Mathematics is a vast scientific subject that assist other scientific fields of engineering, medical and commerce. It is the harbinger of all modern creations and discoveries.

BIE 1st year mathematics consists of 13 chapters, most of the chapters teach students new concepts.

Mathematics examinations conducted by BIE Sindh are lengthy and they will test students concepts and focus. Moreover, the test paper is divided into two parts of subjective (80 marks) and an objective part containing 20 marks worth of mcqs.

With the growing demand for technical education, mathematics has become a valuable subject of study. Here at, we are providing full mathematics course with the help of online recorded lectures and solved exercises. Students can learn under the guidance of Sir Murtaza(MSc mathematics). Not only this, but they can also access multiple games, virtual lab simulations, and animations that will further enhance their learning experience.

Mathematics - XI First Year - Sindh Board


Subject name Mathematics
Class XI/1st year
Board Sindh Board
Subject Affiliation
  • Commerce
  • Pre-engineering
  • ICS
Book Chapters Count 13
Subject Type Compulsory
Paper Type Subjective and Objective
Marks scheme Total= 100

  • Subjective=80
  • Objective=20
Minimum Passing Marks 33/100
Subject features Online recorded lecture, online assessments, solved exercises,mcqs, and games.

1.1 Revision
1.2 A Few Definitions
1.3 Operations on Sets
1.4 Properties of Operations on Sets
1.5 Some Important Laws

2.1 Introduction
2.2 Development of Number Systems
2.3 Distinction of Between Rational and Irrational numbers
2.4 The Real Number System
2.5 The System C of Complex Numbers
2.6 Properties of Complex Numbers
2.7 Definition of Imaginary Numbers
2.8 Conjugate of Complex Numbers
2.9 Modulus of a Complex Number
2.10 The Subtraction of Complex Numbers
2.11 The Division of Complex Numbers
2.12 Geometrical Representation of the Complex Number x + iy as Pair of Real Numbers (x,y)
2.13 The Order Relations
2.14 Vector Interpretation of Complex Numbers
2.15 The Triangle Inequality
2.16 Real and Imaginary Parts of ( x + iy ) Power n

3.1 Quadratic Equations
3.2 Factor Theorem of Polynomials
3.3 Synthetic Division
3.4 Solution of Quadratic Equations
3.5 The Cube Roots of Unity
3.6 Properties of the Cube Roots of Unity
3.7 Equations Reducible to the Quadratic Form
3.8 The Theory of Quadratic Equations
3.9 Nature of the Roots of a Quadratic Equation
3.10 Relations Between the Roots and the Coefficient of a Quadratic Equation
3.11 To Form a Quadratic Equation When its Roots are Given
3.12 Problems Involving Quadratic Equations
3.13 System of Two Equations Involving Two Variables
3.14 Solution of Different Types of Systems of Equations

4.1 Introduction
4.2 Matrices
4.3 Notation
4.4 Special Types of Matrices
4.5 Algebra of Matrices
4.6 Properties of Matrix Operation
4.7 Determinant of a Square Matrix
4.8 Determinants of Order Two and Three
4.9 Properties of Determinants of Order Two
4.10 Alternate Method For Expanding a Third Order Determinant
4.11 Properties of Determinants of Order Three
4.12 Minors and Cofactors of Elements of a Given Matrix A
4.13 The Multiplicative Inverse of a Square Matrix
4.14 Distinction Between Homogeneous and Non-Homogeneous Systems of Linear Equations
4.15 Solving a System of Three Non-Homogeneous Linear Equations in Three Unknowns

5.1 Binary Operations
5.2 Multiplication ( or Composition ) Table
5.3 Properties of Binary Operations
5.4 Algebraic Structure
5.5 Groups

6.1 Introduction
6.2 Arithmetic Sequences or Arithmetic Progression (A.P)
6.3 Standard Form of an A.P
6.4 Arithmetic Series
6.5 Arithmetic Means
6.6 To Insert Arithmetic Means
(i) a single A.M
(ii) n A.M’s
6.7 To Find the Sum of n A.M
6.8 Geometric Sequence or Geometric Progression ( G.P )
6.9 Standard Form of a G.P
6.10 Geometric Series
6.11 Infinite Geometric Series
6.12 Geometric Means
6.13 To Insert
(i) a single geometric Mean
(ii) n geometric means
6.14 Harmonic Sequences or Harmonic Progression ( H.P )
6.15 General Term of an H.P
6.16 The Characteristic Relation for an H.P
6.17 An Important Theorem
6.18 Harmonic Means
6.19 To Insert
(i) a single Harmonic Mean
(ii) n harmonic means
6.20 Relation Between Means

7.1 The Counting Principles
7.2 The Factorial Notation
7.3 Permutations and Combinations
7.4 Number of Permutations
7.6 Circular ( or Cyclic ) Permutations
7.6 Number of Combinations
7.7 Introduction to Probability
7.8 Basic Terminology
7.9 Definition of Probability
7.10 Addition Law of Probability

8.1 The Principle of Mathematical Inducion
8.2 Sum of Positive Integral Powers of Natural numbers
8.3 Binomial Theorem
8.4 The Binomial Theorem for a Positive Integral index
8.5 Some Important Observations
8.6 The General Term
8.7 The Middle Terms
8.8 The Binomial Series
8.9 Approximations
8.10 Application to Summation of Series

9.1 Introduction
9.2 Radian Measure
9.3 General and Its Measure in Degree and Radians
9.4 Relation Between Radian and Degree Measure
9.5 Relation Between Arc-Length, Radius and general angle
9.6 The Radian Function
9.7 Signs of the Trigonometric Function in the Four Quadrants
9.8 Values of Trigonometric Functions

10.1 Trigonometric Identities and Their Applications
10.2 The Distance Formula
10.3 A Fundamental Law
10.4 Deductions From the Funndamental Law
10.5 The Sum and Difference Identities
10.6 Applications
10.7 Identities for Sin2θ, Cos2θ and Tan2θ
10.8 Identities For Sin θ/2, Cos θ/2 and Tan θ/2
10.9 Sum and Product Identities For Trigonometric Functions
10.10 Applications

11.1 Trigonometric Functions
11.2 Periods of Trigonometric Functions
11.3 Graphs of Trigonometric Functions

12.1 The Law of Sines
12.2 The Laws of Cosines
12.3 The Laws of Tangents
12.4 Solutions of Triangles
12.5 Half Angle Formulae in Terms of the Lengths of the sides of a triangle
12.6 Area of a Triangle
12.7 Circles Associated with a Triangle
12.8 Circum-Radius in Terms of the Measure of a Side and the Measure of the Opposite
12.9 Circum-Radius r in Terms of the Measure of three Sides of a Triangle
12.10 The In-Radius of a Triangle
12.11 Radii of e-Circles of a Triangle

13.1 Inverse Trigonometric Functions and Their Domains and Ranges
13.2 Applications
13.3 Solutions of Trigonometric Equations


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Mathematics - XI First Year - Sindh Board


Sir. Murtaza

Mathematics – XI First Year Sindh 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 the 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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  • 6004,590
  • 300 Days

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