Mathematics is considered as the father of all sciences that is why it is assigned as a compulsory subject for the students of Pre-engineering, ICS, and Commerce. Our 1st year mathematics course of Punjab Board consists of 14 chapters, some of these chapters are built upon students old concepts learned in previous classes, while other chapters bestow new mathematical ideas upon the minds of students. In order to make paper simple and interesting, Punjab Board has divided math test into two parts: subjective and objective. The former consists of Long answered questions while the latter is associated with Multiple choices(mcqs) and Short answered questions. To clear the paper, students have to achieve good marks in both sections.        

Students can easily follow this subject at under the guiding light of Sir Murtaza (Master in Mathematics). further enhances students learning experience by supplying them with curriculum notes, online assessments, solved exercises and animations.

Mathematics - XI First Year - Punjab Board

Subject name Mathematics
Class XI/ 1st year
Board Punjab Board
Subject Affiliation
  • Commerce
  • Pre-engineering
  • ICS
Book Chapters Count 14
Subject Type Compulsory
Paper Type Subjective And Objective
Marks scheme Total= 100

  • Subjective=80
  • Objective=20
Minimum Passing Marks 45/100
Subject features Online recorded lecture, online assessments, and games.

1.1 Introduction
1.2 Rational Numbers and Irrational Numbers
1.3 Properties of Real Numbers
1.4 Complex Numbers
1.5 The Real Line
1.6 Geometrical Representation of Complex Numbers
1.7 To Find Real and Imaginary Parts of (x + i y ) ^n

2.1 Introduction
2.2 Operations on Sets
2.3 Venn Diagrams
2.4 Operations on Three Sets
2.5 Properties of Union and Intersection
2.6 Inductive and Deductive Logic
2.7 Implication or Conditional
2.8 ruth Sets, A Link Between Sets Theory and Logic
2.9 Relations
2.10 Functions
2.11 Inverse of a Function
2.12 Binary Operations
2.13 Groups
2.14 Solution of Linear Equations
2.15 Reversal Law of Inverse

3.1 Introduction
3.2 Determinant of a 2×2 Matrix
3.3 Solution of Simultaneous Linear Equations
3.4 Field
3.5 Properties of Matrix Addition, Scalar Multiplication and Matrix Multiplication
3.6 Determinants
3.7 Properties of Determinants Which Help in Their Evaluation
3.8 Adjoint and Inverse of a Square Matrix of Order n = 3 or n > 3
3.9 Elementary Row and Column Operations on a Matrix
3.10 Echelon and Reduced Echelon Forms of Matrices
3.11 Systems of Linear Equations
3.12 Cramer’s Rule

4.1 Introduction
4.2 Solutions of Equations Reducible to the Quadratic Equation
4.3 Three Cube Roots of Unity
4.4 Four Fourth Roots of Unity
4.5 Polynomial Functions
4.6 Theorems
4.7 Synthetic Division
4.8 Relations Between the Roots and the Coefficients of a Quadratic Equation
4.9 Formation of an Equation Whose Roots are Given
4.10 Nature of the Roots of a Quadratic Equation
4.11 Systems of Two Equations Involving Two Variables
4.12 Problems on Quadratic Equations

5.1 Introduction
5.2 Rational Fraction
5.3 Resolution of a Rational Fraction P(x)/Q(x) Into Partial Fractions

6.1 Introduction
6.2 Types of Sequences
6.3 Arithmetic Progression (A.P)
6.4 Arithmetic Mean (A.M)
6.5 Series
6.6 Word Problems on A.P.
6.7 Geometric Progressions (G.P)
6.8 Geometric Means
6.9 Sum of n Terms of a Geometric Series
6.1 The Infinite Geometric Series
6.11 Word Problems on G.P.
6.12 Harmonic Progression (H.P)
6.13 Relations Between Arithmetic, Geometric and Hamonic Means
6.14 Sigma Notation (or Summation Notation)
6.15 To Find Formulae For The Sums

7.1 Introduction
7.2 Permutation
7.3 Combinations
7.4 Probability

8.1 Introduction
8.2 Principle of Mathematical Induction
8.3 Principle of Extended Mathematical Indu
8.4 Binomial Theorem
8.5 The Binomial Theorem When the Index n is a Negative Integer or a Fraction.
8.6 Applications of the Binomial Theorem
8.6 Applications of the Binomial Theorem

9.1 Introduction
9.2 Units of Measures of Angles
9.3 Relation Between the Length of an Arc
9.4 General Angle (Coterminal Angles)
9.5 Angle in the Standard Position
9.6 Trigonometric Functions
9.7 Trigonometric Functions of Any Angle
9.8 Fundamental Identities
9.9 Signs of the Trigonometric Functions
9.10 The Values of Trigonometric Functions of Acute Angles 45,30 and 60 Degrees
9.11 The Values of the Trigonometric Functions of Angles 0, 90, 180, 270, 360 Degrees
9.12 Domains of Trigonometric Functions and of Fundamental Identities

10.1 Introduction
10.2 Deductions From Fundamental Law
10.3 Trigonometric Ratios and Allied Angles
10.4 Further Application of Basic Identities
10.5 Double Angle Identities
10.6 Half-Angle Identities
10.7 Triple Angle Identities
10.8 Sum, Difference and Product of Sines and Cosines

11.1 Introduction
11.2 Period of Trigonometric Functions
11.3 Values of Trigonometric Functions
11.4 Graphs of Trigonometric Functions
11.5 Graph of y = Sin x From – 360⁰ to 360⁰
11.6 Graph of y = Cos x From – 360⁰ to 360⁰
11.7 Graph of y = Tan x From – 180⁰ to 180⁰
11.8 Graph of y = Cot x From – 360⁰ to 180⁰
11.9 Graph of y = Sec x From – 360⁰ to 360⁰
11.10 Graph of y = Cosec x From – 360⁰ to 360⁰

12.1 Introduction
12.2 Tables of Trigonometric Ratios
12.3 Solution of Right Triangles
12.4 a)-Heights and Distances
12.5 b)-Angles of Elevation and Depression
12.6 Engineering and Heights and Distances
12.7 Oblique Triangles
12.8 Solution of Oblique Triangles
12.9 Area of Triangle
12.10 Circles Connected With Triangle
12.11 Engineering and Circles Connected With Triangles

13.1 Introduction
13.2 The Inverse Sine Function
13.3 The Inverse Cosine Function
13.4 The Inverse Tangent Function
13.5 Inverse Cotangent, Secant and Cosecant Functions
13.6 Domains and Ranges of Principal Trigonometric Functions and Inverse Trigonometry
13.7 Addition and Subtraction Formulas

14.1 Introduction
14.2 Solution of General Trigonometric Equations


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Mathematics - XI First Year - Punjab Board

Sir. Murtaza

Mathematics – XI First Year Punjab Board

Sir Murtaza is the mathematics teacher at He has attained qualification of MSc Mathematics from well-renowned University of Karachi. He has an exquisite style of teaching with calm, collected and a soothing voice. But behind his docile demeanor is a mind of a mathematical devil who has an ability to play with equations and formula like a mad scientist.

Students can follow along Sir Murtaza exclusively at in their quest to achieve a high quality yet affordable education.

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