## CBSE Class 3 Mathematics:

When compared to CBSE Class 3, CBSE Class 2 Mathematics covered various simple topics on Addition, subtraction, multiplication without carry, place value in numbering system, simple division, etc., But in CBSE Class 3, next level mathematics is taught to enhance and trigger the brain of the child. For this, they have included the portions just similar to that of Class 1 and Class 2 but in little higher level. Among all the subjects of CBSE Class 3 like Mathematics, Science, Hindi and English let us check out the syllabus of Mathematics below.

### CBSE Class 3 syllabus:

They cover similar syllabus just like that as Class 2 and Class 1.

• Numbers:

Children are taught to write the series of numbers up to 9999 in Class 3. Also, they are trained to pronounce and write the compact and expanded form of such numbers.

Topics covered:

1. Compact and expanded forms of numerals
2. Roman numerals
3. Ascending and descending order of the numbers
4. Rounding off
5. Place value
6. Equivalent numerical names

Examples:

1. Fill up the missing numerals:
• 200 _ _ _ _ 205
• 345_347_ _ 350
• 34_ _ _ 38_ _ 41

• 200 201 202 203 204 205
• 345 346 347 348 349 350
• 34 35 36 37 38 39 40 41
1. Write the equivalent number names for the following:
• 199 = One hundred and ninety nine
• 214 = Two hundred and fourteen
• 3450 = Three thousand four hundred and fifty
1. Write the equivalent numerals for the number names
• Three hundred and sixty six = 366
• Four hundred and thirty five = 435
• Two thousand six hundred and thirty five = 2635
1. Roman numeral VI ______ than VIII
• =

1. How would you write ten in roman letter?
• X
• XII
• V

Addition and Subtraction are rather important chapters for a growing child which triggers his/her brain to solve the questions. In class 1 and class 2, addition and subtraction were little simpler with simple two digit and three digit additions and simple word problems. But in class 3, next level of addition such as four digit addition, subtraction with or without borrowing, addition and subtraction word problems are covered.

Examples:

• 8789 + 5674 = ?
• 567 + 4563 = ?

• 14463
• 5130
1. Find 6090 – ______ = 5590

• 500

• Multiplication and Division:

Covers the topics such as counting using rows and columns, multiplication tables from 2 to 7, multiplying by 1, multiplying by 0, grid multiplication and word problems in multiplication. In division it covers, division by 10 and 100, division with two digit number, multiplication and division mixed problems, division word problems, etc.

Examples:

1. 500 pencils are shared among 5 students of the classroom equally. How many pencils did each one get?

1. There are 20 bags of apples. Each bag contains 100 apples. Totally how many apples are there?

• Fractions:

Fractions are the important part of mathematics and it is very important to understand it clearly. Fraction comes as proper and improper fraction. The terms numerator and denominator are very important in the concepts of fraction.

Numerator = Number that is above the fraction line. Example: 2 in 2/3

Denominator= Number that is below the fraction line. Example: 3 in 2/3

Proper fraction has numerator smaller than the denominator whereas improper fraction has numerator larger than denominator. An improper fraction can be converted into a mixed fraction having a proper fraction and integral part. Fractions can be added, subtracted, divided and also multiplied.

Examples:

1. Find out the fraction of vowels in the word “GREAT”?

2/5

1. There are totally 5 glasses of water in the table. Geetha drank 3 glasses of water. What is the fraction of water did geetha drink?

3/5

• Rupees and paise:

Students are taught how to spend their own money and how to add, subtract, multiply and divide with their own money.

Examples:

1. 6 Rupees is equal to _______ paise

1. 35 is equal to ______ paise

1. 675 paise is equal to _____ rupees

• Time and Date:

Topics covered such as Time taken to finish a task, puzzles for young minds, understanding the calendar, reading the clock and differentiate between AM and PM, etc.

Examples:

1. How many rounds does an hour hand complete in a day?

1. What is the exact time taken by the minute hand to move from one number to the next number?

• Shapes and their properties:

Topics covered such as different shapes and sizes, properties of shapes, edges and corners, vertices and surface, review of shapes and sizes, etc.,

Examples:

1. Which of the following options are measured in cms and m?
• Length of the banana
• Distance from home to office

• In cms
• In cms
• In meters
1. Mention the length of the objects surrounding you:
• Pen
• Sharperner
• Spoon

• 10 cms
• 3 cms
• 8-9 cms

• Measurement of length, mass and capacity:

The basic things like standard unit of length, standard unit of mass, standard unit of capacity, converting meter to centi-meter, milli-meter and kilometer, etc are taught in this section. Students are given the basic understanding that the length of the pencil is measured in centi-meters whereas the distance between two places are measured in meters. Similarly, they are also taught how to measure the mass (in terms of kgs) and capacity (in terms of ml and l).

Examples:

1. 18 L = _____ ml

1. My mother is making noodles for dinner. Each noodles packet weighs 500g. How many grams of noodles will be there in 6 packets.

1. Add 85m 25cm and 56 m 44 cm and write the answer:

• Smart charts:

Pictorial representation of collection of data is called as charts. Topics which are covered are drawing simple charts with two or multiple columns, reviewing simple graphs, pictograph, etc.

Examples:

1. Answer the questions according to the datas given below:
• Painting : 10

Dancing: 8

Music: 5

Craft: 15

Cycling: 13

Gardening: 14

Stamp collection: 10

Questions:

1. Which is the most popular hobby?

1. Which is the least popular hobby?

1. What is the difference between the number of students interested in Stamp collection and Dancing?

• Play with patterns:

This section covers topics such as understanding pattern around us, detecting the number patterns, arranging in alphabetical order, skip counting, growing patterns and even odd patterns.

Examples:

1. Arrange the following names in alphabetical order:
• Abinay
• Xavier
• Harish

• Abinay
• Harish
• Xavier
1. Complete the following numerical patterns:
• 98,198,298,398,_

• 98,198,298,398,498

Thus, these are the topics covered in CBSE Class 3 Mathematics.

## CBSE Class 10 Science:

CBSE Class 10 Science syllabus is divided into two terms such as Term 1 and Term 2. Term 1 includes the following topics such as:

Term 1:

• Chemical substances- Nature and behavior
• World of living
• Effects of current
• Natural resources

Term 2 includes topics such as:

• Chemical substances-Nature and Behavior (Continued)
• World of Living (Continued)
• Natural Phenomena
• Natural Resources (Continued)

The above syllabus in detail are:

• Chemical Substances- Nature and Behavior:

In first Term the above chapter covers the topics such as Chemical reactions, acids, bases and salts, metals and non-metals. In the second Term it covers the chapter such as Chemical substances-Nature and Behavior, Periodic classification of elements.

Chemical reactions:

This chapter explains about the chemical reactions that occur naturally on any given substance. For example, when milk left at the room temperature during summers will turn it from its original nature, why grapes gets fermented and how foods are digested in our body. Thus, a chemical reaction can be defined as a process of conversion or transformation of a set of substances into another form. It is represented by a chemical equation which represents reactants, products and their physical states symbolically.

Any chemical equation is always in a balanced state so that the number of atoms of each type of reactant remains the same on the reactant and product sides of the equation.

The major topics which are covered under this chapter are

• Chemical equations and balanced chemical equations
• Types of chemical reactions
• Effects of oxidation in everyday life
• Understanding and writing chemical reactions

Acids, Bases and Salts:

This is a chapter which indicates the different taste that occurs in the food substances

because of the acids and bases.

Some of the examples of acids and bases reactions are

1. Acids when reacts with a metal, hydrogen gas is evolved and a corresponding salt is formed.
2. When an acid reacts with the metal carbonate or metal hydrogen carbonate, it gives the corresponding salts, carbon dioxide and water.

A scale called as pH scale is used for testing the strength of the acid or alkali. This chapter also covers various topics on preparation and properties of beaching powder, washing soda, plaster of paris, common salt and baking soda.

Metals and non-metals:

Metals are ductile, malleable and are good conductors of heat and electricity. Except the metal Mercury, almost all metals are solids at the room temperature. The extraction of metals from their ores and then refining them for use if known as metallurgy.

Non-metals have the properties just opposite to that of the metals. They are neither ductile nor malleable. They are bad conductors of heat and electricity except for graphite which conducts electricity.

Periodic classification of elements:

Elements can be classified on the basis of the similarities in the properties. Elements can be arranged in an increasing order of atomic masses and according to their chemical properties. Thus, for reference a periodic table is formed mentioning every possible elements.

Examples:

1. Give an example of the metal which
• Is a liquid at the room temperature
• Is a best conductor of heat
• Is a poor conductor of heat
• Can be easily cut with knife

• Mercury
• Silver
• Sodium
1. Why curd and sour substances must not be kept in the brass and copper vessels?

Answer: Brass and copper vessel contains copper which reacts with the acids found in the curd or other sour substances. Thus, this reaction forms soluble salts which are poisonous in nature making curd unfit for the consumption.

1. Why sodium is kept immersed in kerosene oil?

Answer:  Sodium reacting with oxygen catches up fire when kept in open place. Thus, sodium is always immersed in kerosene oil to avoid such accidents.

1. Why should a magnesium ribbon be cleaned before burning in air?

Answer: To remove the protective layer of basic magnesium carbonate from the surface of magnesium ribbon.

1. Write the balanced equation for the following:
• Hydrogen + Chlorine ->Hydrogen Chloride

• World of Living:

This is a chapter which is covered in both first Term and second Term. In first term the topics which are covered are Life processes, control and co-ordination in plants and animals. In second term, the topics which are covered include Reproduction, Heredity and Evolution.

Life process:

Life processes that take place in both plants and animals are covered under this topic. The topic life process includes nutrition, respiration, transportation, excretion in plants and animals. Life process in animals include Digestive system which explains the role of digestive enzymes in the digestion of food. Respiratory system is divided into two types as Aerobic respiration and anaerobic respiration. Aerobic respiration occurs in the presence of oxygen and by-products carbon dioxide, water and energy whereas Anaerobic respiration occurs in the absence of the oxygen and by products are ethanol and carbon dioxide.

Excretory system in animals is the taken place by the functions of nephron which is responsible for purification of blood and urine formation. Just like the life processes in animals, life process in plants is covered under this chapter. Topics such as Transportation of water and minerals, mechanism of Photosynthesis, Respiration during day and night, Excretion in plants, nutrition in plants and so on.

Control and coordination in animals and plants:

When humans step out in the bright sunlight, they partly close their eyes due to the excessive brightness of sunlight. In addition to this, they may start sweating as the temperature rises. These are called as the coordinated responses to stimuli. This not only occurs in humans but also in plants and animals.

Reproduction:

This chapter covers the reproduction process in both plants and animals. It covers many concepts like budding, fragmentation, spore formation and sexual reproduction in humans and plants.

Heredity and Evolution:

This chapter deals with the relationship between our physical appearance and resemblance to our family members. Evolution can be defined as change in the characteristics of living organisms over generations.

Examples:

1. Name the excretory unit of the kidney?

1. Explain the process of Photosynthesis in plants:

Answer: Photosynthesis is a process in which plants use sun light, chlorophyll, carbon dioxide and water to synthesize food.

1. Why does a plant cool the atmosphere? What is that term called as?

• Effects of Current:

This chapter covers the basic topics under “Electricity” such as Ohm’s law, Resistance, Resistivity, Parallel combination of resistors and applications in daily life, electric power, heating effects of the current and its everyday applications, magnetic effects of electric current, etc. The region around the magnet where its influence or attraction is felt is called as the magnetic field of the magnet.

Examples:

1. Define the unit of the current?

Answer: SI unit of the electric current is Ampere

1. List any one property of the magnetic lines of force?

Answer: No two magnetic field lines intersect each other

• Natural Phenomena:

This covers the topics such as reflection of the light by the curved surfaces, mirror formula, concave mirror, convex mirror, reflection and refraction, focal length, principal focus, laws of refraction, etc. Reflection means change in the path of the wave when the bounce-off a barrier. Refraction of the waves means change in the direction of waves when they pass from one medium to another.

Examples:

1. The radius of the curvature of the spherical mirror is 20 cm. What is its focal length?

1. Name the mirror which can give you an erect and enlarged image of an object?

• Natural Resources:

In First Term it covers the topic such as Sources of energy and in the second Term it covers the topics such as regional environment, our environment and management of natural resources.

Sources of energy:

This chapter is based on the concept that “Energy can neither be created nor be destroyed but can be converted to one form to another”.

Management of natural resources:

This covers the topics such as how to conserve and manage the natural resources such as Forest, wildlife, water and mineral. It explains about three R’s such as Reduce, Recycle and Reuse.

Our environment:

It is a study of living things, non-living things, ecosystem, loss of energy in the environment and large number of environmental problems. An ecosystem is a study of interaction between living and non living organisms. Environmental problems arise due to non-biodegradable waste generated by the humans such as plastics, detergent, dyes which get settled into the soil and water bodies and harm our environment.

Examples:

1. What is a good fuel?

Answer: A good fuel is that which releases more heat during burning but do not cause any environmental problems.

1. What are the qualities necessary for a good source of energy?

• It should be easily available
• It should be easy to store and transport
• In should not cause any environmental problems
• It should be economical
• It should have high calorific value
1. In what way does a biodegradable substance effect the environment?

Answer: It gives foul smell, thus causing air pollution

Thus, above are the topics which are covered under the syllabus of CBSE Class 10 Science.

## 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.