The second-year fsc Mathematics is a core subject assigned by BISE Punjab required for the students of Pre-engineering and ICS. Mathematics 2nd year is a more advanced level course as compared to its 1st year counterpart. This subject includes topics of differentiation, integration and linear programming. All these topics assist students during their undergraduate and postgraduate studies. By achieving good marks in this subject, students can prove that they have totally grasped the concepts of mathematics and are prepared for their further studies. has launched an online learning platform where students can follow this long course at any place at any time with the help of recorded lectures, solved excersices, mcqs, animations, a virtual lab, and online assessment.

Mathematics - XII Second Year - Punjab Board

Subject name Mathematics
Class XII/ 2nd year
Board Punjab board
Subject Affiliation
  • Commerce
  • Pre-engineering
  • ICS
Book Chapters Count 7
Subject Type Elective
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, mcqs and games.

1.1 Introduction
1.2 Types of Functions
1.3 Composition of Function and Inverse of
1.4 Limit of a Function and Theorems on Lim
1.5 Limits of Important Functions
1.6 Continous and Discontinuous Functions
1.7 Graphs

2.1 Introduction
2.2 Finding f’x) from Definition of Derivative
2.3 Theorems on Definition
2.4 The Chain Rule
2.5 Derivative of Inverse Functions
2.6 Derivative of Functions Given in the Form of Parametric Equations
2.7 Differentiation of Implicit Relations
2.8 Derivatives of Trigonometric Functions
2.9 Derivatives of Inverse Trigonometric Functions
2.10 Derivative of Exponential Functions
2.11 Derivative of Logarithmic Functions
2.12 Logarithmic Differentiation
2.13 Derivative of Hyperbolic Functions
2.14 Derivatives of the Inverse Hyperbolic Functions
2.15 Successive Differentiation Or Higher Derivatives
2.16 Series Expansion of Functions
2.17 Tailor Series Expansion of Functions
2.18 Geometrical Interpretation of a Derivative
2.19 Increasing and Decreasing Functions
2.20 Relative Extrema
2.21 Critical Values of Critical Points

3.1 Introduction
3.2 Integration as Anti-Derivative
3.3 Integration By Method of Substitution
3.4 Some Useful Substitutions
3.5 Integration By Parts
3.6 Integration Involving Partial Fractions
3.7 The Definite Integrals
3.8 Applications of Definite Integrals
3.9 Differential Equations

4.1 Introduction
4.2 Translation and Rotation of Axes
4.3 Equations of Straight Lines
4.4 Two and Three Straight Lines
4.5 Angles Between Two Lines
4.6 Homogeneous Equations-Second Degree in2 Variables

5.1 Introduction
5.2 Linear Inequalities
5.3 Region Bounded By 2 or 3 Simultaneous Inequalities
5.4 Problem Constraints
5.5 Feasible Solution Set
5.6 Linear Programming
5.7 Linear Programming Problems

6.1 Introduction
6.2 Tangents and Normals
6.3 Analytical Proofs of Important Properties of a circle
6.4 Parabola
6.5 Ellipse and Its Elements
6.6 Hyperbola and Its Elements
6.7 Tangents and Normals
6.8 Translation and Rotation of Axes
6.9 The General Equation of Second Degree

7.1 Introduction
7.2 Introduction of Vector in Space
7.3 The Scalar Product of Two Vectors
7.4 Cross Product or Vector Product of Two Vectors
7.5 Scalar Triple Product of Vectors
7.5 Scalar Triple Product of Vectors


Interactive 3D Simulations to help you build concepts fast.


Quizzes and assignments to prepare you for exams along the way.


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Front board technique to keep you more engaged with an instructor.


Ask questions in comments when in doubt and get answers quickly.


Better learning experience than a crowded classroom in half of a fee.


Mathematics - XII Second Year - Punjab Board


Sir. Murtaza

Mathematics – XII Second 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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Course Curriculum

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  • 6004,590
  • 365 Days

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