Complete Solved Exercises..
Which Include
So ,,
Start It With Chapter 1
Contents & summary
- Rational numbers and irrational numbers
- Properties of real numbers
- Complex numbers
- Operation on complex numbers
- Complex numbers as ordered pairs of real numbers
- Properties of the foundamental operations on complex numbers
- A special subset of
C
- The real line
- Real plane or coordinate plane
- Geometrical representation of complex numbers, the complex plane
- To find real and imaginary parts of (i)
(x+iy)n (ii)
(x1+iy1x2+iy2)n,x2+iy2≠0
Download From below Exercise 1.1 to 1.3
- Chapter 02: Sets, Functions and Groups
Notes (Solutions) of Chapter 02: Sets, Functions and Groups, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
- Introduction
- Exercise 2.1
- Operations on Sets
- Venn Diagrams
- Exercise 2.2
Operations on Three Sets
- Properties of Union and Intersection
- Exercise 2.3
- Inductive and Deductive Logic
- Aristotelian and non-Aristotelian logics
- Symbolic Logic
- Implication or Conditional
- Bicopnditional :
p↔q - Conditionals related with a given Conditional.
- Tautologies
- Quantifiers
- Exercise 2.4
- Truth Seats, A Link between Set Theory and Logic
- Exercise 2.5
- Relations
- Functions
- Linear and Quadratic Functions
- Inverse of a Function
- Exercise 2.6
- Binary Operations
- Properties of Binary Operations
- Exercise 2.7
- Groups
- Solution of Linear Equations
- Reversal Law of Inverses
- Exercise 2.8
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Chapter 03: Matrices and Determinants
Notes (Solutions) of Chapter 03: Matrices and Determinants, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Addition of Matrices
- Scalar Multiplication
- Subtraction of Matrices
- Multiplication of two Matrices
- Determinant of a
2×2 matrix- Singular and nonsingular Matrices
- Adjjoint of a
2×2 matrix - Inverse of
2×2 matrix
- Solution of simultaneous linear equations by using matrices
- Exercise 3.1
- Field
- Properties of Matrix Addition, Scalar Multiplication and Matrix Multiplicaton.
- Exercise 3.2
- Determinants
- Minor and Cofactor f an Element of a Maatrix or its Determinant
- Determinant of a Square Matrix of Order
n≥3
- Properties of Determinants with help in their Evaluation
- Adjoint and Inverse of a Square Matrix of order
n≥3 - Exercise 3.3
- Elementary Row and Column Operations on a Matrix
- Echelon and Reduce Echelon form of Martices
- Exercise 3.4
- System of Linear Equation
- Homogeneous Linear Equation
- Non-Homogeneous Linear Equations
- Cramer`s Rule
- Exercise 3.5
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Chapter 04: Quadratic Equations
Notes (Solutions) of Chapter 04: Quadratic Equations, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board, Lahore.Contents & summary
- Introduction
- Solutions of Quadratic Equations
- Exercise 4.1
- Solutions of Equations Reducible to the Quadratic Equation
- Exercise 4.2
- Exercise 4.3
- Three Cube Roots of Unity
- Properties of Cube Roots of Unity
- Four Fourth Roots of Unity
- Properties of Four Fourth Roots of Unity
- Exercise 4.4
- Polynomial Function
- Theorems
- Synthetic Division
- Exercise 4.5
- Relations between the Roots and the Coefficients of a Quadratic Equation
- Formation of an Equation whose Roots are given
- Exercise 4.6
- Nature of the Roots of Quadratic Equation
- Exercise 4.7
- System of two Equations Involving two Variables
- Exercise 4.8
- Exercise 4.9
- Problems on Quadratic Equations
- Exercise 4.10
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Chapter 05: Partial Fractions
Notes (Solutions) of Chapter 05: Partial Fractions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Rational Fraction
- Proper Rational Fraction
- Improper Rational Fraction
- Resolution of a Rational Fraction
P(x)Q(x) into Partial Fractions- Exercise 5.1
- Exercise 5.2
- Exercise 5.3
- Exercise 5.4
Download as PDF from below :
Exercise 5.3
Exercise 5.4 (Handwritten)
Chapter 06:
Sequences and Series
Notes (Solutions) of Chapter 06: Sequences and Series, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Types of Sequences
- Exercise 6.1
- Arithmetic Progression(A.P)
- Exercise 6.2
- Aritmetic Mean (A.M)
- n Arithmetic Means between two given Numbers
- Exercise 6.3
- Series
- Exercise 6.4
- World Problems on A.P.
- Exercise 6.5
- Geometric Progression(G.P)
- Exercise 6.6
- Geometric Means
- n Geometric Means between two given numbers
- Exercise 6.7
- Sum of n terms of a Geometric Series
- The Infinite Geometric Series
- Exercise 6.8
- World Problems on G.P.
- Exercise 6.9
- Harmonic Progression(H.P)
- Harmonic Means
- n Harmonic Means between two numbers
- Relation between Arithmic, Geometric and Harmonic Means
- Exercise 6.10
- Sigma Notation(or Summation Notation)
- To find the Formulae of Sum
- Exercise 6.11
Chapter 07: Permutation , Combination and Probability
Notes (Solutions) of Chapter 07: Permutation , Combination and Probability, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.
Contents & summary
- Introduction
- Exercise 7.1
- Permutation
- Exercise 7.2
- Permutation of Things not all Different
- Circular Permutation
- Exercise 7.3
- Combinations
- Complementary Combination
- Exercise 7.4
- Probability
- Probability that an Even does not Occur
- Exercise 7.5
- Estimating Probability and Tally Marks
- Exercise 7.6
- Addition of Probabilities
- Exercise 7.7
- Multiplication of Probabilities
- Exercise 7.8
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Chapter 08: Mathematical Induction and Binomial Theorem
Notes (Solutions) of Chapter 08: Mathematical Induction and Binomial Theorem, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Principle of Mathematical Induction
- Principle of Extended Mathematical Induction
- Exercise 8.1
- Binomial Theorem
- The Middle Term in the Expansion of
(a+x)n - Some Deductions from the Binomial Expansion of
(a+x)n - Exercise 8.2
- The Binomial Theorem when the index n is a negative Integer or a FRACTION
- Application of the Binomial Theorem
- Exercise 8.3
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Chapter 09: Fundamentals of Trigonometry
Notes (Solutions) of Chapter 09: Fundamentals of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Units of Measures of Angles
- Sexagesimal System
- Conversion from
D∘M′S′′ to the decimal form and vice versa - Circular System (Radians)
- Relation between the Length of an arc of a Circle and the Circular measure of its Central angle
- Conversion of Radian into Degree and vice versa
- Exercise 9.1
- General Angle (Coterminal Angle)
- Angle in the Standard Position
- Trigonometric Function
- Trigonometric Function of any Angle
- Fundamental Identities
- Signs of the Trigonometric Function
- Exercise 9.2
- The Values of Trigonometric Functions of acute angles
45∘,30∘,60∘ - The Values of Trigonometric Functions of acute angles
0∘,90∘,180∘,270∘,360∘ - Exercise 9.3
- Domains of Trigonometric Functions and of Fundamental Identities
- Exercise 9.4
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Chapter 10: Trigonometric Identities
Notes (Solutions) of Chapter 10: Trigonometric Identities, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Distance Formula
- Fundamental Law of Trigonometry
- Deductions from Fundamental Law
- Trigonometric Ratios of Allied Angles
- Exercise 10.1
- Further Application of Basic Identities
- Exercise 10.2
- Double angle Identities
- Half angle Identities
- Triple angle Identities
- Exercise 10.3
- Sums, Difference and Product of Sines and Cosines
- Exercise 10.4
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Chapter 11: Trigonometric Functions and their Graphs
Notes (Solutions) of Chapter 11: Trigonometric Functions and their Graphs, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Domains and Ranges of Sine and Cosine Functions
- Domains and Ranges of Tangent and Cotangent Functions
- Domain and Range of Secant Function
- Domain and Range of Cosecant Function
- Period of Trigonometric Functions
- Exercise 11.1
- Values of Trigonometric Functions
- Graphs of Trigonometric Functions
- Graph of
y=sinx from−2Ï€ to 2Ï€ - Graph of
y=cosx from−2Ï€ to 2Ï€ - Graph of
y=tanx from−Ï€ to Ï€ - Graph of
y=cotx from−2Ï€ to Ï€ - Graph of
y=secx from−2Ï€ to 2Ï€ - Graph of
y=cscx from−2Ï€ to 2Ï€ - Exercise 11.2
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Chapter 12: Application of Trigonometry
Notes (Solutions) of Chapter 12: Application of Trigonometry, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Tables of Trigonometric Ratios
- Exercise 12.1
- Solution of Right Triangles
- Exercise 12.2
- Heights and Distances
- Engineering and Heights and Distances
- Exercise 12.3
- Oblique Triangles
- The Law of Cosine
- The Law of Sines
- The Law of Tangents
- Half Angle Formulas
- Solution of Oblique Triangles
- Case I : When measure of one side and two angles are given
- Exercise 12.4
- Case II : When measure of two sides and their included angle are given
- Exercise 12.5
- Case III : When measures of three sides are given
- Exercise 12.6
- Area of Triangle
- Exercise 12.7
- Circles Connected with Triangle
- Circum-Circle
- In-Circle
- Escribed Circles
- Engineering and Circles Connected with Triangles
- Exercise 12.8
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Chapter 13: Inverse Trigonometric Functions
Notes (Solutions) of Chapter 13: Inverse Trigonometric Functions, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- The Inverse Sine Function
- The Inverse Cosine Function
- Inverse Tangent Function
- Inverse Cotangent, Scant and Coscant Functions
- Domains and Ranges of Principal Trigonometric Function and Inverse Functions
- Exercise 13.1
- Addition and Subtraction Formulas
- Exercise 13.2
Some important formulas
sin−1A+sin−1B=sin−1(A1−B2−−−−−−√+B1−A2−−−−−−√) sin−1A−sin−1B=sin−1(A1−B2−−−−−−√−B1−A2−−−−−−√) cos−1A+cos−1B=cos−1(AB−(1−A2)(1−B2)−−−−−−−−−−−−−−−−√) cos−1A−cos−1B=cos−1(AB+(1−A2)(1−B2)−−−−−−−−−−−−−−−−√) tan−1A+tan−1B=tan−1A+B1−AB
tan−1A−tan−1B=tan−1A−B1+AB Download as PDF from Below :Chapter 14: Solutions of Trigonometric Equation
Notes (Solutions) of Chapter 14: Solutions of Trigonometric Equation, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.Contents & summary
- Introduction
- Solution of General Trigonometric Equations
- Exercise 14
Some important formulas
sin−1A+sin−1B=sin−1(A1−B2−−−−−−√+B1−A2−−−−−−√) sin−1A−sin−1B=sin−1(A1−B2−−−−−−√−B1−A2−−−−−−√) cos−1A+cos−1B=cos−1(AB−(1−A2)(1−B2)−−−−−−−−−−−−−−−−√) cos−1A−cos−1B=cos−1(AB+(1−A2)(1−B2)−−−−−−−−−−−−−−−−√) tan−1A+tan−1B=tan−1A+B1−AB
tan−1A−tan−1B=tan−1A−B1+AB Download as PDF from Below :
http://urdulovers123.blogspot.com/2015/08/mathematics-notes-for-fsc-part-1.html
ReplyDeleteThese is I think Federal Board English Book. you can see 1st Year English Notes PDF Punjab Board
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