Basic Mathematics Topics

1. Arithmetic & Number System

  1. Types of Numbers (Natural, Whole, Integers, Rational, Irrational, Prime)
  2. Factors, Multiples, and Divisibility Rules
  3. HCF (Highest Common Factor) and LCM (Lowest Common Multiple)
  4. Fractions and Decimals – Conversion and Operations
  5. Ratio, Proportion, and Variation
  6. Percentage – Increase/Decrease, Profit & Loss
  7. Average and Mean Calculation
  8. Simple and Compound Interest
  9. Time, Speed, and Distance Calculations
  10. Work and Time Problems

2. Algebra

  1. Basic Algebraic Expressions and Simplification
  2. Linear Equations and Inequalities
  3. Quadratic Equations and Their Solutions
  4. Simultaneous Equations (Solving for Two Variables)
  5. Exponents and Powers
  6. Logarithms and Their Properties
  7. Polynomials and Factorization
  8. Sequences and Series (Arithmetic & Geometric Progressions)
  9. Functions and Their Graphs
  10. Probability and Permutations & Combinations

3. Geometry & Mensuration

  1. Basic Geometrical Shapes (Lines, Angles, Triangles, Quadrilaterals, Circles)
  2. Properties of Triangles (Pythagoras Theorem, Congruence, Similarity)
  3. Properties of Circles (Radius, Diameter, Chords, Sectors, Arcs)
  4. Coordinate Geometry (Distance Formula, Midpoint, Slope)
  5. Perimeter and Area of Basic Shapes (Rectangle, Triangle, Circle, Trapezium)
  6. Volume and Surface Area of 3D Shapes (Cylinder, Sphere, Cube, Cone)
  7. Angle Measurement and Types (Acute, Obtuse, Reflex, Right)
  8. Parallel Lines and Transversal Theorems
  9. Geometrical Constructions and Practical Applications
  10. Symmetry and Transformations (Reflection, Rotation, Translation)

4. Statistics & Data Interpretation

  1. Types of Data (Qualitative vs. Quantitative)
  2. Collection and Representation of Data (Tables, Charts, Graphs)
  3. Measures of Central Tendency (Mean, Median, Mode)
  4. Measures of Dispersion (Range, Variance, Standard Deviation)
  5. Probability Concepts – Basic Events, Independent & Dependent Events
  6. Pie Charts, Bar Graphs, and Line Graphs Interpretation
  7. Frequency Distributions and Cumulative Frequency
  8. Probability Distributions (Binomial, Poisson, Normal)
  9. Correlation and Regression Basics
  10. Sampling Methods and Errors

5. Trigonometry

  1. Introduction to Trigonometric Ratios (Sine, Cosine, Tangent)
  2. Trigonometric Identities and Their Applications
  3. Heights and Distances – Angle of Elevation and Depression
  4. Trigonometric Equations and Their Solutions
  5. Conversion Between Degrees and Radians
  6. Graphs of Trigonometric Functions
  7. Applications of Trigonometry in Physics and Engineering
  8. Laws of Sines and Cosines
  9. Circular Measure and Sector Area
  10. Inverse Trigonometric Functions

6. Logical & Analytical Reasoning

  1. Number Series and Letter Series Problems
  2. Logical Sequences and Pattern Recognition
  3. Syllogisms and Logical Deduction
  4. Coding and Decoding Problems
  5. Blood Relations and Family Tree Problems
  6. Direction Sense Test
  7. Venn Diagrams and Set Theory
  8. Statement and Assumption/Conclusion Questions
  9. Analogies and Odd One Out Problems
  10. Puzzle-Based Reasoning (Seating Arrangements, etc.)

7. Basic Applied Mathematics in Science

  1. Scientific Notation and Significant Figures
  2. Logarithms in Scientific Calculations
  3. Exponential Growth and Decay
  4. Velocity, Acceleration, and Motion Equations
  5. Work, Power, and Energy Calculations
  6. Heat and Temperature Conversion (Celsius, Fahrenheit, Kelvin)
  7. Pressure and Density Formulas
  8. Electrical Calculations (Ohm’s Law, Resistance, Power)
  9. Fluid Mechanics (Flow Rate, Buoyancy)
  10. Sound Waves and Frequency Calculation

8. Business & Financial Mathematics

  1. Interest Rates (Simple vs. Compound)
  2. Profit and Loss Statements
  3. Discounts and Marked Price Calculations
  4. Taxation and Revenue Calculation
  5. Currency Conversion and Inflation Calculations
  6. Investment and Depreciation Mathematics
  7. Loan and Mortgage Calculations
  8. Break-Even Analysis
  9. Market Share and Growth Rate Calculations
  10. Budgeting and Cost Analysis

9. Applied Mathematics in Computer Science & Engineering

  1. Boolean Algebra and Logic Gates
  2. Matrices and Determinants
  3. Graph Theory Basics
  4. Linear Programming Problems
  5. Algorithms and Complexity (Big-O Notation)
  6. Set Theory and Relations
  7. Cryptography and Number Theory
  8. Differentiation and Integration Basics
  9. Fourier Series and Transformations
  10. Vector Algebra and Its Applications

10. Miscellaneous Important Topics

  1. Time Zones and Calendar Calculations
  2. Speed, Distance, and Time Problems
  3. Clocks and Calendar-Based Questions
  4. Pipes and Cisterns Problems
  5. Boats and Streams Questions
  6. Mixtures and Alligation
  7. Age Problems and Their Calculations
  8. Locus and Pathway Problems
  9. Data Sufficiency Questions
  10. Practical Applications of Mathematics in Daily Life
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