Maths for Government Exams: Notes, Questions & Cheatsheets
Everything published for Maths, gathered in one place: the study series to work through, practice questions with answers and explanations, and the cheatsheets, tips and word lists worth keeping for revision.
Or take them as a set: the Maths practice set
Cheatsheets
Geometric Progression Cheat Sheet
A quick revision cheat sheet on geometric progression (GP) for SSC, Banking, Railway and state exams. It covers the nth-term formula, the sum of the first n terms, the sum to infinity for a decreasing GP, the geometric mean, and the key shortcuts, with worked examples to revise quickly before the exam.
Logarithms Cheat Sheet
A quick revision cheat sheet on logarithms for SSC, Banking, Railway and state exams. It covers the definition of a logarithm, the product, quotient and power laws, the change-of-base rule, the standard values, and the common and natural logs, with worked examples to revise quickly before the exam.
Problems on Ages Cheat Sheet
A quick revision cheat sheet on problems on ages for SSC, Banking, Railway and state exams. It covers how to set up present, past and future ages, the ratio method, the standard equation form, and the quick checks that catch wrong answers, with worked examples to revise quickly before the exam.
Boats and Streams Cheat Sheet
A quick revision cheat sheet on boats and streams for SSC, Banking, Railway and state exams. It covers downstream and upstream speed, how to recover the boat's speed in still water and the stream's speed, the average-speed idea, and the time taken for a round trip, with worked examples to revise quickly.
Surds and Indices Cheat Sheet
A quick revision cheat sheet on surds and indices for SSC, Banking, Railway and state exams. It covers the laws of indices, zero and negative powers, fractional powers, the rules for surds, and how to rationalise a denominator, with worked examples to revise quickly before the exam.
Variance and Standard Deviation Cheat Sheet
A quick revision cheat sheet on variance and standard deviation for SSC, Banking, Railway and state exams. It covers the mean, the variance formula and its shortcut form, the standard deviation, what the two measures tell you about spread, and the effect of adding or multiplying the data, with worked examples to revise quickly.
Permutations and Combinations Cheat Sheet
A quick revision cheat sheet on permutations and combinations for SSC, Banking, Railway and state exams. It covers the factorial, the permutation and combination formulas, when order matters and when it does not, the key identities, and arrangements with repeated letters, with worked examples to revise quickly before the exam.
Problems on Trains Cheat Sheet
A quick revision cheat sheet on problems on trains for SSC, Banking, Railway and state exams. It covers the km/h to m/s conversion, a train crossing a pole, a train crossing a platform, two trains passing in the same and opposite directions, and the relative-speed idea, with worked examples to revise quickly.
Arithmetic Progression Cheat Sheet
A quick revision cheat sheet on arithmetic progression (AP) for SSC, Banking, Railway and state exams. It covers the nth-term formula, the sum of the first n terms in both forms, the arithmetic mean, and the standard shortcuts, with worked examples to revise quickly before the exam.
Pipes and Cisterns Cheat Sheet
A quick revision cheat sheet on pipes and cisterns for SSC, Banking, Railway and state exams. It covers the rate idea, how to combine inlet pipes, how an outlet pipe subtracts, the time for pipes working together, and the net filling rate, with worked examples to revise quickly before the exam.
Mixture and Alligation Cheat Sheet
A quick revision cheat sheet on mixture and alligation for SSC, Banking, Railway and state exams. It explains the rule of alligation and its cross diagram, how to find the ratio in which two ingredients are mixed, the mean-price idea, and the repeated-replacement formula for dilution, with worked examples.
Probability Cheat Sheet
A quick revision cheat sheet on probability for SSC, Banking, Railway and state exams. It covers the basic probability formula, the addition and multiplication rules, the complement rule, and the standard sample spaces for coins, dice and a pack of cards, with worked examples to revise quickly before the exam.
Statistics Cheat Sheet
A quick revision cheat sheet on basic statistics for SSC, Banking, Railway and state exams. It covers the three measures of central tendency — mean, median and mode — with their formulas, how to find each for a set of values, the range, and the empirical relationship between mean, median and mode, with worked examples.
Compound Interest Cheat Sheet
A quick revision cheat sheet on compound interest for SSC, Banking, Railway and state exams. It covers the amount and compound-interest formulas, half-yearly and quarterly compounding, how compound interest differs from simple interest, and the shortcut for the CI-minus-SI difference over two and three years, with worked examples.
Fractions and Decimals Cheat Sheet
A quick revision cheat sheet on fractions and decimals for SSC, Banking, Railway and state exams. It covers the types of fractions, converting between fractions, decimals and percentages, the four operations on fractions, how to compare fractions quickly, and the fraction-percentage values worth memorising for fast calculation.
Algebra Cheat Sheet
A quick revision cheat sheet on algebra for SSC, Banking, Railway and state exams. It gathers the algebraic identities, the special a+b+c=0 result, the laws of indices, and the quadratic-equation formulas — roots, discriminant, and the sum and product of roots — in one place for fast revision before the exam.
Mensuration Cheat Sheet
A quick revision cheat sheet on mensuration for SSC, Banking, Railway and state exams. It gathers the area and perimeter formulas for the common 2D shapes and the volume and surface-area formulas for the common 3D solids — cube, cuboid, cylinder, cone, sphere and hemisphere — in one place for fast revision.
Geometry Cheat Sheet
A quick revision cheat sheet on geometry for SSC, Banking, Railway and state exams. It covers lines and angles, the triangle angle properties and Pythagoras theorem, the types of triangles, the interior and exterior angles of polygons, and the key circle angle rules, in a form you can revise quickly before the exam.
Trigonometry Cheat Sheet
A quick revision cheat sheet on trigonometry for SSC, Banking, Railway and state exams. It covers the six trigonometric ratios, the standard-angle value table for 0 to 90 degrees, the three Pythagorean identities, the complementary-angle rules and height-and-distance basics, in a form built for fast revision.
Simplification Cheat Sheet
A quick revision cheat sheet on simplification and approximation for SSC, Banking, Railway and state exams. It covers the BODMAS order of operations, the order of brackets, the approximation method for fast answers, the algebraic identities, and the fraction and percentage values worth memorising to save time in the exam.
Data Interpretation Cheat Sheet
A quick revision cheat sheet on data interpretation for SSC, Banking, Railway and state exams. It covers the common DI formats — tables, bar graphs, line graphs, pie charts and caselets — the pie-chart angle and percentage formulas, and the core calculations of percentage change, ratio and average used to answer DI questions quickly.
Partnership Cheat Sheet
A quick revision cheat sheet on partnership for SSC, Banking, Railway and state exams. It explains how profit is shared between partners, the difference between simple and compound partnership, how to handle capital invested for different periods, and the working-versus-sleeping-partner salary case, with worked examples.
Time and Work Cheat Sheet
A quick revision cheat sheet on time and work for SSC, Banking, Railway and state exams. It covers the one-day-work idea, the combined-work formula, the efficiency and LCM methods, the men-days-hours relation, and how pipes and cisterns use the same rules, with worked examples.
Average Cheat Sheet
A quick revision cheat sheet on averages for SSC, Banking, Railway and state exams. It covers the basic average formula, the averages of the first n natural, even, odd, square and cube numbers, weighted average, average speed, and the shortcut for a change in average when an item is added, removed or replaced.
Time, Speed and Distance Cheat Sheet
A quick revision cheat sheet on time, speed and distance for SSC, Banking, Railway and state exams. It covers the basic formula, the km/hr to m/s conversion, average speed, relative speed, train problems like crossing a pole or platform, and boats and streams, with worked examples.
HCF and LCM Cheat Sheet
A quick revision cheat sheet on HCF and LCM for SSC, Banking, Railway and state exams. It explains the highest common factor and the lowest common multiple, how to find each by prime factorisation, the product rule linking HCF and LCM to two numbers, the formulas for HCF and LCM of fractions, and the common word-problem types.
Number System Cheat Sheet
A quick revision cheat sheet on the number system for SSC, Banking, Railway and state exams. It covers the types of numbers, the divisibility rules from 2 to 11, the sum of the first n natural numbers, squares and cubes, unit-digit cyclicity, and how to count the factors of a number.
Ratio and Proportion Cheat Sheet
A quick revision cheat sheet on ratio and proportion for SSC, Banking, Railway and state exams. It covers how to read and simplify a ratio, proportion and the cross-multiplication rule, mean, third and fourth proportionals, duplicate and sub-duplicate ratios, dividing a quantity in a given ratio, and the componendo-dividendo shortcut.
Simple Interest Formula Cheat Sheet
A quick revision cheat sheet covering Simple Interest formulas, principal, rate, time, amount, yearly and monthly interest, fractional time periods, rate and time shortcuts, comparison formulas, and common competitive-exam question patterns. Useful for SSC, Banking, Railway, Defence, State Government exams, and other competitive examinations.
Profit & Loss Formula Cheat Sheet
A quick revision cheat sheet covering important Profit and Loss formulas, Cost Price, Selling Price, profit percentage, loss percentage, marked price, discount, successive discounts, dishonest dealer questions, false weights, and common competitive-exam shortcuts. Useful for SSC, Banking, Railway, Defence, State Government exams, and other competitive examinations.
Percentage Formula Cheat Sheet
A quick revision cheat sheet covering important percentage formulas, percentage increase and decrease, successive percentage changes, reverse percentages, fraction-to-percentage conversions, comparison formulas, price-consumption problems, population growth, depreciation, shortcuts, and common exam mistakes. Useful for SSC, Banking, Railway, Defence, State Government exams, and other competitive examinations