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
Example
Solve the following equation.
2x + 2 = 8
2x + 2 = 8
∴ 2x + 2 - 2 = 8 - 2
∴ 2x = 6
∴ x = 3
Example
Solve the following equation.
3x - 5 = x - 17
3x - 5 = x - 17
3x - 5 + 5 - x = x - 17 + 5 - x
∴ 2x = - 12
∴ x = - 6
Example
The length of a rectangle is 1 cm more than twice its breadth. If the perimeter of the rectangle is 50 cm, find its length.
Let the breadth of the rectangle be x cm.
Then the length of the rectangle will be (2x +1)cm.
2 × length + 2 × breadth = perimeter of rectangle
2 (2x + 1) + 2x = 50
∴ 4x + 2 + 2x = 50
∴ 6x + 2 = 50
∴ 6x = 50 - 2 = 48
∴ x = 8
Breadth of rectangle is 8 cm.
Length of the rectangle = 2x + 1 = 2 × 8 + 1
∴ Length of rectangle = 17 cm.
Example
Solve the following equation.
The sum of two consecutive natural numbers is 69. Find the numbers.
Let one natural number be x.
The next natural number is x + 1
(x) + (x + 1) = 69
∴ x + x + 1 = 69
∴ 2x + 1 = 69
2x = 69 - 1
∴ 2x = 68
∴ x = 34
1st natural number = 34
2nd natural number = 34 + 1 = 35.
