbers & Estimation
  • Approximate values and sensible estimation
    Numbers & Estimation
  • Rational numbers: fractions, decimals and recurring decimals
    Numbers & Estimation
  • Percentage increase and decrease
    Percentage, Rate & Ratio
  • Successive percentage changes
    Percentage, Rate & Ratio
  • Rate, ratio and direct proportion
    Percentage, Rate & Ratio
  • Percentage applications: discount, profit and simple interest
    Percentage, Rate & Ratio
  • Simplifying algebraic expressions
    Algebraic Manipulation
  • Laws of integral indices
    Algebraic Manipulation
  • Identities and algebraic expansion
    Algebraic Manipulation
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Clear Number and Algebra lessons for Hong Kong Secondary 2–3 students — formulas, worked examples, written practice and multiple-choice drills.

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Numbers & EstimationPercentage, Rate & RatioAlgebraic ManipulationEquations & InequalitiesExam & Challenge
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