## CBSE Class 8 Mathematics:

Just like other CBSE classes, Class 8 has its unique way of structure of syllabus which helps student to understand the topics better. Since the syllabus are designed by the expert teachers, it is always easy for the students at the level of class 8 to understand their topics better.

Lets check out the syllabus of **CBSE Class 8** Mathematics below:

**Numbers:**

The chapter “Numbers” covers the syllabus just as that of the previous classes. It includes all basic and important features of “numbers” such as Exponent and powers, rational numbers, even and odd numbers, playing with numbers and factorization. Among this, the newest topics which are added for the **CBSE Class 8** level are Square and square root, cube and cube root, playing with numbers, etc.,

**Rational numbers:**

Rational numbers are the numbers which can be expressed in the form of quotient or fraction of two integers. A number is generally said to be a rational number if the numbers in the fraction (for ex) p/q are integers and q is not equal to zero it is said to be a rational number. In other words, it is also expressed as a ratio between two numbers.

**Exponents and powers:**

Exponent can be defined as number of times a number multiplied by itself. Exponents can be expressed as X^{Y} where x is a number and y is the power or exponent.

For example, 2^{4} = 2 * 2 * 2 * 2

**Squares and square roots:**

This can be explained as the number raised to the power of 2. In other words, when we multiply a number by itself it is said to be a square of a number. Similarly, a square root of a number x can be explained as the value which when multiplied by itself gives the number x.

For example, 2 is the square root of 4.

**Cubes and cube roots:**

Just like the square root of a number, we can also find out the cube root of a number by just raising the number to the power 3. In other words, the cube root of a number x when multiplied by itself 3 times we get the number x. The topics which are covered under this chapter are Finding the cube of a number, finding cube root of a perfect cubes, cube roots of perfect integers, cube roots of product of integers, cube roots of rational numbers, etc.,

Example for a cube root of 27 = 3 * 3 *3

**Playing with numbers:**

This is a chapter which is a fun to solve. This includes topics like finding the patterns of a number, properties and divisibility of a number, a number is said to be divisible by another number when the remainder is zero and so on. Interesting topics which are covered under this chapter are playing Sudoku, magic squares, puzzles, interchanging digits of a number, cryptograms and so on.

** Examples:**

- Find the multiplicative inverse of 25?

Answer: 1/25

- What will be the number of zeroes in the square of 5000?

Answer: 6

- Find the square of 39?

Answer: 1521

- Find the cube root of 175616.

Answer: 56

- What is the rational number that does not have a reciprocal?

Answer: 0

**Algebra:**

A collection of symbols and numbers in an equation and solving them together is called as Algebra. Lot of introduction on Algebra is given in the previous classes and thus in the class 8, advanced concepts like division of algebraic expressions, solving linear equations, etc., are covered.

**Identities in Algebra:**

One of the newest topics which has been added in the class 8 is “Identities” of algebra. There are three identities namely

- Identity 1: Multiplication of monomials
- Identity 2: Multiplication of a monomial and binomial
- Identity 3: Multiplication of two binomials

The other topics which are covered under this chapter are knowing the difference between an equation and identity, multiplication of monomials and polynomials, multiplication of binomials and monomials, etc.,

**Factorization:**

Factorization is a process of splitting up an algebraic expression into one or more factors. Topics which are covered under this are common factors and greatest common factor of monomials, factorization of binomial common factor, factorization of grouping the terms, etc.,

** Division of algebraic expression:**

This covers different topics like division of a monomial with same monomial number, division of polynomial with binomial number, division of polynomial with one variable and division of polynomial by using factorization.

** Linear equations:**

This topic covers introduction to the linear equation, solving linear equation with one variable, finding root of an equation, application and solution of a linear equation, cross multiplication method for solving equations, etc.,

** **

**Examples:**

- Solve -36y
^{3}% 9y^{2}= __

Answer: -4y

- In the expression which have the factors of the type (x+a)(x+b), remember the numerical term gives _______

Answer: ab

- Which of the following is the monomial?

- 2x+7
- 4x +y
- 3a
- 3x+5y+7

Answer: 3a

**Ratio and proportion:**

Little advanced problems in ratio and proportion chapter are introduced in class 8. Problems on profit and loss, percentage, discount tax and overhead expenses are covered in this chapter. Other topics which are covered as calculating simple and compound interest, direct variation, inverse variation, time and work problems, etc.

**Simple and compound interest:**

Simple interest means interest calculated on certain amount of money borrowed in a specific period of time. The borrower of the money has to pay back the original principal amount plus the interest amount. It is usually for shorter periods. Compound interest is usually calculated for longer periods. Compound interest is an interest that is added to the principal amount after a specified time period and then the interest is calculated for that new principal amount.

**Direct and inverse proportions:**

In a ratio of x:y, if y increases when x increases it is said to be direct proportion whereas y decreases when x increases it is said to be inverse proportion.

**Time and work:**

This is rather an important topic which mainly divided into two variations such as direct and indirect variations. Two variables are said to be “directly variable” if increase in one quantity leads to the corresponding increase in the other quantity. Two variables are said to be “indirectly variable” if increase in one quantity leads to the corresponding decrease in the other quantity.

**Examples:**

- Find the ratio of Rs.6 to 50 paise.

Answer: 12:1

- ________ means comparing two quantities.

Answer: Ratio

- Write the expression using the exponents: 25 * 25* 25

Answer: 25^{3}

- The cost of 5 metres of a satin cloth is Rs.210. Find the sot of 15 metres of same type of cloth.

Answer: Rs.630

- If 15 workers can build a wall in 48 hours, how many workers are required to do the same work in 30 hours.

Answer: 24

**Geometry:**

As this has become important chapter in the previous classes of CBSE, class 8 covers more important topics under Geometry. This covers various topics like understanding the shapes, properties of different objects like polygon, parallelogram, quadrilateral, etc.,

**Understanding polygons:**

A polygon is a closed figure formed by the line segments. There are different types of polygons such as Convex polygon, concave polygon and regular polygon.

**Understanding Quadrilaterals:**

Quadrilateral is a polygon with four sides and four vertices. Examples of polygons are squares, rhombus and trapezium.

**Representing 3 dimensional objects in 2 D:**

This covers various topics such as drawing 2 D objects in 3 Dimensional form, counting vertices, edges, faces and verifying Euler’s relations, etc.,

**Examples:**

- A two dimensional shape is a ______ shape.

Answer: Plane

- How many edges are there in a triangular pyramid?

Answer: 6

- State the name of the regular polygon of 4 sides.

Answer: Quadrilateral

- The diagonals of a _____ are perpendicular bisectors of each other.

Answer: Square

- State true of false for the following:

- All squares are not parallelograms

Answer: False

**Mensuration:**

This is calculation of volume, area and perimeter of an object. Total boundary sizes covered by an object is said to be perimeter whereas total surface covered by an object is called as Area. Similarly, total amount of space occupied by the 3-D figure is called as volume. This chapter covers many topics like calculating volume of many 3D objects such as cubes, cuboids, prism, pyramid and others.

**Examples: **

- Find the side of a cube whose surface area is 2400 cm
^{2}.

Answer:20 cm

- What is the volume of a cuboid?

Answer: L *B * H

**Introduction to graphs:**

Graphs concepts are introduced in this level of **CBSE Class 8**. Concepts such as axes, Cartesian plane, plotting points from different kinds of situation, reading off from the graphs, reading off linear graphs, reading distance vs time graphs, etc., are covered under this chapter.

**Examples:**

- On which axis does the points (5,0) lie?

Answer: X-axis

- In which quadrant does the point P(-8,1) lie?

Answer: IV

Thus, above topics are the syllabus of **CBSE Class 8** Mathematics.

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