Concepts and formulas

Short pages for each of the 13 topics: the formulas and when they apply, worked examples, shortcuts with their limits, and the mistakes to avoid.

• Number systems and HCF/LCMDivisibility, unit digits, remainders, factors, primes, HCF and LCM.
• PercentagesSuccessive changes, population, consumption and comparisons.
• Profit, loss and discountMarkup, equivalent discounts and false weights.
• Ratio and proportionMixtures, alligation and partnership shares.
• Averages and agesWeighted averages, replacements and age relationships.
• Simple and compound interestSI and CI compared, compounding intervals, time and rate.
• Time, speed and distanceRelative speed, trains, circular tracks, boats and streams.
• Time and workEfficiency, combined work, alternate days, pipes and cisterns.
• Permutation and combinationSelection, arrangement, restrictions and counting.
• ProbabilityCards, dice, balls and simple events.
• Geometry and mensurationPerimeter, area, volume and surface area.
• Data interpretationTables, bar graphs, pie charts, line graphs and connected sets.
• Logical and analytical reasoningSeries, analogies, coding, directions, relations, ranking, syllogisms and arrangements.