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Quantitative Aptitude Syllabus
Number System
Algebra
- Basic Algebraic Concepts
- Variables, Constants, Coefficients
- Algebraic Expressions
- Like and Unlike Terms
- Simplification of Expressions
- Algebraic Identities
- squares and cubic identities
- Basic applications of identities
- Factorisation
- Common Factor
- Factorisation using Identities
- Simple Algebraic Factorisation
- Linear Equations
- Linear Equation in One Variable
- Linear Equations with Fractions
- Simple Equations and Applications
- Word Problems based on Equations
- Simultaneous Linear Equations
- Two Variables
- Substitution Method
- Elimination Method
- Basic Application Problems
- Quadratic Equations
- Basic Concept
- Factorisation Method
- Quadratic Formula
- Simple Application Problems
- Inequalities
- Basic Linear Inequalities
- Comparison of Algebraic Quantities
- Simple Inequality Problems
Arithmetic
- Basic Arithmetic
- Fundamental Operations
- BODMAS/Order of Operations
- Simplification
- Approximation and Estimation
- Percentages
- Basic Percentage
- Percentage Increase and Decrease
- Successive Percentage Change
- Percentage-Based Applications
- Ratio and Proportion
- Ratio
- Proportion
- Direct and Inverse Proportion
- Compound Ratio
- Variation
- Partnership
- Average
- Simple Average
- Weighted Average
- Average of Groups
- Combined Average
- Average-Based Applications
- Profit, Loss and Discount
- Cost Price and Selling Price
- Profit and Loss Percentage
- Marked Price
- Discount
- Successive Discounts
- False Weight and Dishonest Dealer
- Simple and Compound Interest
- Simple Interest
- Compound Interest
- Annual/Half-Yearly/Quarterly Compounding
- Difference Between SI and CI
- Growth and Depreciation
- Time, Work and Wages
- Work and Efficiency
- Individual and Combined Work
- Work Equivalence
- Wages and Payment
- Pipes and Cisterns
- Work and Time-Based Applications
- Time, Speed and Distance
- Basic Speed, Distance and Time
- Relative Speed
- Average Speed
- Problems on Trains
- Boats and Streams
- Races
- Circular Track Problems
- Mixture and Alligation
- Basic Mixture Problems
- Weighted Mixtures
- Alligation Rule
- Replacement Problems
- Partnership
- Investment and Profit Sharing
- Time-Based Partnership
- Working and Sleeping Partners
- Ages
- Present, Past and Future Ages
- Ratio of Ages
- Average Age
- Age-Based Equations and Word Problems
- Sequence and Series
- Arithmetic Progression
- Geometric Progression
- Number Patterns
- Sum of Series
- Arithmetic/Geometric Mean
- Clocks and Calendars
- Clock Angles
- Time Gain and Loss
- Calendar and Odd Days
- Day and Date Problems
- Boats, Streams and Escalators
- Upstream and Downstream
- Relative Speed
- Escalator-Based Problems
- Moving Walkway Problems
- Advanced Arithmetic
- Linear and Quadratic Applications
- Optimization-Based Arithmetic Problems
- Successive Changes
- Multi-concept Word Problems
- Advanced Ratio and Proportion
- Advanced Percentage Applications
- Mixed Competitive Arithmetic
- UPSC/BPSC Level Arithmetic
- SSC/Railway Level Arithmetic
- Banking Level Arithmetic
- CUET Level Arithmetic
- CAT/Advanced-Level Arithmetic
- Previous-Year Questions
- Multi-concept and Data-Based Problems
Geometry and mensuration
- Basic Concepts of Geometry
- Point, Line, Ray and Line Segment
- Plane and Angles
- Types of Angles
- Complementary and Supplementary Angles
- Adjacent and Vertically Opposite Angles
- Linear Pair
- Lines and Angles
- Parallel and Perpendicular Lines
- Transversal
- Corresponding, Alternate and Co-interior Angles
- Angle Properties and Applications
- Triangles
- Types of Triangles
- Properties of Triangles
- Angle Sum Property
- Exterior Angle Property
- Congruence of Triangles
- Similarity of Triangles
- Pythagoras Theorem
- Important Triangle Inequalities
- Special Triangles
- Equilateral Triangle
- Isosceles Triangle
- Right-Angled Triangle
- 30°–60°–90° Triangle
- 45°–45°–90° Triangle
- Properties and Applications
- Basic Trigonometric Ratios
- Sine, Cosine, Tangent
- Cosecant, Secant, Cotangent
- Standard angles and values
- Trigonometric Identities
- Basic identities
- Pythagorean identities
- Simplification of trigonometric expressions
- Heights and Distances
- Angle of Elevation
- Angle of Depression
- Problems involving heights, distances and shadows
- Applications & Basic Equations
- Trigonometric equations
- Complementary angles
- Standard-angle problems
- Basic competitive-exam applications
- Quadrilaterals
- Types and Properties of Quadrilaterals
- Parallelogram
- Rectangle
- Square
- Rhombus
- Trapezium/Trapezoid
- Kite
- Diagonals and Their Properties
- Polygons
- Regular and Irregular Polygons
- Interior and Exterior Angles
- Sum of Interior Angles
- Number of Diagonals
- Regular Polygon Problems
- Circles
- Basic Terms of a Circle
- Radius, Diameter, Chord and Arc
- Sector and Segment
- Circumference and Area
- Angles in a Circle
- Chord Properties
- Tangent and Secant
- Tangent Properties
- Cyclic Quadrilaterals
- Mensuration – 2D
- Perimeter and Area
- Triangle
- Quadrilateral
- Rectangle and Square
- Parallelogram
- Rhombus
- Trapezium
- Circle
- Composite Figures
- Area-based Word Problems
- Coordinate Geometry
- Cartesian Plane
- Coordinates and Quadrants
- Distance Formula
- Midpoint Formula
- Section Formula
- Area of Triangle
- Slope of a Line
- Equation of a Straight Line
- Applications of Coordinate Geometry
- Mensuration – 3D
- Cube and Cuboid
- Cylinder
- Cone
- Sphere and Hemisphere
- Prism and Pyramid
- Surface Area
- Curved/Lateral Surface Area
- Total Surface Area
- Volume
- Conversion and Combination of Solids
- Geometric Constructions
- Basic Constructions
- Bisectors
- Construction of Triangles
- Construction of Perpendiculars and Parallels
- Advanced Geometry
- Similarity and Proportionality
- Advanced Circle Geometry
- Power of a Point
- Ptolemy’s Theorem
- Stewart’s Theorem
- Menelaus’ Theorem
- Ceva’s Theorem
- Advanced Coordinate Geometry
- Locus and Geometric Inequalities
- Mixed Competitive Geometry
- Geometry-Based Logical Problems
- Figure-Based Problems
- Area and Perimeter Applications
- Height and Distance Problems
- Multi-concept Geometry Problems
- UPSC/BPSC Level Problems
- SSC/Railway Level Problems
- Banking/CUET Level Problems
- CAT/Advanced-Level Problems
Permutation, combination and probability
- Basic Counting Principles
- Fundamental Principle of Counting
- Addition and Multiplication Principles
- Counting by Cases
- Permutation
- Meaning of Permutation
- Factorial
- Arrangements of Objects
- Permutation of Distinct Objects
- Permutation of Repeated Objects
- Circular Permutation — basic level
- Arrangement of Letters and Numbers
- Combination
- Meaning of Combination
- Basic Formula of
- Properties of
- Selection Problems
- Selection with Restrictions
- Relationship between Permutation and Combination
- Probability Basics
- Experiment, Outcome and Sample Space
- Events
- Favourable and Total Outcomes
- Classical Probability
- Probability of an Event
- Probability of Complementary Events
- Types of Events
- Certain and Impossible Events
- Mutually Exclusive Events
- Independent and Dependent Events
- Equally Likely Events
- Probability Rules
- Addition Rule of Probability
- Multiplication Rule of Probability
- Complementary Probability
- Conditional Probability — basic level
- Standard Probability Problems
- Coins
- Dice
- Cards
- Balls and Boxes
- Selection Problems
- Arrangement-Based Probability
- At Least / At Most Problems
- Mixed Competitive Problems
- Counting + Probability
- Permutation + Combination
- Case-Based Problems
- Probability-Based Word Problems
- Exam-level problems for UPSC, BPSC, SSC, Railway, Banking, CUET and CAT
Set Theory and Venn Diagram
- Basic Set Concepts
- Sets and Elements
- Representation of Sets
- Types of Sets
- Subsets and Proper Subsets
- Universal Set and Empty Set
- Operations on Sets
- Union
- Intersection
- Difference
- Complement of a Set
- Basic Set Identities
- Venn Diagrams
- Two-Set Venn Diagrams
- Three-Set Venn Diagrams
- Representation and Interpretation of Data
- Number of Elements in Different Regions
- Applications
- Inclusion–Exclusion Principle
- Problems involving Students/People and Multiple Categories
- At Least / At Most / Exactly Problems
- Set Theory-based Quantitative Aptitude Problems