Mathematics is a methodical application of matter. It is said that this subject makes a man systematic. Mathematics makes our life orderly and prevents chaos. Certain qualities that are nurtured by mathematics are the power of reasoning, creativity, critical thinking, problem-solving ability. In short, an organized and successful person can totally be defined on the basis of his mathematical skills. Viewing the importance of mathematics, BIE Sindh has appointed 2nd year mathematics as a compulsory subject for the students of Pre-Engineering, Commerce, and ICS.

The paper pattern of mathematics is same as other subjects. The paper is divided into two parts: subjective and objective(mcqs). However, the subjective part is further divided into two parts i.e., B and C. The former part contains short answered questions while the latter is based on one answered questions. Moreover, the paper has been allotted total of 100 marks with only 33 percent required for a passing grade.
Mathematics – XII Second Year – Sindh Board


Subject name Mathematics
Class XII/2nd year
Board Sindh Board
Subject Affiliation
  • Commerce
  • Pre-Engineering
  • ICS
Book Chapters Count 9
Subject Type Compulsory
Paper Type Subjective and Objective
Marks scheme Total= 100

  • Subjective=80
  • Objective=20
Minimum passing marks 33.5/100
Subject features Online recorded lecture, solved exercises, online assessments, and games.

1.1 Introduction ( Numbers Systems )
1.2 Intervals
1.3 Modulus Function
1.4 Neighbourhood
1.5 Binary Relation
1.6 Functions
1.7 Inverse Function
1.8 Concept of Function in Terms of Variables
1.9 Algebra of Functions
1.10 Polynomial Function
1.11 Rational Function
1.12 Composite Function
1.13 Even and Odd Function
1.14 Circular Trigonometric Function
1.15 Inverse Trigonometric Function
1.16 Formulization of Functions
1.17 Graph of a Relation and of a Function
1.18 Sequence
1.19 Limit of Sequence
1.20 Bounded Set and Monotonic Sequence
1.21 Divergence
1.22 Exponential Function
1.23 Logarithmic Function
1.24 Infinite Series
1.25 Meaning of the Phrase ‘x’ Tends to ‘a’
1.26 Limit of Function
1.27 Limits as x Tends Infinity

2.1 Cartesian Coordinate System
2.2 Distance Between Two Given Points
2.3 Division of Given Line Segment in a Given Ratio
2.4 Rules For the Choice of Axes
2.5 Curves and Equations
2.6 Slope (or Gradient) of a Line
2.7 Slope of the Line Joining Two Given Points
2.8 Condition For Three Points to be Collinear
2.9 Parallel and Perpendicular Lines
2.10 Angle From One Line to Another in the Slope Form
2.11 Lines Parallel to the Axes of Coordinates
2.12 Various Forms of Equation of Straight Line
2.13 Deduction of One Form of an Equation of a Line From Another

3.1 The General Linear Equation
3.2 Angle Between Two Lines From l2 to l1 in the General Form
3.6 Points of Intersection of Two Straight Lines
3.4 Concurrency of Three Lines
3.6 Equations of Lines in the Matrix Form
3.6 Lines Through the Intersection of Two Given Lines
3.7 Position of a Point with Respect to a Given Straight Line
3.8 Distance of a Point From a Line
3.9 Area of a Triangle
3.10 Equation of a Pair of Straight Lines Through the Origin
3.11 The Equation ax2 + 2hxy + by2 = 0, where a, h, b are not all zero

4.1 Derivative of a Function at a Point
4.2 Composite Function
4.3 Implicit Function
4.4 Parametric Function
4.5 Higher Derivatives

5.1 Geometrical Meaning of dy/dx
5.2 dy/dx as a Rate Measurer
5.3 Differential
5.4 Increasing and Decreasing Function

6.1 Antiderivation or Integration
6.2 Integration by Substitution
6.3 Integration by Completing the Squares
6.4 Integration by Parts
6.5 Partial Fractions
6.6 Integration of Rational Fractions
6.7 Area Under a Curve
6.8 Differential Equations

7.1 Introduction
7.2 Equation of a Circle
7.3 Equation of a Circle with a Line Segment and its diameter
7.4 Tangents and Normals to a Circle
7.5 Equation of the Chord Joining Two Points on the circle
7.6 Points of Intersection of the Straight Line y = mx + c and the Circle x2 + y2 = r2
7.7 Condition of Tangency of a Line to a Circle
7.8 The Equation of Tangents and Normals Using Derivatives
7.9 Length of the Tangent from the Point to the Circle
7.10 Condition of Normality
7.11 Some Geometrical Properties of the Circle

8.1 General Conic
8.2 Parabola
8.3 The Standard Equation of an Ellipse
8.4 Hyperbola
8.5 Equation of Chords
8.6 Equations of Tangents and Normals to Conics
8.7 Two Tangents and Condition of Tangency to Conics

9.1 Cartesian Coordinate System for 3D Space
9.2 Scalar and Vectors Quantities
9.3 Equal Vectors
9.4 Position Vector and its Direction Cosines
9.5 Multiplication of a Vector by a Scalar
9.6 Vector Addition
9.7 Components of a Vector in a Plane
9.8 Application to Analytic Geometry
9.9 The Scalar and Vector Products of Two Vectors
9.10 Scalar Products of Three Vectors
9.11 Applications of Vectors to Mechanics


Interactive 3D Simulations to help you build concepts fast.


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


Powerful teaching techniques help you digest information easily.


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 – Sindh Board


Sir. Murtaza

Mathematics – XII Second 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 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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  • 300 Days

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