Maths Universe 1

1st year Physics
Unit # Force and Motion
Very easy and Conceptual
Hand writing notes
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Find the value of C°?

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A **rational number** is a number that can be expressed as the ratio of two integers, where the denominator is not zero. In other words, it can be written in the form **a/b**, where **a** and **b** are integers and **b ≠ 0**. Rational numbers can be whole numbers, fractions, or decimals that either terminate or repeat.

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- **Whole Numbers**: 5, -3, 0
- **Fractions**: 1/2, -7/4, 3/10
- **Decimals**: 0.5, -2.75, 0.333... (repeating)

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An **irrational number** is a number that cannot be expressed as a simple fraction or ratio of two integers. Its decimal representation is non-terminating and non-repeating. Irrational numbers cannot be written in the form **a/b**.

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- **√2** (1.414...), **π** (3.14159...), **e** (2.718...)

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1. **: Prices of goods, like $2.50 or $7.99, are examples of rational numbers because they can be expressed as fractions (e.g., 250/100 or 799/100).
2. **: Time measurements can be rational, like 1.5 hours (which is 1 hour and 30 minutes or 3/2 hours).
3. **: Recipes often use rational numbers in fractions, such as 1/2 cup of flour or 3/4 teaspoon of sugar.
4. **: Length measurements, such as 5.5 meters or 2.25 inches, are rational numbers.

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1. **Geometry and Engineering**: The value of π is used in calculating the circumference and area of circles in construction, design, and architecture.
2. **: Certain physical constants, like √2 or the constant **e** (used in exponential growth or decay), are irrational numbers used in scientific equations.
3. **: Some natural patterns, like the golden ratio (an irrational number), appear in art, architecture, and biological systems.

Both rational and irrational numbers are essential in daily calculations, whether it's for basic activities like buying groceries (using rational numbers) or more complex scientific and engineering tasks (using irrational numbers).

Very Easy Maths Notes Grade 9 Federal Board
National Book Foundation Islamabad
Solved by: Bashir Ahmad Mubashar M.Phil, M.Ed
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Oxford Countdown
Level #8
unit #4
"Number system"
Page #1 to 18

Oxford Countdown Level 7
Exercise # 6 (Direct and Inverse Variation)
Pages: 1 to 15

Nutrition and digestion
Very simple
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Biology notes

Class:10th
Chapter:01 "Quadratic equations"
Exercise:1.1 "all questions solved"
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What is preposition?
Uses of prepositions.

Use of Get/Getting + Adjective
اکثر طلبا پریشان ہو جاتے ہیں کہ اس طرح کے فقرات کو کیسے کہیں۔ مجھے بہت خوشی ہو رہی ہے۔ مجھے دکھ ہو رہا ہے۔ مجھے پریشانی ہو رہی ہے۔ یا میں صبح سے پریشان ہو رہا ہوں۔ آپ انہیں ہر زمانے میں استعمال کر سکتے ہیں یعنی پریشان ہو رہا تھا، پریشان ہو رہا ہوں گا۔ طلبا کے ذہن میں جو سٹرکچر آتا ہے وہ یہ ہوتا۔

I am readying*. (incorrect) میں تیار ہو رہی ہوں۔

For such kind of sentences, we use ‘get’. For instance, ‘I am getting ready’. Some more examples are given below.

I am getting very excited. مجھے بہت خوشی ہو رہی ہے۔
I am getting happy. میں خوش ہو رہا ہوں۔
I will get happy. میں خوش ہوجاؤں گا۔
I got happy. میں خوش ہوا۔
She is getting interested in this subject. وہ اب اس مضمون میں دلچسپ ہو رہی ہے یعنی دلچسپی لے رہی ہے۔
They are getting exhausted. وہ تھک رہے ہیں۔
We are getting late. ہمیں دیر ہو رہی ہے۔
We got shocked. ہمیں دھچکا لگا
They got mad. وہ پاگل ہوگئے۔
I got tired. میں تھک گیا۔
She got married. اسکی شادی ہوگئی۔
I have been getting worried since morning. میں صبح سے پریشان ہو رہا ہوں۔