# 9th Class Math Notes [Updated Edition]

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# Chapter
1 Metrices and Determinants
2 Real and Complex Numbers
3 Logarithms
4 Algebraic Expressions and Algebraic Formulas
5 Factorization
6 Alegraic Manipulation
7 Linear Equations and Inequalities
8 Linear Graphes and Their Application
9 Introduction to Coordinate Geometry
10 Congruent Triangles
11 Parallelograms and Triangles
12 Line Bisectors and Angle Bisectors
13 Sides and Angles of a Triangle
14 Ratio and Proportion
15 Pythagoras Theorem
16 Theorems Related with Area
17 Practical Geometry - Triangles

## Chapter 1: Metrices and Determinants

After studying this unit you will be able to define

• a matrix with real entries and relate its rectangular layout (formation) with real life
• rows and columns of a matrix
• the order of a matrix
• equality of two matrices
##### Unit Outlines
• Introduction to Matrices
• Types of Matrices
• Addition and Subtraction of Matrices

## Chapter 2: Real and Complex Numbers

After studying this unit you will be able to recall the set of real numbers as a union of sets of rational and irrational numbers, depict real numbers on the number line, demonstrate a number with terminating and non-terminating recurring decimals on the number line. To carryout basic operations, apply the laws of exponents to simplify expressions with real exponents.

##### Unit Outlines
• Real Numbers
• Properties of real numbers
• Laws of Exponents / Indices
• Complex Numbers
• Basic operations on complesx numbers

## Chapter 3: Logarithms

After studying this unit you will be able to express a number in standard form of scientfic notation and vice versa, define logarithm of a number y to the base a as the power to which a must be raised to give the number.

• Scientific notation
• Logarithm
• Common and Natural Logarithm
• Laws of Logarithm
• Application of Logarithm

## Chapter 4: Algebraic Expressions and Algebraic Formulas

After studying this unit you will be able to know that a rational expression behaves like a rational number, define a rational expression as the quotient of two polynomials p(x) and q(x) where q(x) is not the zero polynomial, examine whether a given rational algebraic expression is in lowest from or not.

##### Unit Outlines
• Algebraic Expressions
• Algebraic Formulae
• Surds and their Application
• Rationalization

## Chapter 5: Factorization

After studying this unit you will be able to state and prove Remainder theorem and explain through examples, define zeros of polynomial, state and prove factor theorem, use Factor theorem to factorize a cubic polynomial.

##### Unit Outlines
• Factorization
• Remainder Theorem and Factor theorem
• Factorization of a Cubic polynomail

## Chapter 6: Alegraic Manipulation

After studying this unit you will be able to find highest common Factor and Least common Multiple of algebraic expressions, use factor or division method to determine highest common factor and Least common multiple, know the relationship between H.C.F and L.C.F. You will also be able to solve real life problems related to H.C.F and L.C.M.

##### Unit Outlines
• Highest Common Factor and Least common Multiple
• Basic Root of Algebraic Expression
• Square Root of Algebraic Expression

## Chapter 7: Linear Equations and Inequalities

After studying this unit you will be able to recall linear equation in one variable, solve linear equation with rational coefficients, reduce equations, involving radicals, to simple linear form and find their solutions.

##### Unit Outlines
• Linear Equations
• Equations Involving Absolute Value
• Linear InEqualities
• Solving InEqualities

## Chapter 8: Linear Graphes and Their Application

After studying this unit you will be able to indentify pair of real numbers as an ordered pair, recognize an ordered pair through different examples, describe rectangular or Cartesian plane consisting of two number lines interesting at right angles at the point O, draw different geometrical shapes by joining a set of given points, solve appropriate real life problems, interpret conversion graph as a linear graph relating to two quantities which are in direct proportion.

##### Unit Outlines
• Introduction
• Cartesian Plane
• Conversion Graphes
• Graphical Solution of Equations in two variables

## Chapter 9: Introduction to Coordinate Geometry

After sudying this unit you will be able to define coordinate geometry, derive distance formula to calculate distance between two points given in Cartesian plane, use distance formula to find distance between two given points.

##### Unit Outlines
• Introduction
• The distance formula
• Collinear Points
• Mid Point Formula

## Chapter 10: Congruent Triangles

After studying this unit you will be able to prove that in any correspondence of two triangles, if one side and any two angles of one triangle are congruent to the corresponding side and angles of the other, then triangles are congruent. You will also learn to prove that if in the correspondence of two right-angled triangles, the hypotenuse and one side of one are congruent to the hypotenuse and the corresponding side of the other, then the triangles are congruent.

##### Unit Outlines
• Congruent Triangles

## Chapter 11: Parallelograms and Triangles

After studying this chapter you will be able to prove that if two opposite sides of a quadrilateral are congruent and parallel, it is a parallelogram. You will also learn to prove that if three or more parallel lines make congruent segments on a transversal, they also intercept congruent segments on any other line that cuts them.

##### Unit Outlines
• Parallelograms
• Triangles

## Chapter 12: Line Bisectors and Angle Bisectors

After studying this unit you will be able to prove that any point on the right bisector of a line segment is equidistant from its end points, prove that any point equidistant from the end points of a line segment is on the right bisector of it.

##### Unit Outlines
• Bisector of a Line Segment
• Bisector of an Angle

## Chapter 13: Sides and Angles of a Triangle

After studying this unit you will be able to prove that if two sides of a triangle are unequal in length, the longer side has an angle of greater measure opposite to it, prove that if two angles of a triangle are unequal in measure, the side opposite to the greater angle is longer than the side opposite to the smaller angle.

##### Unit Outlines
• Sides of a Triangle
• Angles of a Triangle

## Chapter 14: Ratio and Proportion

After studying this unit you will be able to prove that a line parallel to one side of a triangle, intersecting the other two sides, divides them proportionally, prove that if a line segment intersects the two sides of a triangle in the same ratio, then its is parallel to the third side. You will also learn to prove that if two triangles are similar, the measures of their corresponding sides are proportional.

##### Unit Outlines
• Ratio and Proportion

## Chapter 15: Pythagoras Theorem

After studying this chapter you will be able to prove that in a right-angled triangle, the square of the length of hypotenuse is equal to the sum of the squares of the lengths of the other two sides(Pythagoras Theorem). You will also be to able to prove that if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right angled triangle(converse to Pythagoras Theorem).

##### Unit Outlines
• Pythagoras Theorem

## Chapter 16: Theorems Related with Area

After studying this unit you will be able to prove that parallelograms on the same base and lying between the same parallel lines (or of the same altitude) are equal in area, prove that parallelograms on equal bases and having the same altitude are equal in area, prove that triangles on the same base and of the same altitude are equal in area.

##### Unit Outlines
• Theorems related with area

## Chapter 17: Practical Geometry - Triangles

After studying this unit you will be able to construct a triangle having given: two sides and the included angle, one side and two of the angles, two of its sides and the angle opposite to one of them (with all three responsibilities). You will also learn to construct a triangle equal in area to a given quadrilateral.

##### Unit Outlines
• Construction of Triangles
• Figures with Equal Areas