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Estimating square roots without a calculatorSandwich a root between consecutive squares to estimate its size.Numbers & Estimation· Ms ChuMCQ42
Operations in scientific notationMultiply and divide numbers written as a×10ⁿ and renormalise.Numbers & Estimation· Mr YipMCQ43
Finding a percentage of a quantityConvert percentages to multipliers and find parts of amounts quickly.Percentage, Rate & Ratio· Mr ChanMCQ44
Expressing one quantity as a percentage of anotherWrite A as a percentage of B using (A/B)×100%.Percentage, Rate & Ratio· Ms LamMCQ45
Percentage error and approximate valuesCompute percentage error from true and approximate values.Percentage, Rate & Ratio· Mr NgMCQ46
Profit, loss and markup percentageLink cost, selling price and marked price with clear bases.Percentage, Rate & Ratio· Ms ChuMCQ47
Discount and sale priceApply single and successive discounts to marked prices.Percentage, Rate & Ratio· Mr YipMCQ48
Simple interest: finding P, R or TRearrange I = PRT/100 to find missing principal, rate or time.Percentage, Rate & Ratio· Mr ChanMCQ49
Rates in everyday contextsWork with speed, unit price and currency-style rates with units.Percentage, Rate & Ratio· Ms LamMCQ50
Sharing in a three-part ratioShare amounts in a:b:c and check that the parts add to the total.Percentage, Rate & Ratio· Mr NgMCQ51
Map scales as ratiosConvert between map distance and real distance using 1:n scales.Percentage, Rate & Ratio· Ms ChuMCQ52
Two-step percentage story problemsChain multipliers for mark-up then discount or rise then fall.Percentage, Rate & Ratio· Mr YipMCQ53
Substituting values into algebraic expressionsReplace letters carefully with brackets, especially for negatives.Algebraic Manipulation· Mr ChanMCQ54
Collecting like terms with several variablesSort x, y and constant terms before combining coefficients.Algebraic Manipulation· Ms LamMCQ55
Expanding single bracketsDistribute positive and negative factors across sums and differences.Algebraic Manipulation· Mr NgMCQ56
Expanding two brackets with FOILProduce four products then collect like terms reliably.Algebraic Manipulation· Ms ChuMCQ57
Using perfect square identitiesRecognise and expand (a±b)² without missing the middle term.Algebraic Manipulation· Mr YipMCQ58
Recognising a³ − b³ patterns (intro)Spot cubes and quote a³ − b³ = (a−b)(a²+ab+b²) at junior challenge level.Algebraic Manipulation· Mr ChanMCQ59
Factorising ax² + bx + c when a ≠ 1Split the middle term or use cross method for leading coefficient not 1.Algebraic Manipulation· Ms LamMCQ60
Mixed laws of indices practiceCombine product, quotient and power laws in one simplification.Algebraic Manipulation· Mr NgMCQ
Estimating square roots without a calculatorSandwich a root between consecutive squares to estimate its size.Numbers & Estimation· Ms ChuMCQ42Operations in scientific notationMultiply and divide numbers written as a×10ⁿ and renormalise.Numbers & Estimation· Mr YipMCQ43Finding a percentage of a quantityConvert percentages to multipliers and find parts of amounts quickly.Percentage, Rate & Ratio· Mr ChanMCQ44Expressing one quantity as a percentage of anotherWrite A as a percentage of B using (A/B)×100%.Percentage, Rate & Ratio· Ms LamMCQ45Percentage error and approximate valuesCompute percentage error from true and approximate values.Percentage, Rate & Ratio· Mr NgMCQ46Profit, loss and markup percentageLink cost, selling price and marked price with clear bases.Percentage, Rate & Ratio· Ms ChuMCQ47Discount and sale priceApply single and successive discounts to marked prices.Percentage, Rate & Ratio· Mr YipMCQ48Simple interest: finding P, R or TRearrange I = PRT/100 to find missing principal, rate or time.Percentage, Rate & Ratio· Mr ChanMCQ49Rates in everyday contextsWork with speed, unit price and currency-style rates with units.Percentage, Rate & Ratio· Ms LamMCQ50Sharing in a three-part ratioShare amounts in a:b:c and check that the parts add to the total.Percentage, Rate & Ratio· Mr NgMCQ51Map scales as ratiosConvert between map distance and real distance using 1:n scales.Percentage, Rate & Ratio· Ms ChuMCQ52Two-step percentage story problemsChain multipliers for mark-up then discount or rise then fall.Percentage, Rate & Ratio· Mr YipMCQ53Substituting values into algebraic expressionsReplace letters carefully with brackets, especially for negatives.Algebraic Manipulation· Mr ChanMCQ54Collecting like terms with several variablesSort x, y and constant terms before combining coefficients.Algebraic Manipulation· Ms LamMCQ55Expanding single bracketsDistribute positive and negative factors across sums and differences.Algebraic Manipulation· Mr NgMCQ56Expanding two brackets with FOILProduce four products then collect like terms reliably.Algebraic Manipulation· Ms ChuMCQ57Using perfect square identitiesRecognise and expand (a±b)² without missing the middle term.Algebraic Manipulation· Mr YipMCQ58Recognising a³ − b³ patterns (intro)Spot cubes and quote a³ − b³ = (a−b)(a²+ab+b²) at junior challenge level.Algebraic Manipulation· Mr ChanMCQ59Factorising ax² + bx + c when a ≠ 1Split the middle term or use cross method for leading coefficient not 1.Algebraic Manipulation· Ms LamMCQ60Mixed laws of indices practiceCombine product, quotient and power laws in one simplification.Algebraic Manipulation· Mr NgMCQ