Topics
Rational Numbers
- Concept of Rational Numbers
- Closure Property of Rational Numbers
- Commutativity Property of Rational Numbers
- Associativity of Rational Numbers
- Distributivity of Multiplication Over Addition for Rational
- Identity of Addition and Multiplication
- Negative of a Number
- Additive Inverse of Rational Number
- Rational Numbers on a Number Line
- Rational Numbers Between Two Rational Numbers
Linear Equations in One Variable
- The Idea of a Variable
- Expressions with Variables
- Concept of Equation
- Balancing an Equation
- The Solution of an Equation
- Linear Equation in One Variable
- Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side
- Solving Equations Having the Variable on Both Sides
- Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides
- Reducing Equations to Simpler Form
- Equations Reducible to the Linear Form
Understanding Quadrilaterals
- Concept of Curves
- Different Types of Curves - Closed Curve, Open Curve, Simple Curve.
- Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
- Classification of Polygons - Regular Polygon, Irregular Polygon, Convex Polygon, Concave Polygon, Simple Polygon and Complex Polygon
- Angle Sum Property of a Quadrilateral
- Interior Angles of a Polygon
- Exterior Angles of a Polygon and Its Property
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Properties of Trapezium
- Properties of Kite
- Properties of a Parallelogram
- Properties of Rhombus
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The adjacent angles in a parallelogram are supplementary.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Properties of Rectangle
- Properties of a Square
- Property: The diagonals of a square are perpendicular bisectors of each other.
Practical Geometry
- Introduction to Practical Geometry
- 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
- Some Special Cases
Data Handling
- Concept of Data Handling
- Interpretation of a Pictograph
- Interpretation of Bar Graphs
- Drawing a Bar Graph
- Interpretation of a Double Bar Graph
- Drawing a Double Bar Graph
- Organisation of Data
- Frequency Distribution Table
- Graphical Representation of Data as Histograms
- Concept of Pie Graph (Or a Circle-graph)
- Interpretation of Pie Diagram
- Chance and Probability - Chance
- Basic Ideas of Probability
Squares and Square Roots
- Concept of Square Number
- Properties of Square Numbers
- Some More Interesting Patterns of Square Number
- Finding the Square of a Number
- Concept of Square Roots
- Finding Square Root Through Repeated Subtraction
- Finding Square Root Through Prime Factorisation
- Finding Square Root by Division Method
- Square Root of Decimal Numbers
- Estimating Square Root
Cubes and Cube Roots
Comparing Quantities
- Concept of Ratio
- Concept of Percent and Percentage
- Increase Or Decrease as Percent
- Concept of Discount
- Estimation in Percentages
- Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
- Sales Tax, Value Added Tax, and Good and Services Tax
- Concept of Principal, Interest, Amount, and Simple Interest
- Concept of Compound Interest
- Deducing a Formula for Compound Interest
- Rate Compounded Annually Or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula
Algebraic Expressions and Identities
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials Or Polynomials
- Like and Unlike Terms
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Monomial by a Trinomial
- Multiplying a Binomial by a Binomial
- Multiplying a Binomial by a Trinomial
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b)
- Expansion of (x + a)(x + b)
Visualizing Solid Shapes
Mensuration
Exponents and Powers
Direct and Inverse Proportions
Factorization
- Factors and Multiples
- Factorising Algebraic Expressions
- Factorisation by Taking Out Common Factors
- Factorisation by Regrouping Terms
- Factorisation Using Identities
- Factors of the Form (x + a)(x + b)
- Dividing a Monomial by a Monomial
- Dividing a Polynomial by a Monomial
- Dividing a Polynomial by a Polynomial
- Concept of Find the Error
Introduction to Graphs
- Concept of Bar Graph
- Interpretation of Bar Graphs
- Drawing a Bar Graph
- Concept of Double Bar Graph
- Interpretation of a Double Bar Graph
- Drawing a Double Bar Graph
- Concept of Pie Graph (Or a Circle-graph)
- Graphical Representation of Data as Histograms
- Concept of a Line Graph
- Linear Graphs
- Linear Graphs
- Some Application of Linear Graphs
Playing with Numbers
definition
- Prism: A prism is a polyhedron whose base and top are congruent polygons and whose other faces, i.e., the lateral faces are parallelograms, rectangles, or squares. All prism is polyhedron, which means all faces are flat.
notes
Prism:
A prism is a polyhedron whose base and top are congruent polygons and whose other faces, i.e., the lateral faces are parallelograms, rectangles, or squares. All prism is polyhedron, which means all faces are flat.
Properties of a prism:
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The two parallel and congruent faces of a prism are called bases. The other faces of a prism are called lateral faces.
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The number of lateral faces in a prism is the same as the number of sides of its polygonal bases.
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The line segments created by two intersecting faces are called edges.
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The vertices are points where three or more edges meet.
- If the base of a prism is a regular polygon, it is called a regular prism. Otherwise, it is an irregular prism.
Regular Prism |
Irregular Prism |
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The bases for the regular hexagonal prism are regular hexagons. |
The bases for the hexagonal prism are irregular hexagon. |
2. Types of Prism:
1. Triangle Prism:
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A right triangular prism has rectangular sides A triangular prism is composed of two triangular bases and three rectangular sides. It is a polyhedron made of a triangular base.
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A right triangular prism has rectangular sides, otherwise, it is oblique.
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A uniform triangular prism is a right triangular prism with equilateral bases and square sides.
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A triangular prism looks like the shape of a Kaleidoscope. It has triangles as its bases.
2. Square Prism:
A square prism is a cuboid (a convex polyhedron) which has 6 faces out of which two end-faces are square, 4 lateral faces are rectangles.
3. Pentagonal Prism:
The pentagonal prism is a prism having two pentagonal bases and five rectangular sides. It is a heptahedron with 7 faces, 15 edges, and 10 vertices.
4. Hexagonal Prism:
The hexagonal prism has a total of 8 faces. It has 6 lateral faces that are parallelograms and 2 bases that are hexagons. It also has 18 edges and 12 vertices.
5. Rectangular Prism:
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A rectangular prism is a solid, 3-dimensional object with six faces that are rectangles.
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It has the same cross-section along a length, which makes it a prism. The cross-section is a rectangle.
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A rectangular prism has 8 vertices, 12 sides, and 6 rectangular faces.
6. Right prisms and oblique prisms:
Prisms can also be further classified based on how their lateral faces intersect with their bases. If all the lateral faces are perpendicular to the bases, the prism is called a right prism. If not, it is called an oblique prism.
Right prisms |
Oblique prisms |
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