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FSc Part 2 (KPK Boards)

Notes of FSc Part 2 of “A Textbook of Mathematics For Class XII” published by Khyber Pakhtunkhwa Textbook Board, Peshawar. We are posting the notes chapter-wise. These notes are shared as open educational resources. This page will be continuously updated.

Author: Muhammad Ashfaq
Type: Solutions only
Sender: Muhammad Marwan
Format: PDF Scanned (Handwritten)

Horizontal asymptote to the curve

Objectives

After reading this unit the students will be able to:

  • identify the domain and range of a functions through graphs.
  • draw the graph of modulus function and identify its domain and range.
  • recognize the composition of a function and then to find out the composition of two functions.
  • describe the inverse of a function and then to find out the inverse of composition of two functions.
  • recognize the algebraic and transcendental functions as well as the concepts of explicit, implicit and parametric functions.
  • display graphically the explicit, implicit and parametric functions as well as the compound functions.
  • introduce the limit of a function with respect to real number intervals on the real number line, the open and closed intervals and its location on a real number line.
  • explain the meaning of x tends to zero, x tends to a and x tends to infinity
  • define the limit of a sequence when the limit of a sequence with nth term is given.
  • define the limit of a function and the statement of theorems on limits of sum, difference, product and quotient of functions.
  • evaluate the limits of a function in case of some special functions.
  • evaluate the limit of algebraic, exponential and trigonometric functions.
  • introduce the continuous and discontinuous functions.
  • recognize the left hand and right hand limits through examples.
  • define the continuity of a function at a point and in an interval.
  • test the continuity and discontinuity of a function a point and in an interval.

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ch01-function-and-limits-fsc2-kpk.pdf (1.55 MiB, 3379 downloads) |

Objectives

After reading this unit the students will be able to:

  • distinguish between independent and dependent variables.
  • estimate the change in the dependent variable, when the independent variable is incremented or decremented.
  • explain the concepts of a rate of change.
  • define the derivative of a function as an instantaneous rate of change of variable with respect to another variable.
  • define derivative or differential coefficient of a function.
  • differentiate $y=x^n$ and $y=(ax+b)^n$ by first principle rule.
  • introduce the theorems of differentiation, such as the derivative of a constant function, the derivative of any constant multiple of a function, the derivative of a sum or difference of two functions, the derivative of the product of two functions and the derivative of a quotient of two functions.
  • apply theorems of differentiation in solving problems.
  • introduce chain rule of differentiation in different situations.
  • introduce implicit differentiation of a function.
  • introduce differentiation of trigonometric and inverse trigonometric functions.
  • introduce differentiation of exponential and logarithmic functions.
  • introduce the differentiation of hyperbolic and inverse hyperbolic functions.

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ch02-differentiation-fsc2-kpk.pdf (3.16 MiB, 1624 downloads) |

Geometrical Interpretation of Derivative

Objectives

After reading this unit the students will be able to:

  • Integration

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Objectives

After reading this unit the students will be able to:

  • Differentiation

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Objectives

After reading this unit the students will be able to:

  • Integration

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ch05-integration-fsc2-kpk.pdf (2.73 MiB, 2745 downloads) |

Objectives

This unit tells us, how to:

  • define the differential equation, its order, degree, general and particular solutions, and its identification as linear and nonlinear ordinary differential equations.
  • demonstrate the concept in forming a differential equation.
  • solve the first order linear and nonlinear ordinary differential equations by separable variable form, and homogenuous form and then how to reduce differential equations in standard form of homogenuous.
  • solve the real life problems related to differential equations.
  • define the orthogonal trajectories and then how to show the orthogonal trajectories of the two families of curve.

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