#### Topics

##### Rational and Irrational Numbers

##### Parallel Lines and Transversal

- Pairs of Lines - Transversal
- Pairs of Lines - Angles Made by a Transversal
- Pairs of Lines - Transversal of Parallel Lines
- Properties of Parallel Lines
- Corresponding Angle Theorem
- Alternate Angles Theorems
- Interior Angle Theorem
- To Draw a Line Parallel to the Given Line Through a Point Outside the Given Line Using Set-square.
- To Draw a Parallel Line to a Given Line at a Given Distance.

##### Indices and Cube Root

- Concept 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
- Meaning of Numbers with Rational Indices
- Concept of Cube Number
- Concept of Cube Root
- Cube Root Through Prime Factorisation Method

##### Altitudes and Medians of a Triangle

##### Expansion Formulae

##### Factorisation of Algebraic Expressions

##### Variation

- Direct Variation
- Inverse Variation
- Time, Work, Speed

##### Quadrilateral : Constructions and Types

- Constructing a Quadrilateral
- Constructing a Quadrilateral When the Lengths of Four Sides and a Diagonal Are Given
- Constructing a Quadrilateral When Two Diagonals and Three Sides Are Given
- Constructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known
- Constructing a Quadrilateral When Three Sides and Two Included Angles Are Given
- Properties of Rectangle
- Properties of a Square
- Properties of Rhombus
- Properties of a Parallelogram
- Properties of Trapezium
- Properties of Kite

##### Discount and Commission

- Concept of Discount
- Commission
- Rebate

##### Division of Polynomials

- Polynomials
- Degree of Polynomial
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Divide a Polynomial by a Binomial

##### Statistics

- Arithmetic Mean - Raw Data
- Subdivided Bar Graph
- Percentage Bar Graph

##### Equations in One Variable

- Solution of Equations in One Variable
- Word Problems of Equation in One Variable

##### Congruence of Triangles

- Congruence of Triangles
- Criteria for Congruence of Triangles
- SAS Congruence Criterion
- SSS Congruence Criterion
- ASA Congruence Criterion
- AAS (Or SAA) Test
- RHS Congruence Criterion

##### Compound Interest

##### Area

- Area of a Parallelogram
- Area of a Rhombus
- Area of Trapezium
- Area of a Triangle
- Area of a Triangle by Heron's Formula
- Area of Figures Having Irregular Shape
- Circumference of a Circle
- Area of Circle

##### Surface Area and Volume

##### Circle - Chord and Arc

- Properties of Chord of a Circle
- Arcs Corresponding to the Chord of a Circle

## Formula

- (a + b + c)
^{2}= a^{2}+ b^{2}+ c^{2}+ 2ab + 2bc + 2ac.

## Notes

**Expansion of (a + b + c)**^{2}:

^{2}:

(a + b + c)^{2} = (a + b + c) × (a + b + c).

(a + b + c)^{2} = a(a + b + c) + b(a + b + c) + c(a + b + c).

(a + b + c)^{2} = a^{2} + ab + ac + ab + b^{2} + bc + ac + bc + c^{2}.

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ac.

**∴ (a + b + c) ^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ac.**

## Example

**Expand: **(p + q + 3)^{2}

(p + q + 3)^{2 }

= p^{2} + q^{2} + (3)^{2} + 2 × p × q + 2 × q × 3 + 2 × p × 3

= p^{2} + q^{2} + 9 + 2pq + 6q + 6p

= p^{2} + q^{2} + 2pq + 6q + 6p + 9.

## Example

**Simplify:** (l + 2m + n)^{2} + (l - 2m + n)^{2}.

(l + 2m + n)^{2} + (l - 2m + n)^{2}

= l^{2} + 4m^{2} + n^{2} + 4lm + 4mn + 2ln + l^{2} + 4m^{2} + n^{2} - 4lm - 4mn + 2ln

= 2l^{2} + 8m^{2} + 2n^{2} + 4ln

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