Quantitative Aptitude study notes
Free Quantitative Aptitude notes for UPSC, SSC, banking and railway exams: every topic with the key facts, exam traps and a practice quiz. About 137minutes in all: read them in order, then take each topic's quiz to lock it in.
Percentages: Formulas, Shortcuts & Tricks for SSC and Bank Exams
Percentage-fraction table, successive change, more-than/less-than, consumption, population, marks, elections and discounts, with worked examples.
Number System & Divisibility: Formulas, Shortcuts & Tricks for SSC and Railway Exams
Types of numbers, divisibility rules, unit-digit cycles, number of factors, remainders, sum formulas and trailing zeros, with worked examples.
Simplification & Approximation: Shortcuts & Tricks for Bank PO Prelims
VBODMAS order, algebraic identities, fast multiplication tricks, percentage-fraction swaps and rounding rules for approximation questions.
Decimals & Fractions: Rules, Conversions & Tricks for Railway and SSC Exams
Comparing and ordering fractions, recurring decimals to fractions, terminating decimals, decimal multiplication and division, and fraction word problems.
LCM & HCF: Methods, Remainder Rules & Tricks for Railway and SSC Exams
Prime-factor and division methods, HCF × LCM rule, LCM and HCF of fractions, and the four remainder problem types with worked examples.
Square Roots & Cube Roots: Methods, Tables & Tricks for SSC Exams
Squares and cubes to learn, unit-digit methods for roots, prime factorisation, roots of decimals, nested roots and simplifying surds.
Ratio & Proportion: Formulas, Shortcuts & Tricks for SSC, Bank and Railway Exams
Combining ratios, dividing amounts, fourth, third and mean proportionals, compound and duplicate ratios, income-expenditure and coin problems.
Averages & Problems on Ages: Formulas, Shortcuts & Tricks for SSC and Bank Exams
Average formulas, consecutive numbers, replacement and new-member shortcuts, batsman averages, weighted average, average speed and age-ratio problems.
Simple & Compound Interest: Formulas, Shortcuts & Tricks for SSC, Bank and Railway Exams
SI and CI formulas, doubling rules, half-yearly and quarterly compounding, CI-SI difference for 2 and 3 years, depreciation and effective rate.
Profit, Loss & Discount: Formulas, Shortcuts & Tricks for SSC, Bank and Railway Exams
CP, SP and MP formulas, successive discounts, mark-up with discount, false weights, articles-for-articles, same-SP gain and loss, and offers.
Partnership: Formulas, Shortcuts & Tricks for SSC Exams
Simple and compound partnership, partners joining late or withdrawing, working-partner salary, finding time or capital, and rent-sharing problems.
Mixture & Alligation: Rule, Shortcuts & Tricks for SSC and Bank Exams
The alligation rule, mean price, adding water or milk, repeated replacement, mixing two mixtures, and alligation for interest, speed and profit.
Time, Speed and Distance: Formulas and Shortcuts for SSC & Railway Exams
Speed formula, km/h to m/s, average speed, relative speed, late/early problems and races, with worked examples and common traps.
Boats, Streams and Trains: Notes for IBPS PO & SBI PO
Which distance and which relative speed to use for trains, plus downstream, upstream and still-water formulas for boats, with fresh worked examples.
Time and Work (with Pipes and Cisterns): Notes for SSC, Bank & Railway Exams
The LCM-units method, efficiency, men-days-hours, people leaving midway, pipes and leaks, and sharing wages, with fresh worked examples.
Algebra: Identities, Surds, Indices and Linear Equations for SSC & Railway Exams
Core identities, the x + 1/x family, the a + b + c = 0 rule, linear equations and graphs, laws of indices and surds, with fresh worked examples.
Quadratic Equations: Fast Methods for IBPS PO & SBI PO
Factorise in seconds, use the sign rule, compare x and y roots without slips, and use sum/product and the discriminant, with fresh worked examples.
Geometry: Triangles, Circles and Polygons for SSC & Railway Exams
Triangle centres, right-triangle facts, congruence and similarity, polygon angle and diagonal formulas, and circle theorems, with fresh worked examples.
Mensuration 2D and 3D: Formula Sheet and Tricks for SSC, Bank & Railway Exams
All area, perimeter, surface area and volume formulas in two tables, plus Heron, recasting, paths, scaling and unit traps, with fresh worked examples.
Trigonometry and Heights & Distances: Notes for SSC CGL & CHSL
Standard-angle table, ratios, the three identities, complementary angles, maximum values and heights-and-distances method, with fresh worked examples.
Mean, Median and Mode: Elementary Statistics for RRB NTPC
Mean (simple, weighted, combined, corrected), median for odd and even data, mode, range, the empirical relation and grouped-data median, with examples.
Data Interpretation: Tables, Bar, Line and Pie Charts for SSC & Bank Exams
How to read tables, bar and line graphs, pie charts, histograms and caselets, the formulas you need, fast fraction comparison and the classic DI traps.
Probability, Permutation and Combination: Notes for IBPS PO & SBI PO
Counting principles, nPr and nCr, repeated letters, circular seating, things together, digits with zero, and probability with dice, coins, cards and balls.