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9th Class Notes

Wednesday, February 6, 2019 Notes

9th Class Math Chapter 6 “Algebraic Manipulation” Notes PTB

View and Download the PDF solved Notes, solved numerical problems or 9th Class Mathematics notes of Chapter 6 “Algebraic Manipulation” of Punjab Textbook Board. These 9th class Mathematics notes of 4th Chapter are according to the new syllabus (2019) of Punjab Boards including Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Faisalabad Board, Multan Board, Bahawalpur Board, Federal Board, DG Khan Board and Sargodha Board. Students of 9th Class of all these board can facilitate from the Mathematics notes given below. You can also download 9th Class Mathematics Chapter 6 Solved Questions and Numericals Problems.

Unit 6: Algebraic Manipulation

These are clearly written notes about Chapter 6 Questions/Problems. So first Chapter 6 is all about Algebraic Manipulation.

In this chapter we will learn about Highest Common Factor(HCF) and Least Common Multiple(LCM). Use Factor and division method to find Highest Common Factor and Least Common Multiple. We will also learn the relationship between HCF and LCM. We will use HCF and LCM to solve fractional expression. We will also find square root of Algebaric expressions by factorization and division.

9th-Class-Chapter-6-Notes

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EXCERCISE 6.1

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Wednesday, February 6, 2019 Notes

9th Class Math Chapter 5 “Factorization” Notes PTB

View and Download the solved PDF Notes, solved PDF numerical problems or 9th Class Mathematics notes of Chapter 5 “Factorization” of Punjab Textbook Board. These 9th class Mathematics notes of 4th Chapter are according to the new syllabus (2019) of Punjab Boards including Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Faisalabad Board, Multan Board, Bahawalpur Board, Federal Board, DG Khan Board and Sargodha Board. Students of 9th Class of all these board can facilitate from the Mathematics notes given below. You can also download 9th Class Mathematics Chapter 5 solved PDF Questions and Numericals Problems.

Unit 5: Factorization

These are clearly written notes about Chapter 5 Questions/Problems. So first Chapter 5 is all about Factorization.

In this chapter we will prove Remainder Therorem with enough examples. Finding Remainder when a polynomial is divided by another linear polynomial. We will define zeros of polynomials. State and prove factor theorem.

9th-Class-Chapter-5-Notes

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EXCERCISE 5.1 EXCERCISE 5.2 EXCERCISE 5.3

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Tuesday, February 5, 2019 Notes

9th Class Math Chapter 4 “Algebraic Expressions and Algebraic Formulas” Notes PTB

View and Download PDF solved exercise or 9th Class Mathematics notes of Chapter 4 “Algebraic Expressions and Algebraic Formulas” of Punjab Textbook Board. These 9th class Mathematics notes of 4th Chapter are according to the new syllabus (2019) of Punjab Boards including Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Faisalabad Board, Multan Board, Bahawalpur Board, Federal Board, DG Khan Board and Sargodha Board. Students of 9th Class of all these board can facilitate from the Mathematics notes given below. You can also download 9th Class Mathematics Chapter 4 Solved Questions and Numericals Problems.

Unit 4: Algebraic Expressions and Algebraic Formulas

These are clearly written notes about Chapter 4 Questions/Problems. So first Chapter 4 is all about Algebraic Expressions and Algebraic Formulas.

In this chapter we will learn about Rational Epressions and Polynomials. Examine whether an Algebraic expression is polynomial or rational expression.Reduce a rational expression or polynomial to its lowest form. Divide a rational expression with another and express result in lowest form.Find the value of Algebric Expressions for some particular real number.

Proving basic laws (Addition, Subtraction, Multiplication, Division) of Algebraic Expressions and Algebraic Formulas.

9thClassNotesChapter4AlgebraicExpressions&AlgebraicFormulas

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EXCERCISE 4.1 EXCERCISE 4.2 EXCERCISE 4.3 EXCERCISE 4.4A EXCERCISE 4.4B

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Monday, February 4, 2019 Notes

PTB 9th Class Math Chapter 2 “Real and Complex Numbers” Solved Exercise Questions

View and Download the solved questions, solved numerical problems or 9th Class Mathematics notes of Chapter 2 “Real and Complex Numbers” of Punjab Textbook Board. These 9th class Mathematics notes of 2nd Chapter are according to the new syllabus (2019) of Punjab Boards including Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Faisalabad Board, Multan Board, Bahawalpur Board, Federal Board, DG Khan Board and Sargodha Board. Students of 9th Class of all these board can facilitate from the Mathematics notes given below. You can also download 9th Class Mathematics Chapter 2 Solved Questions and Numericals Problems.

Unit 2: Real and Complex Numbers

These are clearly written notes about chapter 2 problems. This Chapter is all about real numbers and complex numbers as you can see in the below animated picture.

Real numbers as a union of sets of rational and irrational numbers.We will draw numbers on real line, and demonstrate with terminating and non-terminating recurring decimals on the real line.
Differentiate between radical form and exponential form of expression. Transform an expression given in radical form to an exponential form and vice versa.

Apply the laws of exponents to simplify expression with real exponents.
Define Complex number z = a + ib, Conjugate of a complex number. Knowing condition for equality of complex numbers.
Define basic operations (Adddition, Subtraction, Multiplication, Division) of complex numbers.

9thClassReal&ComplexNumbers

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EXCERCISE 2.1 EXCERCISE 2.3 EXCERCISE 2.4 EXCERCISE 2.5 EXCERCISE 2.6

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Monday, February 4, 2019 Notes

PTB 9th Class Math Chapter 3 “Logarithms” Solved Exercise Questions

View and Download the solved questions, solved numerical problems or 9th Class Mathematics notes of Chapter 3 “Logarithms” of Punjab Textbook Board. These 9th class Mathematics notes of 3rd Chapter are according to the new syllabus (2019) of Punjab Boards including Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Faisalabad Board, Multan Board, Bahawalpur Board, Federal Board, DG Khan Board and Sargodha Board. Students of 9th Class of all these board can facilitate from the Mathematics notes given below. You can also download 9th Class Mathematics Chapter 3 Solved Questions and Numericals Problems.

Unit 3: Logarithms

These are clearly written notes about chapter 3 Questions/Problems. So first Chapter 3 is all about Logarithms.

In this chapter we will learn about expressing numbers in Standard Scientific Notation and vice versa.
Define a common logarithm, characteristic and mantissa of log of number. Using Tables to find log of numbers. Concept of Anti-log and using tables to find anti log of number.Laws of Logarithms and differentiate of common and natural logarithms.
Proving basic laws (Addition, Subtraction, Multiplication, Division) of Logarithms.
9thClassNotesLogarithms

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EXCERCISE 3.1 EXCERCISE 3.2 EXCERCISE 3.3 EXCERCISE 3.4

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Saturday, February 2, 2019 Notes

PTB 9th Class Math Chapter 1 “Matrices and Determinants” Solved Exercise Questions

View and Download the solved questions, solved numerical problems or 9th Class Mathematics notes of Chapter 1 “Matrices and Determinants” of Punjab Textbook Board. These 9th class Mathematic notes of 1st Chapter are according to the new syllabus (2019) of Punjab Boards including Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Faisalabad Board, Multan Board, Bahawalpur Board, Federal Board, DG Khan Board and Sargodha Board. Students of 9th Class of all these board can facilitate from the Mathematic notes given below. You can also download 9th Class Mathematics Chapter 1 Solved Questions.

So Start of first Chapter of 9th Class Mathematics. These are clearly written notes about chapter one problems. So first chapter is all about Matrix.

In this chapter Students will learn about Matrix as a tool of solving linear equations with two or three unknowns, Order of matrix, Addition and Subtraction of matrix, Equality of Matrix and types of matrix like Identity matrix, Row matrix, Column matrix, Scalar matrix, Square matrix, Identity matrix, Diagonal matrix Symmetric and Skew Symmetric matrix.

You will learn further advanced concepts like Multiplication of matrices, Inverse of matrices, Solution of Simultaneous Linear equations and clearly explained concepts for 9th Class Mathematics level.

Matrix is rectangular array of numbers arranged in the forms of rows and columns.

9th Class Matrix

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EXCERCISE 1.1 EXCERCISE 1.2 EXCERCISE 1.3A EXCERCISE 1.3B EXCERCISE 1.4
EXCERCISE 1.5A EXCERCISE 1.5B EXCERCISE 1.6A EXCERCISE 1.6B

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Friday, February 13, 2015 Notes

PTB 9th Class Physics Chapter 8 Solved Questions and Numerical Problems

View and Download the solved questions, solved numerical problems or 9th Class Physics notes of Chapter 8 “Thermal Properties of Matter” of Punjab Textbook Board. These 9th class physics notes of 8th Chapter are according to the new syllabus (2013) of Punjab Boards including Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Faisalabad Board, Multan Board, Bahawalpur Board, Federal Board, DG Khan Board and Sargodha Board. Students of 9th Class of all these board can facilitate from the physics notes given below. You can also download 9th Class Physics Chapter 8 Solved Questions and Numericals Problems.

Unit 8: Thermal Properties of Matter

By studying this chapter students will be able to: Define temperature (as quantity which determines the direction of flow of thermal energy). Define heat (as the energy transferred resulting from the temperature difference between two objects). List basic thermometric properties for a material to construct a thermometer. Convert the temperature from one scale to another (Fahrenheit, Celsius and Kelvin scales). Describe rise in temperature of a body in terms of an increase in its internal energy. Define the terms heat capacity and specific heat capacity. Describe heat of fusion and heat of vaporization (as energy transfer without a change of temperature for change of state). Describe experiments to determine heat of fusion and heat of vaporization of ice and water respectively by sketching temperature-time graph on heating ice. Explain the process of evaporation and the difference between boiling and evaporation. Explain that evaporation causes cooling. List the factors which influence surface evaporation. Describe qualitatively the thermal expansion of solids (linear and volumetric expansion). Explain thermal expansion of liquids (real and apparent expansion). Solve numerical problems based on the mathematical relations learnt in this unit.

9th Class Physics Chapter 8 (Thermal Properties of Matter) Short Question Answers

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9th Class Physics Chapter 8 (Thermal Properties of Matter) Solved Numericals

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Friday, February 13, 2015 Notes

PTB 9th Class Physics Chapter 7 Solved Questions and Numerical Problems

View and Download the solved questions, solved numerical problems or 9th Class Physics notes of Chapter 7 “Properties of Matter” of Punjab Textbook Board. These 9th class physics notes of 7th Chapter are according to the new syllabus (2013) of Punjab Boards including Lahore Board, Gujranwala Board, Sahiwal Board, Rawalpindi Board, Faisalabad Board, Multan Board, Bahawalpur Board, Federal Board, DG Khan Board and Sargodha Board. Students of 9th Class of all these board can facilitate from the physics notes given below. You can also download 9th Class Physics Chapter 7 Solved Questions and Numerical Problems.

Unit 7: Properties of Matter

By studying this chapter students will be able to: State kinetic molecular model of matter (solid, liquid and gas forms). Describe briefly the fourth state of matter i.e. Plasma. Define the term density. Compare the densities of a few solids, liquids and gases. Define the term pressure (as a force acting normally on unit area). Explain how pressure varies with force and area in the context of everyday examples. Explain that the atmosphere exerts a pressure. Describe how the height of a liquid column may be used to measure the atmospheric pressure. Describe that atmospheric pressure decreases with the increase in height above the Earth’s surface. Explain that changes in atmospheric pressure in a region may indicate a change in the weather. state Pascal’s law. Apply and demonstrate the use with examples of Pascal’s law. State relation for pressure beneath a liquid surface to depth and to density i.e.,(P=pgh) and solve problems using this equation. State Archimedes principle. Determine the density of an object using Archimedes principle. State the upthrust exerted by a liquid on a body. State principle of floatation. Explain that a force may produce a change in size and shape of a body. Define the terms stress, strain and Young’s modulus. State Hooke’s law and explain elastic limit.

9th Class Physics Chapter 7 (Properties of Matter) Short Question Answers

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9th Class Physics Chapter 7 (Properties of Matter) Solved Numericals

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