Types of numbers: natural, whole, integers, rational, irrational, real Divisibility rules (2, 3, 4, 5, 6, 8, 9, 11) Factors and multiples: prime and composite numbers, prime factorization, number of factors HCF and LCM: word problems Remainders: unit digit, cyclicity, remainder theorem (basic) Squares, cubes, roots: perfect squares, estimation Surds, indices and BODMAS: simplification
Unit 2: Arithmetic
Percentage: conversion, successive percentage, population and depreciation Profit and loss: discount, marked price, successive discounts, dishonest dealings Ratio and proportion: partnership, mixtures and alligation, variation Average: weighted average, replacement problems, average of ages Simple and compound interest: difference between SI and CI, installments Time and work: efficiency, pipes and cisterns, alternate days Time, speed and distance: relative speed, trains, boats and streams, races, circular tracks Ages: present, past, future ages
Unit 3: Algebra
Linear equations in one and two variables Quadratic equations: roots, nature of roots Algebraic identities and factorization Inequalities (basic) Sequences and series: AP, GP Functions and graphs (basic) Logarithms (basic)
Unit 4: Geometry
Lines and angles, parallel lines Triangles: types, congruence, similarity, Pythagoras theorem Triangle centres: centroid, incentre, circumcentre, orthocentre Quadrilaterals and polygons Circles: chords, tangents, angles in a circle Coordinate geometry: distance, section formula, slope
Unit 5: Mensuration
2D: area and perimeter of triangle, rectangle, square, parallelogram, rhombus, trapezium, circle, sector 3D: cube, cuboid, cylinder, cone, sphere, hemisphere (surface area and volume)Combination and conversion of solids
Unit 6: Trigonometry and Height & Distance
Trigonometric ratios and identities Standard angles (0°, 30°, 45°, 60°, 90°) Height and distance: angle of elevation and depression
Unit 7: Data Interpretation (DI)
Tables Bar graphs Line graphs Pie charts Mixed graphs and caselets Data sufficiency (in some exams)
Unit 8: Statistics, Probability and Counting
Mean, median, mode, range, standard deviation (basic) Permutations and combinations Basic probability: coins, dice, cards
Mental Ability and logical Reasoning
Unit 1: Series and Patterns
Number series: missing term, wrong term
Alphabet series: letter-based patterns
Mixed series: alphanumeric patterns
Figure series: pattern of shapes
Unit 2: Analogy and Classification
Analogy: word, number, letter, figure
Classification (odd one out): word, number, letter, figure
Unit 3: Coding-Decoding
Letter coding and number coding Substitution coding Mixed and conditional coding Coding using symbols
Unit 4: Relations and Directions
Blood relations: family tree, coded relations Direction sense: distance and direction, shadow problems Ranking and order: position from left, right, top, bottom Alphabet and number test: position-based problems, letter and digit arrangements Time and calendar: clocks (angle, gain and loss), calendars (odd days, day of the week)
Unit 5: Mathematical Operations
Symbol substitution Fictitious operators and equations Balancing equations Mathematical reasoning based on given rules
Unit 6: Non-Verbal Reasoning
Mirror image and water image Paper folding and cutting Embedded figures Counting figures: triangles, squares, cubes Cubes and dice: painted cubes, dice opposite faces Figure completion and missing figures Pattern completion: matrix reasoning
Unit 7: Venn Diagrams and Arrangements
Venn diagrams: representing relations among sets Linear seating arrangement Circular seating arrangement Floor and box arrangements Matrix and puzzle arrangements
Unit 8: Deductive Reasoning
Statements and conclusions: two and three statements Syllogism: All, Some, No, Some-not; Venn method and possibility cases Immediate and mediate inferences
Unit 9: Critical Reasoning
Statement and assumptions Statement and arguments: strong and weak arguments Statement and course of actionCause and effect Strengthening and weakening an argument Inference and conclusion Paradoxes and flaw detection
Unit 10: Logical Puzzles
Linear and circular seating puzzles Scheduling and ordering puzzles: days, months, floors Comparison puzzles: who is taller, older, richer Selection and grouping puzzles: teams, committees Truth-teller and liar puzzles Matching and grid puzzles Double-lineup puzzles
Unit 11: Logical Connectives and Conditionals
And, or, not, if-then, if and only if Necessary and sufficient conditions Contrapositive and converse Truth tables (basic)
Unit 12: Data Arrangement and Sets
Venn diagram and set problems (two and three sets) Input-output (machine inputs and arrangement) Sorting and ranking Data sufficiency (logic-based)
Unit 13: Analytical Reasoning
Course of action and decision making Assertion and reason Passage-based reasoning: inferences from short passages Logical sequence of words and events Direction and distance, networks and routes: graphs and paths
Data Interpretation Syllabus
Unit 1: Calculation Foundations
Percentage and fraction conversions: percentage equivalents of 1/2 to 1/20, such as 1/8 = 12.5% and 1/12 = 8.33%
Approximation and estimation: nearest value, rounding
Speed-calculation techniques: squares and cubes, multiplication shortcuts, tables from 11 to 20
Unit 2: Tabular Data Interpretation
Single and multiple tables Completing missing data Ratio, percentage, average, and growth questions Comparing data across rows and columns Rank and position based questions
Unit 3: Bar Graph
Simple bar graph: one data series Multiple (grouped) bar graph: two or more series Stacked bar graph: components and totals
Percentage stacked bar graph Question types: difference, ratio, percentage change, average, maximum and minimum
Unit 4: Line Graph
Single line graph: trend analysis Multiple line graph: comparison across series Growth rate, percentage change, and average Intersection points and relative comparison
Unit 5: Pie Chart
Percentage pie chart: finding share and value Degree-based pie chart: converting angles to percentages (360° = 100%, so 1% = 3.6°) Dual pie charts: combining two charts in one question Ratio, difference, and total-value questions
Unit 6: Mixed (Combination) Charts
Table + bar graph Bar graph + line graph Pie chart + table Pie chart + bar graph
Multi-step calculations across charts
Unit 7: Caselets (Paragraph-Based DI)
Data given in text form (percentages, ratios, quantities) Converting the data into a table or diagram Finding missing values Logical and arithmetic deductions
Unit 8: Advanced DI Formats (CAT, XAT, Bank Mains)
Radar/web charts
Venn diagram DI: two and three sets
Network and flow diagrams: routes, flows, and dependencies
Scatter plots and bubble charts
Cumulative frequency, histogram, and frequency polygon
