# FSc Part 1 (KPK Boards)

From this year, the book has been changed. These notes will be updated soon. Compilation of the solutions of new book has been started here 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 Solutions only Muhammad Kareem 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.

#### 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.

#### 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).

#### 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.

#### Objectives

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 $$\frac{a}{a(a+d)}+\frac{a}{(a+d)(a+2d)}+...$$

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.