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# Class 8 Maths

Class 8 maths is the base for developing higher-level computational skills in students. Students in class 8 learn to work basic algebraic equations, the arithmetic of rational numbers, factorization, and more. Learning class 8 maths requires students to have a clear understanding of previously studied concepts and skills. It focuses on working with advanced concepts related to geometry, arithmetic, and numbers. In class 8 maths, the basic arithmetic operations shift to a bit complex algebraic word problems that students have to interpret and understand. Thus, having complete knowledge of the class 8 maths syllabus is a must for students.

## Class 8 Maths Syllabus

**Class 8 maths** is proficient in facilitating analytical growth and primary skillset in students. The syllabus of class 8 maths comprises topics related to shapes, number system, exponents, algebraic expressions, and more. Some of the skills to develop in Class 8 maths are based on the following:

**Number System**

- Rational Numbers
- Properties of rational numbers(including identities). Using the general form to describe properties
- Consolidation of operations on rational numbers.
- Representation of rational numbers on the number line
- Between any two rational numbers there lies another rational number (Making children see that if we take two rational numbers, we can keep finding more and more numbers that lie between them.)
- Word problems (including higher logic like two operations, area, etc)

**Powers**

- Integers as exponents.
- Laws of exponents with integral powers

**Squares, Square roots, Cubes, Cube roots.**

- Squares and square roots
- Square roots using the factor method and division method for numbers containing (a) no more than total of 4 digits and (b) no more than 2 decimal places
- Cubes and cube roots (using factor method to find cubes and cube roots of numbers containing at most 3 digits)
- Estimating square roots and cube roots. Learning the process of moving nearer to the actual number.

**Playing with numbers**

- Writing and understanding a 2 and 3-digit number in generalized form (like ab = 10a + b and abc = 100a + 10b + c, where a, b, c can be only digits from 0-9) and engaging with various puzzles concerning this. (Like finding the missing numerals represented by alphabets in sums involving any of the four operations.) Children solve and create problems and puzzles
- Number puzzles and games.
- Deriving the divisibility test rules of 2, 3, 5, 9, and 10 for a two-digit and three-digit numbers expressed in the general form

**Algebraic Expressions and Identities**

- Multiplication and division of algebraic expressions. (Coefficient should be integers)
- Solving linear equations in one variable in contextual problems involving multiplication and division (word problems) (avoid the complex coefficient in the equations)
- Basic 4 algebraic identities that are helpful for finding (a + b)
^{2}, (a - b)^{2}, (a + b) (a - b), and (x + a) (x + b) - Factorizing algebraic expression by using the above identities

**Ratio and Proportion**

- Advanced problems involving ratios, percentages, profit & loss, discounts, and taxes.
- Difference between simple interest and compound interest (compounded yearly up to 3 years or half-yearly up to 3 steps only), arriving at the formula for compound interest through patterns and using it for simple problems.
- Direct variation – Simple and direct word problems
- Inverse variation – Simple and direct word problems
- Time & work problems – Simple and direct word problems

**Geometry**

Understanding shapes:

- properties of quadrilaterals – The sum of angles of a quadrilateral is equal to 360° (By verification)
- Properties of a parallelogram (By verification)

(i) Opposite sides of a parallelogram are equal

(ii) Opposite angles of a parallelogram are equal

(iii) Diagonals of a parallelogram bisect each other at right angles

(iv) Adjacent angles of a parallelogram add up to 180 degrees - Properties of other quadrilaterals include:

(i) Diagonals of a rectangle are equal and bisect each other

(ii) Diagonals of a rhombus bisect each other at right angles

(iii) Diagonals of a square are equal and bisect each other at right angles

**Representing 3-D in 2-D**

- Identify and match pictures with objects (more complicated Ex: nested, joint 2-D shapes and 3-D shapes)
- 2-D representation of 3-D objects
- Counting vertices, edges and faces and verifying them Euler’s relation for 3-D figures with flat faces (cubes, cuboids, tetrahedrons, prisms, and pyramids)

**Construction:**

Construction of Quadrilaterals:

- Given four sides and one diagonal
- Three sides and two diagonals
- Three sides and two included angles
- Two adjacent sides and three angles

**Mensuration**

- Area of a trapezium and a polygon
- volume – measurement of volume using a basic unit
- volume of a cube, cuboid, and cylinder
- Surface area of a cube, cuboid, cylinder

**Data Handling**

- Reading bar graphs – arranging ungropued data into groups, representation of grouped data through bar graphs, constructing and interpreting bar graphs.
- Simple pie charts with reasonable data numbers
- Consolidating and generalizing the notion of chance in events like tossing coins, dice, etc.
- Relating it to chance in life events. Visual representation of frequency outcomes of repeated throws of the same kind of coins or dice. Throwing many identical dice/coins together and aggregating the result of the throws to get many individual events.
- Observing the aggregating numbers over a large number of repeated events.
- Comparing with the data for a coin. Observing strings of throws, the notion of randomness.

**Introduction to graphs**

- Axes (Same units), cartesian plane
- Plotting points for different kinds of situations – perimeter vs length for squares, area as a function of side of a square, plotting of multiples of different numbers, simple interest vs a number of years, etc.
- Reading from the graphs

(i) Reading of linear graphs

(ii) Reading of distance vs time graph

## Developing 8th Class Maths Skills

8th class maths focuses on developing various real-life skills in students. Students attain basic computational skills at this upper primary stage such as finding cube roots, and square roots, plotting graphs, determining area and volume, etc. The best way to develop class 8 maths skills is through practical application and visualization.

**Geometry**

In 8th class maths, students learn the application of the Pythagorean Theorem in mathematics and in solving real-world problems. Students in class 8 must also know the use of various formulas for finding the volume of cubes, cuboids, and cylinders. They should also learn the formulas for the area and circumference of a circle.

**Number System**

The students of 8^{th} class maths study numbers beyond rational numbers and irrational numbers. They can find both irrational and rational numbers on a number line. It is important to build this knowledge in students for performing various mathematical calculations in higher grades.

## Class 8 Maths Tips and Tricks

**Solve Interactive Worksheets**

Strengthening basic Class 8 maths skills requires reinforcement of concepts. Parents can promote the hands-on practice of these skills through interactive worksheets. Interactive worksheets offer visualization of concepts which is highly useful in comprehensive learning. The engaging format of interactive worksheets is also appropriate for improving math interest in children.

**Refer to Reliable Study material**

Refer to reliable study material like textbooks and websites with accurate solutions related to the corresponding curriculum for the preparation of class 8 maths. At the same time focus on the solved examples in the textbook as well.

## Class 8 Maths Formulas

Memorizing class 8 maths formulas would help the students to solve their applications very easily. Make a list of all the formulas of 8th class maths and take a look at them very often. Some of these formulas are listed below:

- Volume of a cylinder = πr
^{2}h - Volume of a cube = (side)
^{3} - Volume of a cuboid = length × width × height
- Discount = marked price - sale price
- Simple interest = PTR/100
- Compound interest = P (1 + r/n)
^{nt}, etc

For the complete list of class 8 maths formulas, visit our page by clicking here.

## Class 8 Maths Worksheets

By solving class 8 maths worksheets, students can develop logical and reasoning skills. Since these worksheets are planned such that they cover all topics and all difficulty levels. By practicing these worksheets with a time limit, one can learn time management skills which are very helpful during exam time. Also, by checking the answers with the answers given in the worksheet after solving it, the students can identify the areas of their weakness and rework those topics again.

## Solved Examples on Class 8 Maths

**Example 1:** Class 8 has a total of 60 children among which 45% are interested in maths. Then how many students are not interested in maths?

**Solution:**

The total number of children = 60.

The number of students interested in maths = 45% of 60 = 45/100 × 60 = 27.

Then the number of students who are NOT interested in maths = 60 - 27 = 33.

**Answer:** The required number of students is 33.

**Example 2:** Factorize the expression 6x^{2}y - 3xy^{2}. Also, verify your answer by distributive property.

**Solution:**

The terms of the given expression are 6x^{2}y and -3xy^{2}.

Here, 3 is the HCF of 6 and 3; and xy is the HCF of x^{2}y and xy^{2}. Thus, we can factorize the given expression as follows:

6x^{2}y - 3xy^{2 }= 3xy (2x - y) as we get 2x and -y by dividing 6x^{2}y and -3xy^{2} respectively by 3xy.

**Verification by Distributive Property:**

3xy (2x - y) = 3xy · 2x - 3xy · y = 6x^{2}y - 3xy^{2}.

Hence the answer is verified.

**Answer:** The factorized form of the given expression is 3xy (2x - y).

## FAQs on Class 8 Maths

### What are the Topics in Class 8 Maths?

The topics of **Class 8 maths** are listed below. For detailed information, scroll up on this same page.

- Rational numbers
- Exponents and powers
- Squares and square roots; Cubes and cube roots
- Linear equations (one variable)
- Playing with numbers
- Algebraic expressions and identities
- Ratio and proportion
- Representing 2D and 3D shapes
- Quadrilaterals and properties
- Construction of Quadrilaterals
- Surface area and volume of cube, cuboid, and cylinder
- Bar graphs and pie charts
- Introduction to the cartesian plane

### How are Class 8 Maths Solutions Helpful?

Having detailed solutions handy is very helpful while practising. If we are unable to solve any questions during practice, we can directly go to solutions and check the process of solving.

### How to Prepare for Class 8 Maths Olympiads?

To prepare for the olympiads of class 8 maths, first practice the school textbook's problems. Then move on to sample papers of that olympiad to understand what kind of questions are being asked. To get more understanding of olympiad's preparation, visit the page by clicking here.

### What is Mensuration in Class 8 Maths?

Mensuration in class 8 maths covers the surface area and volume of cuboids, cubes, and cylinders. Also, in this chapter, the area of the trapezoid and rhombus are also covered.

### How Do I Start My Class 8 Maths?

Class 8 maths practice should be started by studying the textbook. First focus on easy topics like rational numbers, squares and square roots, exponents and powers, direct and inverse variations, etc., and then move on to the harder ones like mensuration, quadrilaterals, algebraic identities, etc. Always solve the sample papers and worksheets before appearing for the exam.

### What are the Most Important Chapters of Class 8 Maths?

The most important chapters of class 8 maths are the ones that even help the students on moving to higher grades. Some of them are exponents and powers, algebraic expressions and identities, squares and square roots, cubes and cube roots, mensuration, introduction to graphs, etc.

### How Many Hours Should a Class 8 Student Practice Maths?

We know "practice makes a man perfect". Ideally, a class 8 maths student should work at least 1 to 1.5 hrs a day for a minimum of 5-6 days a week. While practicing the students should make sure that all the concepts and all question types are covered.

### Is Class 8 Maths Tough?

Class 8 maths is a mix of easy and moderate topics. It is not very hard as long as the student prefers in learning the concept before starting to solve the problems.

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