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
Definition
- Rational algebraic expressions: If A and B are two algebraic expressions then `"A"/"B"` is called a rational algebraic.
Notes
Rational algebraic expressions:
- If A and B are two algebraic expressions then `"A"/"B"` is called a rational algebraic expression.
- While simplifying a rational algebraic expression, we have to perform operations of addition, subtraction, multiplication, and division.
Example
Simplify: `(a^2 + 5a + 6)/(a^2 - a - 12) xx (a - 4)/(a^2 - 4)`
`(a^2 + 5a + 6)/(a^2 - a - 12) xx (a - 4)/(a^2 - 4)`
`= ((a + 3)(a + 2))/((a - 4)(a + 3)) xx (a - 4)/((a + 2)(a - 2))`
`= 1/(a - 2)`
Example
Simplify: `(7x^2 + 18x + 8)/(49x^2 - 16) xx (14x - 8)/(x + 2)`
`(7x^2 + 18x + 8)/(49x^2 - 16) xx (14x - 8)/(x + 2)`
`= ((7x + 4)(x + 2))/((7x + 4)(7x - 4)) xx (2(7x - 4))/(x + 2)`
= 2
Example
Simplify: `(x^2 - 9y^2)/(x^3 - 27y^3)`.
`(x^2 - 9y^2)/(x^3 - 27y^3)`.
`= ((x + 3y)(x - 3y))/((x - 3y)(x^2 + 3xy + 9y^2))`
`= (x + 3y)/(x^2 + 3xy + 9y^2)`
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