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FSc Part 1 (KPK Boards)

Notes of FSc Part 1 of “A Textbook of Mathematics For Class XI” 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: Engr. Majid Amin
Type: Solutions only
Sender: Muhammad Kareem
Format: PDF Scanned (Handwritten)

Objectives

After reading this unit the students will be able to:

  • know complex numbers, its conjugate and absolute value.
  • understand algebraic properties of complex numbers.
  • recongnize real and imaginary parts of different types of complex numbers.
  • know the solution of simultaneous linear equations with complex co-efficients.
  • write the polynomial $P(z)$ as product of linear factors.
  • solve quadratic equations in complex variable with real co-efficients.

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Objectives

After reading this unit the students will be able to:

  • know a matrix and its notations, order of a matrix and equality of two matrices.
  • understand types of matrices, algebra of matrices and some properties of matrix addition and scalar multiplication.
  • describe determinant of a square matrix and its evaluation using cofactors.
  • know adjoint of a square matrix and use of adjoint method to calculate inverse of a square matrix.
  • state and prove properties of determinants.
  • know elementary row and column operations on matrices.
  • recognize echelon and reduced echelon form of a matrix and rank of a matrix.
  • solve a system of linear equations of both homogeneous and non-homogeneous equations.

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Objectives

After reading this unit the students will be able to:

  • differentiate between scalar and vector quantities.
  • give geometrical representation of a vector in a space.
  • know the fundamental defintion of vector using geometrical as well as analytical representation.
  • use vector to prove simple theorems of descriptive geometry.
  • recognize rectangular coordinate system in space.
  • define unit vectors i, j and k.
  • repeat all fundamental definitions of vector in plane for space.
  • know properties of vector addition and cross or vector product.
  • define scalar triple product of vectors.
  • express scalar triple product of vectors in terms of components (determinantal form).

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Geometric series

Objectives

After reading this unit the students will be able to:

  • define a sequence and its terms.
  • recognize triangle, factorial and Pascal sequence.
  • know the definition of an arithmetic sequence.
  • define arithmetic mean and arithmetic series.
  • solve real life problems involving arithmetic series.
  • define a geometric sequence.
  • solve problems involving geometric sequences.
  • define geometric mean and geometric series.
  • solve real life problems involving geometric series.
  • recognize a harmonic sequence and find its nth term.
  • define harmonic mean and insert n harmonic means between two numbers.

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Objectives

arithmetic-series-pattern.jpg After reading this unit the students will be able to:

  • know sigma $(\sum)$ sign and evaluation of $\sum n$, $\sum n^2$ and $\sum n^3$.
  • understand arithmetical-geometric series and its sum of $n$ terms.
  • know method of differences and its uses.
  • use the partial fraction to find the sum to $n$ terms and to infinity of the series of the type $$\frac{a}{a(a+d)}+\frac{a}{(a+d)(a+2d)}+\ldots$$

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Objectives

After reading this unit the students will be able to:

  • know Kramp's factorial notation to express the product of first n natural numbers by n!.
  • recognize the fundamental principle of counting and its illustration by using tree diagram.
  • understand the concept of permutation and know the notation $^nP_r$.
  • Prove the formula ^nP_r=n(n-1)(n-2)…(n-r+1), its deductions and application to solve relevant problems
  • define combination and know the notation $^nC_r=\left(\begin{smallmatrix}n\\ r\end{smallmatrix} \right)=\frac{n!}{r!(n-r)!}$, its deduction and application to solve relevant problems.
  • define kind of events.
  • recognize the formula $P(E)=\frac{n(E)}{n(S)}$, $0\leq P(E)\leq1$ for probability of occurrence of an event $E$ and to know its application.
  • recognize the addition theorem (or law) of probability and its deduction.
  • recognize the multiplication theorem (or law) of probability and its deduction.
  • Use theorem of addition and multiplication of probability to solve related problems.

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Objectives

After reading this unit the students will be able to:

  • know the principle of mathematical induction.
  • apply the principle to prove the statements, identities or formulae.
  • state and prove binomial theorem for positive integral index.
  • expand $(x+y)^n$ using binomial theorem and find its general form.
  • understand pascal's triangle and its use to obtain the coefficients of the binomial expansion $(x+y)^n$ when $n$ is a small number.
  • know binomial series and its use to find the sum of the given series.

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Objectives

After reading this unit the students will be able to

  • know linear, quadratic and square root functions.
  • define inverse functions and find their domain and range.
  • sketch the graph of the function $y=x^n$ for different values of $x$.
  • sketch the graph of quadratic function.
  • predict function from their graph.
  • find the intersecting point of intersecting graphs of a linear functions and coordinate axes, two linear functions and a linear and quadratic function.
  • solve graphically appropriate problems from daily life.

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Objectives

After reading this unit the students will be able to

  • define linear programming (LP) as planning of allocation of limited resources to obtain optimal result.
  • understand linear inequalities in one and two variables and its importance in real life problems.
  • know the feasible region and identification of feasible region of simple LP problems.
  • define optimal solution of an LP problem.
  • find optimal solution graphically of LP problems.
  • solve real life simple LP problems.

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Objectives

After reading this unit the students will be able to

  • know the fundamental law of trigonometry and deduction of trigonometric identities from it.
  • understand trigonometric ratios and allied angles.
  • use fundamental law and its deduction to derive trigonometric ratios of allied angles.
  • derive double, half and triple angle identities from fundamental law and its deduction.
  • express the product of sines and cosines as sum or differences of sines and cosines.
  • express the sums or differences of sines and cosines as product.

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Objectives

After reading this unit the students will be able to

  • find the solution of right angles triangle.
  • understand oblique triangles and find solution of such triangles, using the law of sines, cosines and tangents.
  • derive the formula for finding the areas of triangles.
  • know circum-circle, in-circle and escribed circle.
  • derive the formula for finding circum-radius, in-radius, escribed radii and deduction of different identities.

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Objectives

After reading this unit the students will be able to

  • know trigonometric functions and their domain and range.
  • define periodic, even/odd and translation properties of the graph of $\sin \theta$, $\cos \theta$ and $\tan \theta$.
  • solve trigonometric equations of the type $\sin\theta=k$, $\cos\theta=k$ and $\tan\theta=k$.
  • solve graphically the trigonometric equations of the type $\sin\theta=\frac{\theta}{2}$, $\cos\theta=\theta$ and $\tan\theta=2\theta$ when $-\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}$.
  • define inverse trigonometric functions and their domain and range.
  • prove the addition and subtraction formulae of inverse trigonometric functions and know their applications.
  • solve general trigonometric equations.

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