## CBSE Class 9 Mathematics:

This is a little higher grade of class which consists of many advanced topics like coordinate geometry, herons formula, Trigonometry, Graphical representation of data, etc., in Mathematics. As per the terms of conditions of CCE (Continuos and Comprehensive Evaluation), the syllabus of **CBSE Class 9** and Class 10 has been divided term wise. Each units in both terms will be assessed through Formative and summative assessment. Each term carries two formative assessment each carrying 10% of weightage. It has been declared that the summative assessment for term 1 carries 30% of weightage and summative assessment for the term 2 carries same 30% of weightage.

Let us check the chapters in **CBSE Class 9** Mathematics below:

**Term 1:**

- Numbers:
- Geometry
- Coordinate Geometry
- Mensuration
- Algebra

**Term 2:**

- Algebra (Continued from Term 1)
- Geometry (Continued from Term 1)
- Mensuration (Continued from Term 1)
- Statistics
- Probability

Thus, let us see the chapters one by one:

**Numbers:**

As this is the first chapter in all the classes, **CBSE Class 9** also includes “Numbers” chapter as the first and foremost chapter. This covers the topics widely as natural numbers, real numbers, rational numbers, terminating / non-terminating recurring decimals, n^{th} root of a real number, etc.

A set of all rational and irrational numbers are called as real numbers. A number which cannot be represented in the form of p/q, where p and q are integers and q not equal to 0. The decimal expansion of a number is its representation in base 10 of decimal system.

**Examples: **

- The value of 2
^{1/3 }* 2^{4/3 }= ___

Answer: ½

- √8 is equal to _______

Answer: 2√2

- Find 6 rational numbers between 6/5 and 7/5.

Answer: 61/50,62/50,63/50,64/50,65/50,66/50

**Geometry:**

Just like other classes general topics on Geometry like lines and angles, triangles, circles, quadrilaterals, etc. Another special topic is covered under this chapter which is known as “Euclidean Geometry”. Euclidean Geometry is a mathematical system where geometrical results are proved based on the previously proved results and assumptions called axioms. There are different axioms and theorems based on the Euclidean Geometry.

In first term, Geometry includes Euclid’s Geometry, Lines & Angles and Triangles whereas in the second term the chapters of Geometry are Quadrilaterals, Area, Circles and construction.

**Examples:**

- The edges of a plane surface:

Answer: Line

- Given four points in which no three of them are collinear, then there exists.

Answer: 6 Lines

- Which is the correct statement in the following?

- The line segment has one and only end point
- Three points are said to be collinear if they lie on the same line
- Two lines are coincident if they have one point in common
- The ray AB is same as the ray BA

Answer: Two lines are said to be collinear if they lie on the same line

- Two angles of triangles are 65 degree and 45 degree respectively. Find the third angles.

Answer: 70 degree

- Using the Heron’s formula find the area of the triangle whose sides are 3cm, 4cm and 10 cm.

Answer: 24 sq cm

**Coordinate Geometry:**

This is a chapter which deals how to plot a point in a plane when its coordinates are given. The Cartesian plane is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers.

The two numbers are called as x-coordinate which measures the distance of the point from y-axis and y coordinate which measures the distance of the point from the x-axis. This chapter is covered only during the term 1 of **CBSE Class 9** Mathematics.

**Examples:**

- The point (0,-5) lies on

Answer: -Ve y-axis

- The distance of the point from the (3,0) from the x-axis

Answer: 3 Units

- Which of the following points belongs to x-axis?

- (2,0)
- (3,3)
- (0,1)
- (-2,0)

Answer: (2,0) and (-2,0) belongs to x-axis

**Mensuration:**

This includes topics such as Area of triangle using Heron’s formula, Area of quadrilateral and its application and so on. This chapter is covered during the term 1 and term 2 of **CBSE Class 9** Mathematics.

**Examples:**

- Find the area of Equilateral triangle whose side is 12 cm

Answer: 36√3 sq cm

- The perimeter of a Rhombus ABCD is 80 cm. Find the area of the Rhombus if its diagonal BD measures 12 cm.

Answer: 228.8 sq cm

- Find the area of isosceles Triangle whose equal sides is 6cm, 6cm and 8 cm.

Answer: 17.8 sq cm

**Algebra:**

The topics which are covered in the first term of Algebra are Polynomials whereas in the second term it covers Linear equations in two variables. The topics which are covered are definition of polynomials, its coefficients, its counter examples, degree of polynomial, constant, linear, quadrilateral and cubic polynomials. The topics which are covered in the second term are linear equations with one variable, linear equations with two variables, graph of linear equations, etc.

** Examples:**

- The degree of a constant function is ______

Answer: 0

- If x+y+x=0, then x
^{3}+y^{3}+z^{3}is

Answer: 2xyz

- Evaluate 105 * 95

Answer: 9975

**Statistics:**

This chapter includes introduction to the statistics, representation of collection of data in a tabular form, ungrouped and grouped charts, bar charts, frequency polygons, mean, median and mode of ungrouped data. This chapter is covered during the second term of CBSE Class Mathematics.

**Examples:**

- What is the upper class limit of the class 37-43?

Answer: 43

- What is the class size of the intervals 10-20?

Answer: 10

- Find the sum of the deviations from the variety of values 3,4,6,8,14 from their mean.

Answer: 0

**Probability:**

The probability is a chance of occurrence of a given event which means that how likely that an event can take place. For better understanding, if we toss a coin, the probability of getting either head or tail is 50% chance. The topics which are covered under this chapter are definition of probability, examples of probability, real life examples of probability and so on. This chapter is covered under the second term of **CBSE Class 9** Mathematics.

**Examples:**

- What is the probability of a number greater than 6 for a single row of a die?

Answer: 0

- A coin is tossed two times. What is the probability of getting two at most 2 heads?

- ¼
- ½
- ¾
- None of these

Answer: None of these

- A card is drawn from a pack of cards. Find the probability that it is queen?

Answer: 1/13

Thus, above topics sare the syllabus of **CBSE Class 9** Mathematics.

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