This textbook is designed for first-year college students in Pakistan. It introduces students to advanced algebra, trigonometry, coordinate geometry, and basic calculus concepts. The focus is on both theory and problem-solving, preparing students for mathematics at higher levels (engineering, computer science, economics, etc.). Contents Summary 1. Sets, Functions, and Groups o Basic set theory, operations on sets. o Functions and their types. o Introduction to groups (algebraic structures). 2. Matrices and Determinants o Types of matrices, matrix operations. o Determinants and properties. o Application in solving simultaneous equations (Cramer’s Rule). 3. Quadratic Equations o Nature of roots, relationships between roots and coefficients. o Formation of quadratic equations. o Symmetric functions of roots. 4. Partial Fractions o Expansion of algebraic fractions into partial fractions. o Use in integration and algebraic simplification. 5. Sequences and Series o Arithmetic progression (A.P.). o Geometric progression (G.P.). o Harmonic progression (H.P.). o Summation of series. 6. Permutations, Combinations, and Probability o Fundamental principle of counting. o Permutations & combinations with applications. o Probability rules and simple problems. 7. Binomial Theorem o Statement and proof of theorem. o General term and middle term. o Applications in expansions and approximations. 8. Trigonometry o Fundamental identities. o Trigonometric functions and transformations. o Multiple-angle and half-angle formulas. o Inverse trigonometric functions. o Solutions of trigonometric equations. 9. Functions and Limits o Concept of function and graphing. o Introduction to limits and continuity. o Evaluation of standard limits. 10. Differentiation o Concept of derivative (first principle). o Rules of differentiation. o Applications to tangents, normals, and rate of change. 11. Introduction to Analytic Geometry o Cartesian coordinates and distance formula. o Equation of straight line (slope, intercept form). o Circle equation and basic properties. Learning Outcomes By the end of Mathematics Intermediate Part 1, students should be able to: • Apply algebraic methods to solve equations and inequalities. • Use matrices, determinants, and partial fractions in problem-solving. • Analyze trigonometric identities and equations. • Understand the basics of probability and counting principles. • Use limits and differentiation for calculus applications. • Apply coordinate geometry to lines and circles.