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CBSE Class 1 Mathematics Syllabus

CBSE Class I Mathematics:

CBSE Class 1:

             CBSE Class 1 students have various subjects like Mathematics, Science, English, Computer and Hindi. Among this, let us check the details about the CBSE Mathematics below:

 

Chapters covered in CBSE Class I Mathematics:

                         Math is a very important subject to trigger the brain right from the childhood. Students get familiar with this subject right from their younger age through counting and number systems. Keeping this in mind, CBSE board has developed suitable Mathematics syllabus for every Classes. Through CBSE Class I Math, students get adapted to a sequential system of learning math which can make them to learn it comfortable. With few small examples and simple exercises, CBSE trains even the small kid to brilliantly solve the mathematical questions.

Thus, let us check the chapters covered in the CBSE Class 1 Mathematics here:

  • Shapes and Spaces:

     Students are trained to find out various shapes and sizes. In addition to this, they are trained to know the special relations such as Top, bottom, under, above, near, far, before, etc.

Example:

               Shapes like Hexagon, square, pentagon, cube, oval and various other shapes are trained through real time objects.

Exercises for this chapter:

  1. Students have to collect different objects from the surroundings such as stones, pebbles, cones, pipes and name their shapes in their notes.
  2. They are taught to observe the effects caused due to rolling and sliding of the shaped objects.
  3. Sorts and finds out the 2D objects which are made out of card board.

 

  • Number system:

     Developing the knowledge in counting and numbering systems. They are taught to count from one to hundred at this stage.

Exercises for this chapter:

  1. Counts the number of toys, dolls which are in their surroundings.
  2. Recognizes and speaks numbers from 1 to 9.
  3. Forms number sequence from 10 to 20.
  4. Knows the difference between group of tens and ones in numbering system.
  5. Writes the numerals from 11 to 19. Also, spells the numerals.

 

  • Addition and Subtraction:

             Addition and Subtraction is rather an important part in mathematics. Students are taught to add and subtract using the real objects and pictures. Learns to add and subtract the numbers upto 20. Knows the importance of Zero in addition and subtraction.

      For example:

       5+5=10

       5-5=0

 

  • Telling time:
  1. Knows the importance of time. Learns to check the events occurring earlier and later.
  2. Introduction to time. Difference between morning, afternoon, day and night.
  3. Reading the clock.
  4. Understanding which activities takes longer time.
  5. Difference between analog and digital clocks.
  6. Sequencing student activities according to the time occurrence.

Examples:

  1. The time now is 8 o’ Clock.
  2. 1 minute is equal to 60 seconds.
  3. 60 minutes is one hour.

 

  • Days, weeks, months patterns:

               Students are taught the basic things in Days, months and week patterns.

Exercises:

  1. Students are taught that there are 12 months in a year, 4 weeks in a month and each week has 7 days.
  2. Learn the names of the months and days.
  3. Exercises given to identify the month and day.

               Example:

  1. The day after Sunday is Monday.
  2. Number of days in the month of January is 31.

 

  • Money:

           Students are trained to identify common currencies and notes. Learns the importance of currency and different values of Indian currencies. Adds and subtracts few sums of money.

Example:

  1. Father has a balance of 10 rupees after he purchased shampoo for Rs.10 from the total money Rs.20.

20-10=10

 

  • Measurement:
  1. Differentiates between near, far, thick, thin, longer, shorter, high and low.
  2. Exercises are given to find out the longer and shorter distance, higher and lower prices, thicker and thinner persons, etc.

                Example:

  1. Meera is shorter than Latha with pictures.
  2. Milk is costlier than egg with pictures and numbers.

 

  • Data handling:
  1. Counting letters in a name.
  2. Grouping names with the same number of letters
  3. Counting and recognizing shapes, etc.,

                   Example:

  1. Total number of letters in “welcome” is 7.
  2. Sample of 4 letter words are “Good”, “Best”, “Baby”, etc.,
  3. There are 3 squares and 2 ovals in this picture.

These are the topics which are covered for the Class 1 CBSE students.

 

CBSE Class 3 Mathematics Syllabus

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

        Answer:

  • 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
  • =

               Answer: <

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

                 Answer: X

 

  • Addition and Subtraction:

                 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:

  1. Answer the following:
  • 8789 + 5674 = ?
  • 567 + 4563 = ?

    Answer:

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

    Answer:

  • 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?

Answer: 100

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

Answer: 2000

 

  • 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”?

Answer:

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?

Answer:

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

Answer: 360 Paise

  1. 35 is equal to ______ paise

Answer: 575 Paise

  1. 675 paise is equal to _____ rupees

Answer: Rs.11.25

 

  • 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?

Answer: 2 rounds

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

Answer: 5 minutes

 

  • 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
  • Height of your father
  • Distance from home to office

         Answers:

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

             Answers:

  • 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

Answer: 18000

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

Answer: 3000 grams

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

Answer: 141m 69 cm

 

  • 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

Reading: 9

     Questions:

  1. Which is the most popular hobby?

Answer: Craft

  1. Which is the least popular hobby?

Answer: Music

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

Answer: 2

 

  • 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

               Answer:

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

                 Answer:

  • 98,198,298,398,498

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

CBSE Class 2 Mathematics Syllabus

CBSE Class 2 Mathematics:

                     Just like CBSE Class 1 Subjects, Class 2 includes subjects such as Mathematics, English, Hindi and others. In Class 1, students are taught some basic topics in all the above subjects whereas in Class 2, subjects are going to get little deeper than Class 1.

                    Among all the subjects like Mathematics, English, Science and Hindi let’s get a deeper look into “Mathematics” and its syllabus for CBSE Class 2 students.

 

Syllabus for CBSE Class 2 Mathematics:

  • Numbers:

                Understanding the sequence of numbers, names of the number and grouping the numbers. The topics which are covered under the “Number system” are:

  • Introduction to counting the numbers in groups
  • Looking and guessing the numbers
  • Formation of things in group
  • Concept of Greater than(>) and Lesser than(<) symbols
  • Order of numbers
  • Names of the numbers (up to 9999)
  • Formation of ascending/descending order of numbers.
  • Learning about odd and even numbers
  • Comparing numbers (After/before/in between)

 

      Examples:

  1. Write the below numbers in words:
  • 33
  • 406
  • 345

     Answers:

  • Thirty Three
  • Four hundred and Six
  • Three hundred forty five
  1. Circle the numbers that are more than 234:
  • 235
  • 233
  • 222

     Answers:

  • 235
  1. Arrange the following numbers in ascending and descending order:
  • 45,78,13,9,5,64,79,109 (in ascending order)
  • 67,87,34,12,09,7,1,45 (In descending order)

     Answers:

  • 5,9,13,45,64,78,79,109
  • 87,67,45,34,12,09,7,1
  1. Write the numerals for the following number names:
  • Forty six
  • Sixty seven
  • Thirty two

    Answers:

  • 44
  • 67
  • 32
  1. Fill in the blanks:
  • 50 + 20 + 6= _ + 20 + 50
  • 12 + 13 + 4 = 13 + _ + 12
  • 7 + 5 + 7 = 7 + 7 + _

    Answers:

  • 50 + 20 +6= 6 +20 +50
  • 12 + 13 + 4= 13 + 4 +12
  • 7 + 5 +7= 7 + 7 + 5

 

  • Place value:

                Students have to know the importance of the place values in the numbering system and they should be able to identify whether the place value is “Ones”, “Tens” or “Hundreds”.

For example, in a two digit number, the position of each digit gives its values. In 25, it has 2 tens and 5 ones.

Examples:

  1. Write the place value for the following numbers:
  • 235
  • 789
  • 603

            Answers:

  • 2 is in hundreds place
  • 8 is in tens place
  • 3 is in ones place
  1. Compete the following:
  • 5 tens + 2 ones
  • 4 tens + 4 ones
  • 5 hundreds + 3 tens + 2 ones

            Answers:

  • 52
  • 44
  • 532

 

  • Skip counting:

       Skip counting means finding the next number in the series. For example, in the series of 10, 20, 30…the next number which comes is “40” and “50” respectively.

Examples:

  1. Fill up the blanks with skip counting:
  • 5,15,20…..50?

                 Answers:

  • 5, 15, 20, 25, 30,35,40,45, 50.
  1. Fill up the following series:
  • 2, 12, 22,…?

                       Answers:

  • 2, 12,22, 32,42,52

 

  • Addition and Subtraction:

                 In CBSE Class 1, students would have learnt only basics in addition and subtraction. But in Class 2, students are taught to solve word problems in addition and subtraction. In Class 2, students learn to add or subtract a number using zero, observes commutative property of addition through patterns, solves problems described through pictures and verbal description. Other topics covered are Addition with carry over, adding 4 digit numbers, adding two digit numbers, addition word problems, etc.,

Examples:

  1. 10 -10=0
  2. 9-2=7
  3. 435+100=535

 

  • Multiplication and Division:

         The topics which are covered here are multiplication without carry, multiplication tables of 2,3,4,5,6, etc., skip counting to multiply and simple division.

Examples:

  1. Fill up the following:
  • 5 * 10 = _
  • 4 * 3= _
  • 3 * 9 =_

     Answers:

  • 50
  • 12
  • 27
  1. 450 * 10 = 4510
  2. 16 % 4 =4
  3. 25 % 5=5

 

  • Money:

           Learns to identify important currencies, coins, etc., Adds and subtracts money through mental arithmetic.

Examples:

  1. Write the amount in words:
  • 50 = Seventy six rupee and 50 paisa
  1. Write the amount in figures:

Five hundred and sixty six rupees and 10 paisa = Rs.566.10

 

  • Time and date, calendar:

            Students are taught basic things about year, month, days. They should have a clear understanding that 12 months are in a year, 7 days form a week and 4 week for every month, etc.,

Examples:

  1. Differentiate the months and days below:
  • January
  • Monday
  • Tuesday

        Answer:

  • January is the name of the month
  • Monday is the name of the day
  • Tuesday is also the name of the day
  1. The longer hand of the clock is called as Minute hand.
  2. A leap year has 366 days.
  3. Which month comes before March? February
  4. Which is the first month of the year? January

 

  • Basic shapes, symmetry in everyday life:

  Learns to identify 3-d shapes of rectangle, triangle, cuboid, cylinder, cone and sphere.

Examples:

  1. A closed figure with four equal sides is said to be a Cube
  2. A bangle is in the shape of

 

  • Lines:

           Learns to identify the differences of vertical, horizontal and straight lines.

Examples:

  1. Please identify the number of vertical lines in the given picture.

 

  • Word problems based on Addition and Subtraction:

Along with solving small problems in addition and subtraction, students are trained to solve word problems in addition and subtraction areas.

Examples:

  1. Latha has 25 apple sweets and 15 orange sweets. Totally how many sweets does she have?

        Answer:  40

  1. Seetha has 20 stamps out which she gave 5 stamps to rama. Now, how many stamps does seetha have?

          Answer:  15

 

  • Measurement of Mass, Length, capacity:

     Learns to measure the lengths in units, measure the mass in terms of internal volume, and compares one or more objects with their weights.

Measurement of Mass:

          Using the formulas of simple balance calculates the weight of given objects. Also differentiates between heavier and lighter objects.

Measurement of Length:

          Using simple units to measure length, calculates an objects Length.

Measurement of Weights:

         Calculates volume of the containers using simple formulas of calculating volume.

Examples:

  1. Length of the boundary of the wall is measured in
  • m
  • Kg
  • l

           Answers:  M (Meter)

  1. A teaspoon of medicine is measured in
  • l
  • ml
  • cm

             Answer:   ml (milli litre)

  1. Your weight is measured in
  • g
  • kg
  • l

            Answer:  Kg (Kilo gram)

Thus, above are the syllabus covered under the CBSE Class 2 Mathematics.

 

 

CBSE Class 10 Mathematics Syllabus

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

         Answer: The mode is 120

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

Answer: 17

  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.

Quadratic Equations:

           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).

Answer: a

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

Answer: Three points

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

Answer: Infinitely many

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

Answer: Straight line

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

Answer: 13,14

 

  • 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_______

Answer: 4 : 5

  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.

Answer: -168

  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 ______

           Answer: 0

  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?

           Answer: 25 m

 

  • 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_____

Answer: 1

 

  • 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)?

Answer: √2 c

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

Answer: (0,-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.

Answer: 11cm/min

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

Answer: 76 cm

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

 

 

CBSE Class 9 Mathematics Syllabus

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 = ___

Answer: ½

  1. √8 is equal to _______

Answer: 2√2

  1. 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:

  1. The edges of a plane surface:

Answer: Line

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

Answer: 6 Lines

  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.

Answer: 70 degree

  1. 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:

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

Answer: -Ve y-axis

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

Answer: 3 Units

  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

Answer: 36√3 sq cm

  1. 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

  1. 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:

  1. The degree of a constant function is ______

Answer: 0

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

Answer: 2xyz

  1. 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:

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

Answer: 43

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

Answer: 10

  1. 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:

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

Answer: 0

  1. 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

  1. 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.

CBSE Class 8 Mathematics Syllabus

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 XY where x is a number and y is the power or exponent.

For example, 24 = 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:

  1. Find the multiplicative inverse of 25?

Answer: 1/25

  1. What will be the number of zeroes in the square of 5000?

Answer: 6

  1. Find the square of 39?

Answer: 1521

  1. Find the cube root of 175616.

Answer: 56

  1. 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:

  1. Solve -36y3 % 9y2 = __

Answer: -4y

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

Answer: ab

  1. 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:

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

Answer: 12:1

  1. ________ means comparing two quantities.

Answer: Ratio

  1. Write the expression using the exponents: 25 * 25* 25

Answer: 253

  1. 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

  1. 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:

  1. A two dimensional shape is a ______ shape.

Answer: Plane

  1. How many edges are there in a triangular pyramid?

Answer: 6

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

Answer: Quadrilateral

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

Answer: Square

  1. 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:

  1. Find the side of a cube whose surface area is 2400 cm2.

Answer:20 cm

  1. 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:

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

Answer: X-axis

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

Answer: IV

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

CBSE Class 7 Mathematics Syllabus

CBSE Class 7 Mathematics:

               The syllabus of CBSE Class 7 Mathematics is an upper primary syllabus for developing the mathematical understanding and interest among the growing children.

The topics which are covered in the CBSE Class 7 are mostly similar to that of class 6. Few of the new topics that are added new in class 7 are Exponents and powers, Congruence of triangle, Triangle and its properties, etc.,

So, let’s check the syllabus of CBSE Class 7 Mathematics below:

 

  • Numbers:

        Just similar to all the previous classes of CBSE, Numbers is the first and foremost chapter in the syllabus of CBSE Class 7 Mathematics. Since this is a upper primary syllabus, Number chapter includes various topics such as

  • Integers
  • Fractions and rational numbers
  • Exponents and powers

      Integers:

                           Integers are the special group of numbers which consists of set of positive and negative    

       whole numbers and do not contain any fractional or decimal part. The syllabus which are covered

       under the topic of “integer” are,

  • Multiplication and Division with integers
  • Addition and subtraction with integers
  • Word problems on integers
  • Properties of integers

       Properties such as Closure property, Commutative, Associative, Distributive are very important properties in the syllabus.

       Examples:

  1. In an exam, positive mark is given for every right answer and negative marks are every wrong answer. If sekar scores 23, 4, -7,-4, 10 in five successive rounds, what is his total at the end?

Answer: 26

  1. When two positive integers are added, we get result in _______

Answer: Positive

Fractions and Rational numbers:

                Fractions can be explained as “number of parts in a whole”. This is represented with a slash. The number above the slash is called as a numerator and the number which is below the slash is called as denominator. Any number which can be represented in a fractional form is called as Rational number. This is represented with “:”. The numerator and denominator are whole numbers in a fraction for a rational number. This includes topics such as multiplication of fraction, fraction as an operator, reciprocal of a fraction, division of a fraction, word problems on mixed fractions and decimal fractions, etc.,

 Examples:

  1. 2 * 1/7 = ___

Answer: 2/7

  1. 3/7*4/11 = ___

Answer: 12/77

  1. Is 1.5 a rational number?

Answer: Yes

Exponents and Powers:

                   Exponent is number of times a number multiplied by itself. This covers different laws of Exponents such as First law, second law up to fifth law. The topics which are covered under this are expressing the number in exponential form, laws of exponent, standard forms of exponent, solving the exponential expressions, expressing decimal number system in exponential form using power of 10, etc.,

Examples:

  1. Simplify the following: (220 % 215) * 25 = _____

Answer: 256

  1. The usual form of 1.001 * 109 = ___

Answer: 1001000000

 

  • Algebra:

         As we already know, introduction to Algebra is given in the previous class 6 and thus this is a continuation of advanced concepts of Algebra. Algebra is a branch of Mathematics which deals with the symbol and rules for manipulating those symbols. The topics which are covered under this chapter are Generating algebraic expressions involving one or two variables, identifying constants, coefficients and powers, addition and subtraction of algebraic expression, simple linear equations in one variable, etc.,

Examples:

  1. Subtract the following:

         3a-b+4 – a –b

Answer: 2a +4

  1. Terms which have same algebraic factors are called as ______

Answer: Like terms

  1. The sum or difference of two like terms is called as ______

Answer: Like term

 

  • Geometry:

   This covers vast topics in Geometry like Lines and Angles, Triangle and its properties, Congruence of Triangle, practical geometry and finding out the perimeter and area.

Lines and Angles:

       A line is a single dimensional object which does not have end point. When two lines meet at a point they form an angle. The point at which the angles are formed is called as vertex. There are different types of angles such as acute angles, adjacent angles, interior angles, exterior angles and so on.

Triangle and its properties:

               Triangle is one of the geometrical shapes which is a polygon with three sides, 3 vertices or 3 corners. There are different types of Triangles such as equilateral triangle, isosceles triangle, scalene triangle and so on. Similarly, each triangle has its own properties such as Angle sum Property of a triangle, Triangle inequality Property and so on. The topics which are covered under this topic are Medians and Altitudes of the Triangles, Exterior angle of a triangle and its properties, Right angled triangle and Pythagoras theorem, sum of the lengths of two sides of a triangle, etc.,

Congruence of a Triangle:

               Two triangles are said to be congruent if their respective angles and sides are equal. This topic covers rules of the congruency of triangles, axioms and so on. The topics which are covered under this are congruence of line segments, angles and plane figures, criteria for congruence of Triangles such as SSS, SAS, ASA, AAS, RHS.

       Examples:

  1. When two angles are supplementary, each angle is said to be ____ of each other.

Answer: Supplement

  1. _____ has no end points.

Answer: Line

  1. According to the Pythagoras property, in a right angled triangle , a square on the ____ = sum of the squares on the legs.

Answer: Hypotenuse

  1. Determine the angle for the following triangle with the sides 3 cm, 4 cm, 5 cm respectively.

Answer: Right angled.

  1. How many medians does a Triangle have?

Answer: Three

  1. An ____ is formed when line segment or lines meet?

Answer: Angle

  1. If two angles have same measurement, then they are said to be ______ angle.

Answer: Congruent

 

  • Collection and Organization of data:

                Collection of data which are represented graphically to understand the structure and organization of the data. This is because it is easier to understand and interpret when it is pictorially represented. Thus, a collection of data can be represented using different types of graphs such as :

  • Bar graphs
  • Tally graphs
  • Pictographs
  • Pie charts

    Examples:

  1. Any type of graphs or charts is given. Questions are based on the given pie chart or bar graph. Answers are solved according to the pictorial representation of data.

 

  • Mensuration:

                 This covers the topics such as finding the perimeter and area of the given object. Perimeter means total boundary size of an object whereas Area is the total surface covered by an object. Different objects such as circle, rhombus, Trapezium are covered under this topic. Topics such as area of rhombus, parallelogram, trapezium, circle, finding the circumference and area of the circle, area between two rectangles and two concentric circles and so on.

        Examples:

  1. Write ¾ in the form of percentage?

Answer: 75%

  1. One fourth of the perimeter of a square gives _____

Answer: Side of the square

  1. What is the area of the parallelogram _____

Answer: Base * Height

 

  • Comparing quantities:

             This covers the new topics such as Profit and loss, calculating percentage and simple interest, etc., This is rather very important chapter for a growing child to understand and calculate this day to day mathematical problems.

Examples:

  1. The cost price of 20 articles is same as the selling price of x articles. If the profit is 25%, then the value of x is:

Answer: 16

  1. If the selling price is doubled, the profit triples. Find the profit percentage?

Answer: 100%

 

  • 3-Dimentional visualization:

               This topic deals with the objects which have three dimensions such as length, height and depth. Examples of such object are sphere, prism, pyramid, cube and cuboid.

Examples:

  1. Which is the three dimensional figure which has six rectangular faces at right angles to each other?

Answer: Cuboid

  1. A three dimensional figure which is bounded by polygons are called as ______

Answer: Polyhedrons

Thus, these are the topics which are covered under the syllabus of CBSE Class 7 Mathematics.

 

 

CBSE Class 6 Mathematics Syllabus

CBSE Class 6 Mathematics:

              CBSE Class 6 consists of variety of chapters in Mathematics including all the regular topics introduced in the previous classes. In CBSE Class 6, additional topics which are introduced are

  • Algebra
  • 2 Dimensional and 3 Dimensional Geometrical shapes
  • Perimeter and area of an object
  • Integers
  • Mensuration
  • Practical geometry and construction

The syllabus which are covered under the CBSE Class 6 Mathematics are follows:

 

  • Numbers:

           There are many sub topics covered under the chapter “Numbers”. Topics such as Knowing our numbers, playing with numbers, whole numbers, negative numbers and integers, fractions, etc.,

Knowing our numbers:

            It covers the topics such as comparison of numbers using <.>,+ symbols, ascending and descending order of numbers, calculations of large numbers up to 8 digits, place value of a number, etc.,

Even or odd numbers:

            Integers which are divisible by 2 are said to be even numbers whereas numbers which are not divisible by 2 are said to be odd numbers.

Prime or composite numbers:

             A natural number which has only two distinct factors which is “1” and the number itself, is said to be a prime number. A number other than “1” and not a prime number is said to be a composite number.

Relatively prime or co-prime numbers:

             A set of numbers which do not have any common factor other than “1”, are said to be co-prime numbers or relatively prime number.

Perfect Numbers:

              Perfect numbers are the natural numbers, whose sum of positive divisors (except the number itself) is equal to the number itself.

Playing with numbers:

             It is part of mathematics which is fun to solve. It involves concepts such as even, odd numbers, prime and composite numbers, divisibility rules, multiple and factors, prime factorization, HCF and LCM and simplification of brackets.

Negative numbers and integers:

            Importance of negative numbers, arranging the negative numbers in ascending and descending order, introduction to integers, how to solve the problem with integers, how to solve the problems involving addition and subtraction of integers, etc.,

Whole numbers:

           Whole numbers are a set of positive integers. They do not have any fractional or decimal part. Natural numbers along with zero are whole numbers. This topic covers the concepts such as natural numbers, whole numbers, properties of numbers such as commutative, associative, distributive, multiplicative identity, additive identity), solving problems involving whole numbers, knowing the difference between whole numbers and natural numbers, etc.,

Fractions:

           Fractions and decimals are the most important chapters in “Numbers”. Fractions are the representation of a number with “/” whereas decimal is the representation of a number with “.”(Decimal point).

Examples:

  1. 783422 _____ 783426
  • =
  • None

             Answer: <

  1. What is the predecessor of 3456?
  • 3455
  • 3478
  • 3422
  • 3498

             Answer: 3455

  1. If the product of two whole numbers is zero, then ________ of them will be zero.

Answer: one

  1. _____ is the factor of 50
  • 10
  • 3
  • 7
  • 6

           Answer: 10

  1. Fourth multiple of 8 is ___
  • 16
  • 24
  • 32
  • 40

           Answer: 32

 

  • Introduction to Algebra:

       Algebra is an important branch of Mathematics which is introduced right from the CBSE Class 6th level. Algebra can be defined as a part of mathematics which deals with the symbols and rules for manipulating those symbols. The main concept in Algebra is “Equations”. Every equation in algebra describes the relationship between two variables. Any equation has two parts in LHS and RHS with “=” in between. The topics which are covered under this are recognizing the Algebraic expression, expressing an algebraic equation, introduction to different terms of expression, solving algebraic expression, etc.,

Examples:

  1. Find out the expression with numbers only?
  • 2y+5
  • (20%5) -3z
  • 3x+3
  • 3(23-5)+5*2

               Answer: 3(23-5)+5*2

  1. An equation has ____ sides with = sign between LHS and RHS.
  • Two
  • Three
  • Four
  • Six

               Answer: Two

 

  • Ratio and Proportion:

         Ratios are the concepts which are used to compare two values. They make us understand the difference between two numbers. If total number of boys in a class is 5 and total girls in that class is 4, then the ratio of boys in the class can be represented as 5/9. Proportion is a name which is given when two ratios are equal. This can be represented as a:b=c:d. The above topics covers the syllabus such as ratio and proportion of a number, unitary method and word problems based on Ratio and proportion.

Examples:

  1. Meetu weight is 25 kg and her mother’s weight is 75 kg. What is the ratio of weight of meetu to weight of her mother?
  • 1:3
  • 1:2
  • 1:4
  • 3:1

             Answer: 1:3

  1. If two ratios are equal then we say that they are ______

Answer: Proportional

 

  • Geometry:

         This topic covers concepts such as Basic 2 dimensional geometrical ideas, understanding elementary shapes (2 dimensional and 3 dimensional), symmetry and construction of Geometrical objects.

Examples:

  1. How many end points does a ray have?
  • 0
  • 2
  • 3
  • 1

           Answer: 1

  1. The end points of same sides of a polygon are called the _______ vertices.
  • Parallel
  • Same
  • Different
  • Adjacent

             Answer: Adjacent

 

  • Mensuration:

           Already students would have learned about the basic concepts of finding the perimeter, area of a given object in the previous classes.

Perimeter is the total number of boundary size that an object can cover whereas area is the total number of surface that an object covers. The other concepts which are covered under this topic are concept of Area, area of a rectangle and triangle, calculating the perimeter of a rectangle and square.

Examples:

  1. Find the perimeter of a regular octagon with each side measuring 3 cm.
  • 24 cm
  • 20 cm
  • 10 cm
  • 15 cm

             Answer: 24 cm

  1. Find the side of the square whose perimeter is 20 m.
  • 4 m
  • 3 m
  • 6 m
  • 5 m

             Answer: 5 m

 

  • Practical Geometry and construction:

                 This is a branch of Geometry which deals with the construction of geometrical objects. There are specific instruments or tools and specific rules to construct the geometrical objects. The tools such as ruler, compass, protractor can be used to construct every geometrical object.

               The topics which are covered under this are construction of line segment using ruler and compass, construction of circle, construction and measuring angles, construction of perpendicular bisector, how to bisect angles, etc.,

Examples:

  1. Find out the correct type of the triangle which has sides 7 cm, 8 cm and 9 cm.
  • Isosceles triangle
  • Scalene Triangle
  • Equilateral triangle
  • None of these

               Answer: Scalene Triangle

  1. The measure of right angle is ____
  • 60 degree
  • 90 degree
  • 180 degree
  • 30 degree

             Answer: 90 degree

 

  • Statistics and data handling:

         Collection of information is said to be data. These data can be pictorially represented using graphs, charts, bar charts, etc. The reason behind representing the data through pictorial representation is it gives a clear understanding of the data and its organization. Graphs such as pictographs, tally graphs, bar charts and pie charts are used to represent the data.

        The topics which are covered under the “Statistics and Data Handling” are definition of data, construction of pictograph, collection and organizing data using the charts such as bar charts, interpret data using the pictograms and graphs.

Examples:

  1. A _____ represents data through pictures of objects.

Answer: Pictograph

  1. The _______ each bar gives required information.

Answer: Length

 

  • 3 D shapes:

                 This covers the topics such as 3 dimensional shapes and sizes of an object, recognizing different 3d shapes, understanding the concepts of vertices, edges and faces , etc.,

Examples:

  1. A _______ is a polygon with four sides.

Answer: Quadrilateral

  1. Two faces meet at a line segment called as ______

Answer: Edge

Thus, the above topics are covered under the syllabus of CBSE Class 6 Mathematics.

 

 

CBSE Class 5 Mathematics Syllabus

CBSE Class 5 Mathematics:

             Mathematics gets little tougher this time when compared to the previous classes such as CBSE class 3 and class 4. CBSE Class 5 includes many concepts such as Percentage, lines and angles, shapes and their properties, multiples and factors along with the regular topics of previous classes.

The syllabus covered for CBSE Class 5 mathematics are below:

  • Numbers and Arithmetic operations on it:

             Few advanced concepts in “Numbers” topic are covered such as introduction to abacus, handling prime and composite number , knowing the differences between face value and place value of a number, rounding of numbers and number patterns. Word problems on addition, subtraction, multiplication and division are covered under this topic.

Examples:

  1. The smallest odd prime number ________

Answer: 3

  1. All even numbers are divisible by ___

Answer: 2

  1. Round off 5117 to the nearest ten:
  • 5120
  • 5130
  • 5115
  • 5100

Answer: 5120

  1. Build a five digit number from the following:
  • 3+35+0+1000+70000

               Answer: 71,038

  1. Answer the following using BODMAS rule:
  • 75*(4-2)

               Answer: 150

 

  • Multiplication and Division:

                    Advanced word problems in multiplication and division are covered under this syllabus.

Examples:

  1. Alia saves Rs.546 per month. How much does she save in a full year?

Answer: 6,552

  1. There are 675 pages in a book. How many pages are there in 15 books?

Answer: 10,125

  1. How many weeks are there in 205 days?

Answer: 29 weeks 2 days

 

  • LCM and HCF:

     This comes under the topic of “Multiples and factor”. LCM stands for Lowest Common Mutiple and HCF stands for Highest Common factor.

Examples:

  1. What is the HCF for the numbers 20 and 30?

Answer: 10

  1. What is the common multiple for 5 and 7?

Answer: 35

  1. Sunil planted 35 apple and 30 peach trees. If he wants to plant same number and type of plants in a row, what is the maximum number of trees that he can plant in a row?

Answer: 10

  • Fractions and decimals:

                 The concept of fractions consists of two main parts such as numerators and denominators. Numerator is the number which is above the fraction line whereas denominator is the number which is below the fraction line. The concept of decimals can be defined as the numbers which contains the decimal point. The number to the left of decimal point is an ordinary whole number and the number to the right of the decimal point is called as “tenths” digits. For example, 1.5 is same as 1 plus 1/5.

Examples:

  1. Find out the answer for the following:
  • 85*0.25

               Answer: 0.2125

  1. 10/40 is equal to ____

Answer: 0.25

  1. 3 3/4 % 1 2/3 = ?

Answer: 9/4 which is equal to 2 1/4

 

  • Ratio and percentage:

     Ratio shows relative sizes of two or more values. It is represented with the symbol “:”. If there are totally 4 boys and 5 girls in a classroom, then it can be represented though ratio system as: 4:5 which means there are 4 boys out of 9 students (4/9) and 5 girls out of 9 students (5/9). Percentage can be expressed as a value on the basis of rate or proportion per hundred. For example, 36/100 is equal to 0.36 or 36%.

Examples:

  1. Calculate the following ratios:
  • 2:3 = 36 : _
  • 4:6 = 8 : _
  • 8:3 = 24 : _

               Answer: 36: 54

                               8 : 12

                               24 : 9

  1. 72% of 11 is _ of 40% of 97?
  • =

               Answer: <

 

  • Lines and angles:

           A line is a straight path that goes on and in opposite directions. There are different types of lines such as parallel lines and perpendicular lines. Parallel lines are the lines that never intersect or cross each other. Perpendicular lines are the lines which cross each other or intersect at right angles. An Angle is a two lines that meet at an endpoint called a vertex. There are different types of angles such as acute angles, obtuse angles, supplementary angles,etc. Acute angle is an angle which measures less than 90 degrees through the protractor. Obtuse angle is an angle which measures greater than 90 degrees through the protractor. Two angles whose measurement adds up to 180 degrees are supplementary angles.

Examples:

  1. Questions are based on pictorial representation of angles asking students to identify the type of angles.

 

  • Perimeter and area:

       As these concepts are covered in the previous class 4, a little more advanced syllabus are added under this topic. Perimeter is the total boundary size of the object whereas area is the total surface covered by the object.

Examples:

  1. There are 5 cm cubes which are glued together to form a cuboid. Find the volume of the cuboid.

Answer: 192 cubic cm

  1. How much water does a rectangular tank hold with a square base of 2.5 yards and a height of 4 yards hold?

Answer: 10 cube yards

 

  • Shapes and their properties:

                 This is a part of geometry which covers different types of triangles such as Scalene, isosceles, equilateral, acute, right and obtuse triangle.

Examples:

  1. Questions based on classifying triangles and properties related to that.

 

  • Patterns and Symmetry:

             An object which has evenly balanced properties called as symmetrical. A shape is symmetrical when its two halves are mirror images along the line of symmetry. Different types of lessons such as mirror games, turning mirror images by ½ turn, examples and problems, identifying different patterns, etc.

Examples:

  1. Pictorial representation of various figures are given to find out the lines of symmetry of each object.

Along with the above topics, regular topics like Time and date, measurement of length, mass and capacity, smart charts are also covered in the syllabus of CBSE Class 5 Mathematics.