FSc Part 1 (KPK Boards)

These are the notes of old book. The notes of new book is AVAILABLE 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.

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.

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.

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).

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.

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

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.

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.

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.

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.

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.

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.

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.