## CBSE Class 10 Mathematics:

Just like the CBSE Class 9 Mathematics, CBSE Class 10 Mathematics syllabus is also divided into two terms such as Term 1 and Term 2. Term 1 covers the following syllabus such as:

• Number systems
• Algebra
• Geometry
• Trigonometry
• Statistics

Term 2 syllabus are:

• Algebra (Continued)
• Geometry (Continued)
• Trigonometry (Continued)
• Probability
• Coordinate geometry
• Mensuration

The syllabus are in detail below:

• Number systems:

This includes topics such as proof of irrationality, decimal representation of rational numbers, Fundamental theorem of Arithmetic, Euclid’s division lemma, etc.,

Fundamental theorem of arithmetic:

Any integer which is greater than one is either a prime number or can be expressed as a product of prime numbers and this factorization is unique except for the order in which the prime factor occurs.

Euclid’s Division lemma:

Euclid’s Division lemma can be used to find out the HCF (Highest Common Factor) for any two positive integers for showing the common properties of numbers.

Theorems on rational numbers:

These are the theorems which satisfies the following properties of rational numbers such as:

1. The sum of any two rational number is rational
2. The double of rational number is rational
3. Every integer is a rational number

Theorems to prove that the number is irrational:

These are the theorems which prove that the number is irrational.

Examples:

1. Find the mode of the following data:
• 120,110, 130,110,120,140, 130,120,140,120

1. Find the largest positive integer that will divide 398, 436, and 542 leaving reminders 7, 11, 15 respectively.

1. If p is a prime number, then prove that √p as irrational:

• Algebra:

In Term 1 it covers the topics such as Polynomials and Pair of linear equations in two variables whereas in Term 2 it covers the topics such as quadratic equation and arithmetic progression.

Polynomials:

A polynomial is a mathematical expression that consists of variables and constants combined using addition, multiplication, subtraction and division. The degree of a polynomial is an exponent of the highest degree term.

For example: Constant polynomial is a polynomial of degree 0

Liner polynomial is a polynomial of degree 1

Quadratic polynomial is a polynomial of degree 2

Cubic polynomial is a polynomial of degree 3

Here the topics such as zeroes of polynomials, relationship between zeroes and coefficient of quadratic polynomials, cubic polynomials, linear polynomials, statement and simple problems on division algorithm, etc.,

Pair of liner equations with two variables:

A linear equation is an equation of algebraic expression which may consist either constants or variables. Similarly, linear equation for two variables is a form of ax + by + c=0, where x and y are variables, a, b and c are real numbers. The graph of a linear equation of two variables plotted on a Cartesian plane is a straight line.

Just like the linear equations are expressed in the form of algebraic expression, a quadratic equation also can be expressed in the form of algebraic expression such as ax2+bx+c=0, where a not equal to zero. This covers the topics such as Roots of quadratic equation, solution of quadratic equation by factorization, solution of quadratic equation by completing the square, formulation of quadratic equation, etc.

Arithmetic progression:

A sequence of a1, a2, a3…an is said to be an arithmetic progression if there is a constant difference between each successive terms which can be expressed as

A2-a1 = d,

A3-a2= d,

Where d is a common difference.

Examples:

1. If (y-a) is a factor of f(y) then ______ is a zero of f(y).

1. Cubic polynomial x=f(y) puts the y-axis at almost

1. Every linear equation in two variables has _______ solutions.

1. Graph of every linear equation in two variables represent a _____

1. Find two consecutive positive integers, sum of whose squares is 365.

• Geometry:

This covers the regular topics such as Triangles, circles and construction of geometrical objects.

Triangles:

A Triangle which is a basic shape of geometry is a polygon with 3 sides and 3 vertices/corners. It is necessary to prove certain conditions in order to prove that two triangles are similar. Conditions such as AAA (Angle-angle-angle), AA (Angle-Angle), SSS (Side-Side-Side) must be satisfied in order to prove two triangles are equal.

Circles:

A circle is a geometrical object which has no edges or corners. Any circle has a centre point and a circumference. A circumference is a set of all points at a fixed distance from the centre of the circle. Radius of a circle is measured as a distance between the centre of the circle to the circumference of the circle. Diameter of a circle is measured as two times the radius of the circle. Other topics which are covered under this chapter are Tangent of a circle, arc, chord, secant, sector and segments.

Construction of geometrical objects:

This is an important branch of Geometry which makes used of specific tools and instruments, specific rules and objects for the construction of Geometrical objects. This chapter covers different ways to construct the 2D objects using compass, ruler and protractor, etc.

Examples:

1. The areas of two isosceles triangles are in the ratio 16:25. The ratio of their corresponding heights is_______

1. The inner circumference of a circular track is 440m. The track is 14 m wide. Find the diameter of the outer circle of the track.

1. If quadrilateral ABCD is drawn to circumscribe a circle then prove that AB + CD =AD + BC.

• Trigonometry:

This includes the topics such as Introduction to Trigonometry, Trigonometrical identities, heights and distances in Trigonometry, etc. Trigonometry is a branch of the mathematics which deals with the measurement of angles and sides of a triangle and the problems that comes with the angles. The ratios of the sides of the Triangle with respect to its acute angle are called as Trigonometric ratios. If the trigonometric ratios of an angle of an equation are true for all the values of angle, then it is called as Trigonometric identity.

Examples:

1.The value of cosec 70° – sec 20° is ______

1. A ladder 50 m long just reaches the top of the vertical wall. If the ladder makes an angle of 60 ° with the wall, what is the height of the wall?

• Statistics and probability:

Statistics:

There are three measures for central values of a given data such as Mean, Median and Mode. Problems related to Mean, Median and Mode are covered under this syllabus.

Probability:

Probability is a chance of occurrence of a given event. In other words, how likely an event is about to take place. For example, when we toss a coin, the probability of getting either head or tail is 50 %.

Examples:

1. Questions based on calculating mean, median and mode are covered under the chapter of Statistics.
2. The probability of an event that is certain to happen is_____

• Coordinate Geometry:

This is a part of geometry which guides to plot a point in the Cartesian plane. A Cartesian plane is a plane with a rectangular coordinate system that associates each point with a pair of numbers which are called as x-coordinate and y-coordinate respectively. X-coordinate measures the distance of the point from the y-axis which is also called as abscissa whereas the y-coordinate measures the distance of the point from the x-axis which is also called as ordinate.

Examples:

1. What is the distance between the points A(c,0) and B(0,-c)?

1. Find the point on y-axis which is equidistant from the points (5,-2) and (-3,2).

• Mensuration:

This covers the topics such as areas related to the circles, surface areas and volumes, etc.,

Area of circles:

This covers various topics such as perimeter and area of the circle, area of the sector and segment of the circle, areas of combination of plane figures, etc.,

Surface areas and volumes:

Surface area is the total measurement of the surface area covered by all the flat and covered surfaces of 3D objects. Volume is a measure of amount of space occupied by the 3D objects.

Examples:

1. If the minute hand of a big clock is 1.05 m long, find the rate at which its tip is moving in cm per minute.

1. Find the perimeter of the figure, where AED is a semi-circle and ABCD is a rectangle.

Thus, these are the syllabus covered in the CBSE Class 10 Mathematics.

## 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, nth 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:

1. The value of 21/3 * 24/3 = ___

1. √8 is equal to _______

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

• 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:

1. The edges of a plane surface:

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

1. 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

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

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

1. The point (0,-5) lies on

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

1. 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:

1. Find the area of Equilateral triangle whose side is 12 cm

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

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

1. The degree of a constant function is ______

1. If x+y+x=0, then x3+y3+z3 is

1. Evaluate 105 * 95

• 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:

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

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

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

• 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:

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

1. A coin is tossed two times. What is the probability of getting two at most 2 heads?
• ¼
• ½
• ¾
• None of these