#### Topics

##### Geometrical Constructions

- Constructing a Bisector of an Angle
- Drawing a Perpendicular to a Line at a Point on the Line
- The Property of the Angle Bisectors of a Triangle
- Perpendicular Bisectors of the Sides of an Acute-angled Triangle
- Perpendicular Bisectors of the Sides of an Obtuse-angled Triangle
- Construction of Triangles
- Construct a Triangle Given Two Sides and the Angle Included by Them
- Construct a Triangle Given Two Angles and the Included Side
- Construct a Right-angled Triangle Given the Hypotenuse and One Side
- Congruence Among Line Segments
- Congruence of Angles
- Congruence of Circles

##### Multiplication and Division of Integers

- Concept for Natural Numbers
- Concept for Whole Numbers
- Negative and Positive Numbers
- Concept of Integers
- Addition of Integers
- Addition of Integers on Number line
- Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Division of Integers
- Multiplication of Two Positive Integers

##### HCF and LCM

##### Angles and Pairs of Angles

##### Operations on Rational Numbers

- Concept of Rational Numbers
- Addition of Rational Number
- Additive Inverse of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Decimal Representation of Rational Numbers
- BODMAS - Rules for Simplifying an Expression

##### Indices

- Concept of Exponents
- Concept of Square Number
- Concept of Cube Number
- Laws of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Expressing Large Numbers in the Standard Form
- Finding the Square Root of a Perfect Square

##### Joint Bar Graph

##### Algebraic Expressions and Operations on Them

- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Like and Unlike Terms
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Binomial by a Binomial
- Equations in One Variable

##### Direct Proportion and Inverse Proportion

##### Banks and Simple Interest

##### Circle

##### Perimeter and Area

##### Pythagoras’ Theorem

##### Algebraic Formulae - Expansion of Squares

##### Statistics

#### notes

**Construct a Triangle Given Two Angles and the Included Side:**

1) Construct ∆XYZ such that l(YX) = 6 cm, m∠ZXY = 30°, m∠XYZ = 100°.

∠XYZ is an obtuse angle and that is shown in the rough figure.

**Steps:**

- According to the rough figure, draw seg YX as the base of length 6 cm.
- Draw ray YR such that m∠XYR = 100°.
- On the same side of seg YX as point R, draw ray XD so that m∠YXD = 30°. Name the point of intersection of rays YR and XD, Z.

∆XYZ is the required triangle.

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