12th Class Math MCQ Tests Punjab

Math English Medium Book

• Chapter 1 Functions and Limits
  Introduction, Concept of Function, Definition (Function - Domain - Range), Notation and Value of Function, Graphs of Algebraic Functions, Graphs of Functions defined piece-wise, Types of Functions, Algebraic Functions, Trigonometric Functions, Inverse Trigonometric Functions, Exponential Function, Logarithmic Function, Hyperbolic Functions, Inverse Hyperbolic Functions, Explicit Function, Implicit Function, Even Function, Odd Function, Exercise, Cpmposition of Functions and Inverse of a Function, Composition of Functions, Inverse of a Function, Algebraic method to find the Inverse Function, Exercise, Theorems, Meaning of the phrase x approaches zero, Meaning of the phrase x approaches infinity, Meaning of the phrase x approaches a, Concept of limit of a function, Limit of a Function, Theorems, Limits of important Functions, limit at infinity, Method for Evaluating the limits at Infinity, the sandwitch theorem, Exercise, Continuous and Discontinuous Functions, one-sided Limits, Criterion for Existence of limit of a Function, Continuity of a function at a number, Exercise, Graphs, Graph of the Exponential function f(x) = ax, Graph of the Exponential function f(x) = ex, Graph of common Logarithmic Function f(x)=lgx, Graphs of Natural logarithmic Function f(x)=lnx, Graphs of implicit Functions, Graph of parametric Equations, Graphs of Discontinuous Functions, Graphical Solution of the Equations, Exercise 35
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• Chapter 2 Differentiation
  Introduction, Average rate of Change, Derivative of a Function, Finding f(x) from definition of Derivative, Derivation of xn where neZ, Differentiation of Expressions of the types, Exercise, Exercise, Theorems, Derivative of a sum or a Difference of Functions, Derivative of a product (The product Rule), Derivative of a Quotient (The Quotient Rule), Exercise, The Chain Rule, Derivatives of Inverse Funtions, Derivative of a Function given in the form of Parametric Equations, Differentiation of Implicit Relations, Exercise, Derivatives of Trigonometric Functions, Derivatives of inverse Trigonometric Functions, Exercise, Derivative of Exponential Functions, Derivative of the Logarithmic Function, Logarithmic Differentiation, Derivative of Hyperbolic Functions, Derivatives of the inverse Hyperbolic Functions, Exercise, Successive Differentiation (or Higher Derivatives), Exercise, Series Expansions of Functions, Tailor Series Expansions of Funtions, Exercise, Geometrical Interpretation of a Derivative, Increasing and Decreasing Functions, Relative Extrema, Critical Values and Critical Points, Second Derivative Test, Exercise, Application of Maxima and Minima, Exercise 59
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• Chapter 3 Integration
  Introduction, Differentials of Variables, Distinguishing Between dy and delta-y, Finding dy/dx by using differentials, Simple application of differentials, Exercise, Integration as Anti Derivative (Inverse of Derivative), Some Standard Formulae for Anti Derivatives, Theorems, Anti-Derivatives of [f(x)]n f ’(x) and [f(x)]-1 f ’(x), Exercise, Integration by Method of Substitution, Some useful Substitutions, Exercise, Integration by parts, Exercise, Integration involving partial Fractions, Exercise, The Definite Integrals, The Area Under The Curve, Theorem, Exercise, Application of Definite integrals, Exercise, Differential Equations, Solution of a Differential Equation of first order, Initial Conditions, Exercise 33
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• Chapter 4 Introduction to Analytic Geometry
  Introduction, The Distance Formula, Point Dividing the Join of Two Points in a given Ratio, Exercise, Translation and Rotation of Axes, Exercise, Equation of Straight lines, Slope or Gradient of a Straight Line Joining Two Points, Equation of a Straight Line Parallel to the x-axis (or perpendicular to the y-axis), Derivation of Standard Forms of Equations of Straight Lines, A Linear Equation in two Variables Represents a Straight Line, To Transform the General Linear Equation to Standard Forms, Position of a point with respect to a line, Two and Three Straight Lines, The Point of Intersection of two Straight Lines, Condition of Concurrency of Three Straight Lines, Equation of Lines through the point of intersection of two lines, Distance of a point from a line, Distance Between two Parallel Lines, Area of a Triangular Region Whose Vertices are Given, Exercise, Angle between Two Lines, Equation of a Straight Line in Matrix form, Exercise, Homogeneous Equation of the Second Degree in two variables, Homogeneous Equation, To find measure of the angle between the lines represented by, Exercise 30
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• Chapter 5 Linear Inequalities and Linear Programming
  Introduction, Linear Inequalities, Graphing of A Linear Inequality in Two Variables, Region Bounded by 2 or 3 simultaneous Inequalities, Exercise, Problem Constraints, Feasible Solution Set, Exercise, Linear programming, Linear Programming Problems, Exercise 20
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• Chapter 6 Conic Section
  Introduction, Equation of a Circle, General Form of an Equation of a Circle, Equations of Circles Determined by Given Conditions, Exercise, Tangents and Normals, Length of the tangent to a circle (Tangential Distance), Exercise, Analytic proof of important properties of a Circle, Exercise, Parabola, General Form of an Equation of a Parabola, Other Standard parabolas, Graph of the Parabola, Exercise, Ellipse and its Elements, Standard Form of an Ellipse, Graph of an Ellipse, Exercise, Hyperbola and its Elements, Standard Equation of Hyperbola, Graph of the hyperbola, Exercise, Tangents and Normals, Intersection of Two Coincs, Exercise, Translation and Rotation of Axes, Exercise, The General Equation of Second Degree, Classification of Conics by the Discriminant, Exercise 45
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• Chapter 7 Vector
  Introduction, Geometric Interpretation of vector, Multiplication of Vector by a Scalar, Addition and Subtraction of Two Vectors, Position Vector, Vectors in a Plane, Properties of Magnitude of a Vector, Another notation for representing vectors in plane, A unit vector in the direction of another given vector, The Ratio Formula, Vector Geometry, Exercise, Introduction of vector in Space, Concept of a vector in space, Properties of Vectors, Another notation for representing vectors in space, Distance Between two Points in Space, Direction Angles and Direction Cosines of a Vector, Exercise, The Scalar Product of two Vectors, Deductions of the Important Results, Perpendicular (Orthogonal) Vectors, Properties of Dot Product, Analytical Expression of Dot Product u.v (Dot product of vectors in their components form), Angle between two vectors, Projection of one Vector upon another Vector:, Exercise, The Cross Product or Vector Product of Two vectors, Derivation of useful results of cross products, Properties of Cross product, Analytical Expression of u x v (Determinant formula for u x v), Parallel Vectors, Area of Parallelogram, Area of Triangle, Exercise, Scalar Triple Product of Vectors, Analytical Expression of u.(v x w), The Volume of the Parallelepiped, The Volume of the Tetrahedron, Application of Vectors in Physics and Engineering, Exercise 25
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