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 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 = a2 + b2 + c2 + 2ab + 2bc + 2ac.
Notes
Expansion of (a + b + c)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 = a2 + ab + ac + ab + b2 + bc + ac + bc + c2.
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac.
∴ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac.
Example
Expand: (p + q + 3)2
(p + q + 3)2
= p2 + q2 + (3)2 + 2 × p × q + 2 × q × 3 + 2 × p × 3
= p2 + q2 + 9 + 2pq + 6q + 6p
= p2 + q2 + 2pq + 6q + 6p + 9.
Example
Simplify: (l + 2m + n)2 + (l - 2m + n)2.
(l + 2m + n)2 + (l - 2m + n)2
= l2 + 4m2 + n2 + 4lm + 4mn + 2ln + l2 + 4m2 + n2 - 4lm - 4mn + 2ln
= 2l2 + 8m2 + 2n2 + 4ln
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