most important definitions Class 11 Mathematics

 Here are the most important definitions from each chapter of Class 11 Mathematics (Punjab Textbook 2025 Syllabus) — specially selected to help in short questions, MCQs, and concept clarity.

🔢 Chapter 1: Complex Numbers

  • Complex Number: A number of the form a + bi, where a and b are real numbers and i = √–1.

  • Imaginary Unit: The symbol i such that i² = –1.

  • Modulus: |z| = √(a² + b²) for z = a + bi.

  • Conjugate: If z = a + bi, then its conjugate is a – bi.

✖️ Chapter 2: Matrices and Determinants

  • Matrix: A rectangular array of numbers arranged in rows and columns.

  • Order of a Matrix: Number of rows × number of columns.

  • Determinant: A scalar value associated with a square matrix used in solving linear equations.

  • Inverse of a Matrix: A⁻¹ such that AA⁻¹ = I.

🔁 Chapter 3: Quadratic Equations

  • Quadratic Equation: An equation in the form ax² + bx + c = 0, where a ≠ 0.

  • Discriminant: D = b² – 4ac, determines the nature of roots.

  • Roots of Equation: Solutions of the quadratic equation.

  • Nature of Roots: Real & equal, real & distinct, or complex based on D.

➕ Chapter 4: Partial Fractions

  • Proper Rational Function: Degree of numerator < degree of denominator.

  • Improper Rational Function: Degree of numerator ≥ degree of denominator.

  • Partial Fractions: Decomposition of a rational function into simpler fractions.

🧮 Chapter 5: Sequences and Series

  • Sequence: A set of numbers arranged in a definite order.

  • Arithmetic Sequence: Constant difference between consecutive terms.

  • Geometric Sequence: Constant ratio between consecutive terms.

  • Series: The sum of terms of a sequence.

📐 Chapter 6: Permutation, Combination and Probability

  • Permutation: Arrangement of objects in a specific order (nPr).

  • Combination: Selection of objects regardless of order (nCr).

  • Probability: Likelihood of occurrence of an event = favorable outcomes / total outcomes.

  • Factorial: n! = n × (n – 1) × ... × 1.

🔄 Chapter 7: Mathematical Induction and Binomial Theorem

  • Mathematical Induction: Method to prove a statement true for all natural numbers.

  • Binomial Theorem: Expansion of (a + b)ⁿ using binomial coefficients.

  • Pascal’s Triangle: A triangular array of binomial coefficients.

🧩 Chapter 8: Fundamentals of Trigonometry

  • Radian: Angle subtended at center of circle by arc equal to radius.

  • Principal Angle: The smallest positive coterminal angle (0 to 360° or 0 to 2π).

  • Trigonometric Ratios: sin, cos, tan, etc.

  • Coterminal Angles: Angles differing by multiples of 360° or 2π.

🔁 Chapter 9: Trigonometric Identities

  • Identity: An equation true for all values of the variable.

  • Basic Identities: sin²θ + cos²θ = 1, etc.

  • Double Angle Formulas: Like sin(2θ) = 2sinθcosθ.

🔃 Chapter 10: Graphs of Trigonometric Functions

  • Amplitude: Height from middle to peak in sine/cosine graphs.

  • Period: The length after which the function repeats.

  • Phase Shift: Horizontal shift in graph.

  • Frequency: Reciprocal of period.

📈 Chapter 11: Linear Inequalities and Linear Programming

  • Inequality: Mathematical statement with <, >, ≤, ≥.

  • Feasible Region: Area of solution satisfying all inequalities.

  • Objective Function: Function to maximize/minimize in linear programming.

  • Constraints: The conditions (inequalities) of the problem.

🧭 Chapter 12: Introduction to Analytical Geometry

  • Coordinate Geometry: Study of geometry using coordinates.

  • Distance Formula: √[(x₂ – x₁)² + (y₂ – y₁)²].

  • Midpoint Formula: ((x₁ + x₂)/2, (y₁ + y₂)/2).

  • Slope: m = (y₂ – y₁)/(x₂ – x₁).

📉 Chapter 13: Linear Graphs and Circles

  • Line Equation: y = mx + c.

  • Circle: Set of points at constant distance from a center.

  • Standard Circle Equation: (x – a)² + (y – b)² = r².

  • Chord: Line joining two points on a circle.

📐 Chapter 14: Limits and Derivatives

  • Limit: The value a function approaches as the input approaches a point.

  • Derivative: Rate of change or slope of a function at a point.

  • Differentiation: Process of finding the derivative.

  • Continuity: Function has no break or jump.


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