Topics
Geometrical Constructions
- Concept of Angle Bisector
- 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
- Constructing a Triangle When the Length of Its Three Sides Are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
- 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
- Concept for Ordering of Integers
- Addition of Integers
- Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Multiplication of Two Positive Integers
- Division of Integers
HCF and LCM
Angles and Pairs of Angles
Operations on Rational Numbers
- 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
- Crores
- Finding the Square Root of a Perfect Square
Joint Bar Graph
- Concept of Joint Bar Graph
- Interpretation of a Joint Bar Graph
- Drawing a 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
- Concept of Circle
- Circumference of a Circle
- Relationship Between Circumference and Diameter
- Arc of the Circle
- Central Angle and the Measure of an Arc
Perimeter and Area
Pythagoras’ Theorem
Algebraic Formulae - Expansion of Squares
Statistics
Notes
Additive Inverse of Rational Number:
`(- 4)/7 + 4/7 = (- 4 + 4)/7 = 0`.
Also, `4/7 + ((- 4)/7) = 0`.
Similarly, `(- 2)/3 + 2/3 = 0 = 2/3 + ((- 2)/3)`.
In the case of integers, we call – 2 as the additive inverse of 2 and 2 as the additive inverse of – 2.
For rational numbers also, we call `(−4)/7` as the additive inverse of `4/7 "and" 4/7` as the additive inverse of `(−4)/7`.
Similarly, `(−2)/3 "is the additive inverse of" 2/3 and 2/3 "is the additive inverse of" (−2)/3`.
Example
What will be the additive inverse of `(-3)/9`?
`(-3)/9 "as the additive inverse of" 3/9`
Example
What will be the additive inverse of `(- 9)/11`?
`(- 9)/11 "as the additive inverse of" 9/11`.
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