Topics
Number System
Integers
- Integers
- Multiplication and Division of Integers
- Properties of Operations on Integers
- Concept for Commutativity, Associativity, Existence of Identity
- Inverse and Distributivity
- Problem Solving Using Operations on Integers
- Statement Problems on Integers Using All Fundamental Operations.
Rational Numbers
- Rational Numbers
- Word Problems on Rational Numbers (All Operations)
- Decimal Representation of Rational Numbers
- Concept for Problem Solving Using Operations on Rational Numbers
- The Decimal Number System
Fractions (Including Problems)
Decimal Fractions (Decimals)
Exponents (Including Laws of Exponents)
- Concept of Exponents
- Concept for Exponents Only Natural Numbers.
- Laws of Exponents (Through Observing Patterns to Arrive at Generalisation.)
- Concept for Application of Laws of Exponents in Simple Daily Life Problems
Commercial Arithmetic
Ratio and Proportion (Including Sharing in a Ratio)
Unitary Method (Including Time and Work)
Percent and Percentage
Profit, Loss and Discount
- Concept of Discount
- Concept for Application to Profit and Loss (Single Transaction Only)
Simple Interest
Algebra
Fundamental Concepts (Including Fundamental Operations)
- Fundamental Concepts
- Terms, Factors and Coefficients of Expression
- Algebraic Expressions
- Performs Operations (Addition and Subtraction) on Algebraic Expressions with Integral Coefficients Only.
Simple Linear Equations (Including Word Problems)
- Word Problems on Linear Equations
- Concept for Inequalities
- Concept for Solution of Simple Inequalities in One Variable
Set Concepts (Some Simple Divisions by Vedic Method)
- Concept of Set Concepts
- Concept for Revision Idea of Sets
- Universal Set
- Cardinality of a Set
Geometry
Lines and Angles (Including Construction of Angles)
- Introduction to Lines and Angles
- Concept of Pairs of Angles
- Parallel Lines
- Construction of a Line Parallel to a Given Line from a Point Outside It .
Triangles
- Basic Concepts of Triangles
- Concept for Angle Sum Property
- Concept for Exterior Angle Property
- Concept for Construction of Simple Triangles.
Pythagoras Theorem
Symmetry (Including Reflection and Rotation)
Recognition of Solids (Representing 3-d in 2-d)
- Concept of Recognition of Solids
- Faces, Edges and Vertices of Polyhedron
- Concept for Mapping the Space Around Approximately Through Visual Estimation.
Congruency: Congruent Triangles
- Congruence of Triangles
- Concept for Congruence Through Superimposition
- Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
- Criteria for Congruence of Triangles
Mensuration
- Basic Concepts in Mensuration
- Concept of Perimeter
- Circumference of a Circle
- Concept of Area
- Concept of Measurement Using a Basic Unit Area of a Square, Rectangle, Triangle, Parallelogram and Circle, Rings and Combined Figures.
Data Handling (Statistics)
Data Handling
Probability
- Concept of Probability
- Concept for Feel of Probability Using Data Through Experiments.
- Concept for Notion of Chance
- Concept for Tabulating and Counting Occurrences
- Comparing the Observation with that for a Coin. Observing Strings of Throws, Notion of Randomness.
- Introduction
- Formula: Speed
- Formula: Distance
- Formula: Time
- Units Used
- Example 1
- Example 2
- Key Points Summary
Introduction
Have you ever wondered how fast your school bus goes or how quickly you can run in a race? In our daily life, we see moving vehicles, running people, and flying birds—all travelling different distances in different amounts of time.
To compare how quickly things move, we use the idea of speed. Speed tells us how fast or slow something is moving. It is measured by how much distance an object covers in a certain amount of time. For example, when a car travels 60 kilometres in one hour, we say its speed is 60 kilometres per hour.
Formula: Speed
Speed = `"Distance" / "Time"`
Formula: Distance
Distance = Speed × Time
Formula: Time
Time = `"Distance" / "Speed"`
Units Used
-
Distance: meters (m), kilometers (km)
-
Time: seconds (s), minutes (min), hours (h)
-
Speed: meters per second (m/s), kilometers per hour (km/h)
Tip:
-
To change minutes to hours, divide by 60.
-
To change hours to minutes, multiply by 60.
Example 1
A bus travels 60 km in 2 hours. What is the speed?
-
Distance = 60 km
-
Time = 2 h
- Speed = `"Distance" / "Time"`
-
Speed = 60 ÷ 2 = 30 km/h
Example 2
Problem: a boy covers a distance of 1.2 km in 40 minutes. Find his speed in
(i) km per hour (km h⁻¹)
(ii) metre per second (m s⁻¹)
Solution:
(i) In order to get speed in km per hour, the distance covered must be in km
and the time taken must be in hours.
Given: distance = 1.2km and time = 40 min = `40/60` h = `2/3` h
∴ Speed = `"Distance" / "Time"`
= `"1.2 km" / "2/3 h"`
= 1.2 × `3/2 ` km h⁻¹
= 1.8 km h⁻¹
(ii) In order to get speed in metres per second, the distance covered must be in metres, and the time taken must be in seconds.
Given: distance = 1.2 km = 1.2 × 1000 m = 1200 m
And, time = 40 min = 40 × 60 sec = 2400 sec
∴ Speed = `"Distance" / "Time"`
= `"1200 m" / "2400 sec"`
= `"1" / "2"` m s⁻¹ = 0·5 m s⁻1
Key Points Summary
-
Speed measures “how fast”
-
Always make sure units match before calculating
Test Yourself
Related QuestionsVIEW ALL [38]
In one trip the logboat brings about 20 kg of fish. But other types of boats bring a bigger catch as given in the table. The table also shows the speed of each type of boat, which is how far each boat goes in one hour. Look at the table and calculate -
- About how far can a motorboat go in six hours?
| Type of boat | Catch of fish in one trip (in kg) |
Speed of the boat (how far it goes in one hour) |
| Log boat | 20 | 4 km per hour |
| Long tail boat | 600 | 12 km per hour |
| Motorboat | 800 | 20 km per hour |
| Machine boat | 6000 | 22 km per hour |
