Course Content
Chapter 01 – Operations on Sets
The set operations are performed on two or more sets to obtain a combination of elements as per the operation performed on them. In a set theory, there are three major types of operations performed on sets, such as: Union of sets (∪) The intersection of sets (∩) Difference of sets ( – ) In this lesson we will discuss these operations along with their Venn diagram and will learn to verify the following laws: Commutative, Associative, Distributive, and De-Morgans' law.
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Chapter 02 – Real Numbers
All real numbers follow three main rules: they can be measured, valued, and manipulated. Learn about various types of real numbers, like whole numbers, rational numbers, and irrational numbers, and explore their properties. In this chapter, we will learn about Squares and cubes of real numbers and find their roots.
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Chapter 03 – Number System
The number system or the numeral system is the system of naming or representing numbers. There are different types of number systems in Mathematics like decimal number system, binary number system, octal number system, and hexadecimal number system. In this chapter, we will learn different types and conversion procedures with many number systems.
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Chapter 04 – Financial Arithmetic
Financial mathematics describes the application of mathematics and mathematical modeling to solve financial problems. In this chapter, we will learn about partnership, banking, conversion of currencies, profit/markup, percentage, and income tax.
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Chapter 05 – Polynomials
In algebra, a polynomial equation contains coefficients, exponents, and variables. Learn about forming polynomial equations. In this chapter, we will study the definition and the three restrictions of polynomials, we'll tackle polynomial equations and learn to perform operations on polynomials, and learn to avoid common mistakes.
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Chapter 06 – Factorization, Simultaneous Equations
In algebra, factoring is a technique to simplify an expression by reversing the multiplication process. Simultaneous Equations are a set of two or more algebraic equations that share variables and are solved simultaneously. In this chapter, we will learn about factoring by grouping, review the three steps, explore splitting the middle term, and work examples to practice verification and what simultaneous equations are with examples. Find out how to solve the equations using the methods of elimination, graphing, and substitution.
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Chapter 07 – Fundamentals of Geometry
Geometry is the study of different types of shapes, figures, and sizes. It is important to know and understand some basic concepts. We will learn about some of the most fundamental concepts in geometry, including lines, polygons, and circles.
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Chapter 08 – Practical Geometry
Geometric construction offers the ability to create accurate drawings and models without the use of numbers. In this chapter, we will discover the methods and tools that will aid in solving math problems as well as constructing quadrilaterals and right-angled triangles.
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Chapter 09 – Areas and Volumes
The volume and surface area of a sphere can be calculated when the sphere's radius is given. In this chapter, we will learn about the shape sphere and its radius, and understand how to calculate the volume and surface area of a sphere through some practice problems. Also, we will learn to use and apply Pythagoras' theorem and Herons' formula.
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Chapter 10 – Demonstrative Geometry
Demonstrative geometry is a branch of mathematics that is used to demonstrate the truth of mathematical statements concerning geometric figures. In this chapter, we will learn about theorems on geometry that are proved through logical reasoning.
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Chapter 11 – Trigonometry
Sine and cosine are basic trigonometric functions used to solve the angles and sides of triangles. In this chapter, we will review trigonometry concepts and learn about the mnemonic used for sine, cosine, and tangent functions.
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Chapter 12 – Information Handling
Frequency distribution, in statistics, is a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. Measures of central tendency describe how data sets are clustered in a central value. In this chapter, we will learn to construct the frequency distribution table, and learn more about three measures of central tendency, its importance, and various examples.
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Mathematics – VIII
About Lesson

An income tax is a governmental tax placed on the earnings of people and enterprises.

 

What exactly is income tax?

Income tax is a proportion of money that people or corporations must pay the government depending on their earnings (income) in a particular year.

 

Who Is Responsible for Paying Income Tax?

Individuals and businesses in Pakistan who earn a particular amount of money are liable for income tax. Individuals who work, own a business or generate money through investments or rental properties fall into this category.

 

Taxable Income:

The amount of income on which you must pay taxes is referred to as “taxable income.” According to Pakistani tax laws, in order to calculate taxable income, you must deduct various expenses and deductions from your total income.

 

Tax Slabs:

Income tax is not levied at the same rate for everyone. It is instead divided into various “tax slabs,” each with its own tax rate. The higher your income, the higher the tax rate on the share of your income that falls inside that particular bracket.

 

Filing Income Tax Return:

Individuals in Pakistan are required to file an income tax return every year. This is a form where you declare your income, deductions, and tax liabilities. Based on this return, the government determines how much tax you owe or if you are eligible for a tax refund.

 

Withholding Tax:

In some cases, individuals may not need to file an income tax return separately if their employer deducts taxes directly from their salary. This is known as “withholding tax.”

 

Importance of Paying Taxes:

Income tax is essential for the government to generate revenue. This revenue is then used to provide public services, build infrastructure, support social welfare programs, and fund various government activities for the benefit of the country and its citizens.

 

Tax Filing Deadline:

The government sets a deadline for filing income tax returns, usually around the end of the financial year or shortly after it. It’s crucial to file your taxes on time to avoid penalties and to stay compliant with the tax laws.

 

Let’s differentiate between taxable and exempted income, understand the rate of income tax, and define net income:

 

Taxable income is the portion of your total income that is subject to income tax. It includes all incomes, profits, and gains that are not tax-exempt. Simply put, it is the money you make on which you must pay income tax. Deducting permitted deductions and exemptions from your total income yields taxable income.

 

Exempted income, on the other hand, is the portion of your overall income that is not taxed. The government exempts certain forms of income, which means you do not have to pay taxes on that income. Exempted income in various nations can include gifts, specific allowances, agricultural revenue up to a particular threshold, and so forth.

 

Rate of Income Tax:

Rate of Income Tax: The rate of income tax is defined as the percentage of your taxable income that you must pay as income tax. Income tax rates vary according to the country’s tax legislation and income tax brackets or slabs. Higher-income levels typically have higher tax rates, whereas lower-income levels typically have lower tax rates. Governments utilize progressive tax rates to ensure that higher-income earners pay a greater share of their income in taxes.

 

Net Income:

Net income is the amount you have left after deducting all the allowable expenses, deductions, and exemptions from your total income. It is the actual income you receive in your hands after paying all the necessary taxes. Net income is also known as “take-home pay” or “after-tax income.” It’s the money you can use for your day-to-day expenses, savings, or investments.

 

To summarize:
  • Taxable Income: The part of your total income on which you need to pay income tax.
  • Exempted Income: The part of your total income that is not subject to income tax.
  • Rate of Income Tax: The percentage of your taxable income that you must pay as income tax, which can vary depending on your income level.
  • Net Income: The amount of income you receive after deducting taxes, exemptions, and deductions from your total income.
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