CRPF HC Part II Syllabus

CRPF HC Part II: topic-wise syllabus

1. 1

   Number System & Arithmetic

   ~6 marks

   • Number System — Natural, Whole, Integers, Rational, Real, Complex, HCF/LCM, Divisibility, Surds, Indices
   • Percentages, Profit & Loss, Discount, Simple & Compound Interest, Ratio & Proportion, Averages, Mixture, Alligation
   • Time, Work, Speed, Distance, Boats & Streams, Pipes & Cisterns, Races, Clocks & Calendars
   • Mensuration — Areas, Volumes, Surface Areas (2D, 3D), Unit Conversion, Trigonometric Ratios (Basics)
   • Practical Maths — Estimation, Unit Conversion, Cost, Tax, GST, EMI, Budgeting, Maps, Scale
2. 2

   Algebra

   ~5 marks

   • Algebraic Expressions, Identities, Polynomials, Factorization, Simplification
   • Linear Equations, Quadratic Equations, Equations in Two Variables, Simultaneous Equations, Word Problems
   • Inequalities, Graphical Solutions, Linear Programming Basics
   • Arithmetic Progression (AP), Geometric Progression (GP), Harmonic Progression (HP), Sum of Series
   • Sets, Relations, Functions, Venn Diagrams, Binary Operations
3. 3

   Geometry & Trigonometry

   ~5 marks

   • Basic Geometry — Lines, Angles, Polygons, Triangles, Quadrilaterals, Circles, Parallel Lines, Properties
   • Triangles — Congruence, Similarity, Pythagoras, Areas, Heights & Distances, Centroid, Incenter, Circumcenter
   • Circles — Tangent, Chord, Secant, Angles in Same Segment, Cyclic Quadrilateral, Areas
   • Areas & Volumes — Squares, Rectangles, Triangles, Circles, Cubes, Cuboids, Cylinder, Cone, Sphere, Prism, Pyramid
   • Trigonometry — Ratios, Identities, Heights & Distances, Applications, Tables, Values
4. 4

   Statistics & Probability

   ~5 marks

   • Statistics — Mean, Median, Mode, Range, Quartiles, Variance, Standard Deviation, Frequency Distribution, Bar/Pie/Line/Histrogram, Ogive
   • Probability — Theoretical, Empirical, Sample Space, Events, Conditional, Independent, Bayes' Theorem, Random Variables
   • Data Interpretation — Tables, Charts, Graphs, Caselets, Data Sufficiency, Comparisons
5. 5

   Coordinate Geometry & Vectors

   ~4 marks

   • Coordinate Geometry — Cartesian Plane, Distance, Section, Mid-Point, Area of Triangle, Slope, Equation of Line, Circle, Parabola
   • Vectors, 3D Geometry — Basics, Direction Cosines, Plane, Line, Distance
   • Transformations — Translation, Reflection, Rotation, Scaling, Symmetry