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Mathematical Reasoning: Arithmetic

Percentage, profit and loss, interest, time and work, speed and distance — with shortcuts that save minutes

20 lessons 20 lesson quizzes 100 questions 2h 9m Certificate
ArithmeticPercentageInterestTime and workSpeed and distanceMental maths

What you'll learn

  • Solve percentage, ratio, profit and loss and interest problems quickly and accurately
  • Apply standard formulas for time and work, pipes, speed, trains, boats and mixtures
  • Use shortcuts and approximation to save time under exam pressure
  • Avoid the calculation traps that cost marks under negative marking
  • Show full working for the written mathematics paper

About this course

Mathematical Reasoning carries **15 marks** in the BCS preliminary and **50 marks** in the written Mathematical Reasoning and Mental Ability paper. Bank exams weight mathematics even more heavily. The good news is that the syllabus is small and completely predictable: the same dozen topics recur year after year. This course covers arithmetic in twenty lessons: number systems, HCF and LCM, fractions, simplification, indices and surds, ratio, percentage, profit and loss, simple and compound interest, averages, time and work, pipes and cisterns, time-speed-distance, trains, boats and streams, partnership, mixtures, ages, calendars and clocks, and exam strategy. Every lesson gives the formula, at least two fully worked examples and a quiz. Work each example with pen and paper before reading the solution — arithmetic is learned by doing, not by reading.

Course content

20 lessons20 quizzes1 final exam2h 9m total
01Numbers, Divisibility and FactorsTypes of numbers, divisibility rules and the basics every other topic depends on. Quiz · 5 7 min02HCF and LCMHighest common factor, lowest common multiple and the word problems built on them. Quiz · 5 6 min03Fractions, Decimals and SimplificationHandling fractions and decimals fast, and applying BODMAS correctly. Quiz · 5 6 min04Indices, Surds and Square RootsPowers, roots and the rules that make them manageable. Quiz · 5 6 min05Ratio and ProportionDividing quantities, comparing values and solving proportion problems. Quiz · 5 7 min06PercentageThe most useful arithmetic topic, and the base for profit, interest and data questions. Quiz · 5 6 min07Profit, Loss and DiscountCost price, selling price, margins, discounts and the traps in each. Quiz · 5 6 min08Simple InterestInterest that does not compound, and the four ways it is asked. Quiz · 5 6 min09Compound InterestInterest on interest, and the difference from simple interest. Quiz · 5 6 min10AveragesMeans, weighted averages and the replacement problems built on them. Quiz · 5 6 min11Time and WorkThe unit-work method that solves every problem in this family. Quiz · 5 7 min12Pipes and CisternsThe same logic as time and work, with one pipe working against another. Quiz · 5 7 min13Time, Speed and DistanceThe formula triangle and the unit conversions that decide the answer. Quiz · 5 6 min14Trains, Boats and StreamsRelative speed applied to two of the most common exam settings. Quiz · 5 7 min15Partnership, Shares and MixturesDividing profits and mixing quantities — two reliable exam topics. Quiz · 5 6 min16Ages, Calendars and ClocksThree small topics that reliably supply one or two marks each. Quiz · 5 7 min17Number Series and ApproximationSpotting patterns and estimating fast enough to beat the clock. Quiz · 5 6 min18Number Problems and Word EquationsTranslating sentences into equations — the skill behind most word problems. Quiz · 5 7 min19Data Interpretation: Tables, Charts and GraphsReading data quickly and answering percentage, ratio and average questions from it. Quiz · 5 7 min20Exam Strategy for ArithmeticHow to convert knowledge into marks under time pressure and negative marking. Quiz · 5 7 minFinal exam30 random questions from the whole course · 60% to pass 30 min

Who this course is for

  • BCS preliminary and written candidates
  • Bank, non-cadre and other government job candidates
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