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====== FSc Part 1 (KPK Boards) ======
These are the notes of old book. The notes of new book is [[:math-11-kpk|AVAILABLE HERE]]
{{ :fsc:fsc-part-1-kptb.jpg?nolink&600x315|FSc Part 2 KPTP}}
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) |
===== Chapter 01: Complex Numbers =====
=== 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.
=== Download ===
**{{:fsc:kpk_fsc_part_1:ch01-complex-numbers-fsc1-kpk.pdf|Download PDF}}** | **[[fsc:kpk_fsc_part_1:chapter_01_complex_numbers|View Online]]**
===== Chapter 02: Matrices and Determinants =====
=== 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.
=== Download ===
**{{:fsc:kpk_fsc_part_1:ch02-matrices-and-determinants-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 02 matrices and determinants|View Online]]**
===== Chapter 03: Vectors =====
=== 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).
*
=== Download ===
**{{:fsc:kpk_fsc_part_1:ch03-vectors-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 03 vectors|Online view]]**
===== Chapter 4: Sequences =====
=== 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.
===Download===
**{{:fsc:kpk_fsc_part_1:ch04-sequences-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 04 sequences|Online view]]**
===== Chapter 5: Miscellaneous Series =====
=== 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 $$\frac{a}{a(a+d)}+\frac{a}{(a+d)(a+2d)}+...$$
===Download===
**{{:fsc:kpk_fsc_part_1:ch05-miscellaneous-series-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 05 Miscellaneous Series|Online view]]**
===== Chapter 6: Permutation, Combination and Probability =====
=== 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.
===Download===
**{{:fsc:kpk_fsc_part_1:ch06-permutation-combination-and-probability-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 06 Permutation Combination and Probability|Online view]]**
===== Chapter 7: Mathematical Induction and Binomial Theorem =====
=== 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.
===Download===
**{{:fsc:kpk_fsc_part_1:ch07-mathematical-induction-and-binomial-theorem-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 07 mathematical induction and binomial theorem|Online view]]**
===== Chapter 8: Functions and Graphs =====
=== 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.
===Download===
**{{:fsc:kpk_fsc_part_1:ch08-functions-and-graphs-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 08 functions and graphs|Online view]]**
===== Chapter 9: Linear Programming =====
=== 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.
===Download===
**{{:fsc:kpk_fsc_part_1:ch09-linear-programming-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 09 linear programming|Online view]]**
===== Chapter 10: Trigonometric Identities of Sum and Difference of Angles =====
=== 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.
===Download===
**{{:fsc:kpk_fsc_part_1:ch10-trigonometric-identities-of-sum-and-difference-of-angles-fsc1-kpk.pdf|Download PDF}}** | **[[:fsc:kpk fsc part 1:chapter 10 trigonometric identities of sum and difference of angles|Online view]]**
===== Chapter 11: Application of Trigonometry =====
=== 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.
===Download===
**{{:fsc:kpk_fsc_part_1:ch11-application-of-trigonometry-fsc1-kpk.pdf|Download PDF}}** | **[[fsc:kpk fsc part 1:Chapter 11 application of trigonometry|Online view]]**
===== Chapter 12: Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations =====
=== 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.
===Download===
**{{:fsc:kpk_fsc_part_1:ch12-graph-of-trigonometric-and-inverse-trigonometric-functions-and-solutions-of-trigonometric-equations-fsc1-kpk.pdf|Download PDF}}** | **[[fsc:kpk fsc part 1:Chapter 12 Graph of Trigonometric and Inverse Trigonometric Functions and Solutions of Trigonometric Equations|Online view]]**
{{tag> FSc KPK_FSc_Part1}}