Monday, May 3, 2021

7 MATHEMATICS 2021-2022

 R/12                                                          
 01/10/2021, 04/10/2021, 05/10/2021, 06/10/2021, 07/10/2021, 08/10/2021, 09/10/2021 
LINKS
Click on the chapter’s name to download the chapter's name in PDF form.
TOPIC: Introduction, Ratio, Comparison of Ratios, Equivalent Ratios, Proportion,    Continued Proportion, Mean Proportional, Unitary Method

EXPLAINED
1. Introduction

1.1 Ratio: The ratio of two quantities of the same kind and in the same units is a fraction that shows how many times the one quantity is of the other.

The ratio of two quantities a and b (b ¹ 0) is a ÷ b or a/ b and is denoted by a : b.

In the ratio a : b, the quantities (numbers) a and b are called the terms of the ratio.

The former ‘a’ is called the first term or “antecedent” and the later ‘b’ is known as the second term or “consequent”.

1.2 Ratio in the simplest form: A ratio a : b is said to be in the simplest form if its antecedent ‘a’ and consequent b have no common factor other than 1.

2. Comparison of ratios

3. Equivalent Ratios

Equivalent Ratio: A ratio obtained by multiplying or dividing the numerator and denominator of a given ratio by the same number is called an equivalent ratio.

4. Proportion

Proportion: An equality of two ratios is called a proportion.

4.1 Continued Proportion: Three numbers a, b, c are said to be in continued proportion if a, b, b, c are in Proportion.

4.2 Mean Proportional: If a, b, c are in continued proportion, then b is called the mean proportional between a and c.

5. Unitary Method
and
Value of required number of articles = (Value of one article) x (Required number of articles)

Example:

If 6 bowls cost Rs 96. What will be the cost of 15 such bowls?

Solution: We have,

                Cost of 6 bowls = Rs 96

                 Cost of 1 bowl = Rs 96/6

          Hence, Cost of 15 bowls = Rs (96/6 x 15)

                                                = Rs (16 x 15)

                                                = Rs 240

MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Introduction
2. Ratio
3. Ratio vs Fraction
4. Equivalent Ratios
5. Proportion
6. Unitary Method
MAIN TEACHING
Online oral explanation and some written work

STUDENTS TAKE AWAY
Complete all questions of Exercise 7(A), 7(B), and 7(C) from given link of chapter.


ASSIGNMENT
I. Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.

 R/11                                                          
 24/09/2021, 25/09/2021, 27/09/2021, 28/09/2021, 29/09/2021, 30/09/2021 
LINKS
Click on the chapter’s name to download chapter’s name in PDF form.
REVISION
TOPIC: : Introduction, Types of Angles, Pairs of Angles, Angles formed by a Transversal, Parallel Lines, Angles formed by Parallel lines and Transversals, Construction.

EXPLAINED
1. Introduction (Lines and Angles)
1.1 POINT
1.2 LINE
1.3 LINE SEGMENT
1.4 RAY
2. Types of Angles
2.1 Acute angle: An angle whose measure is more than 0o but less than 90o is called an acute angle.
2.2 Right angle: An angle whose measure is 900 is called a right angle.
2.3 Obtuse angle: An angle whose measure is more than 90o but less than 180o is called an obtuse angle.
2.4 Straight angle: An angle whose measure is 180o is called a straight angle.
2.5 Reflex angle: An angle whose measure is more than 180o but less than 360o is                                 called a reflex angle.
2.6 Complete angle: An angle whose measure is 360o is called a complete angle.
3. Pairs of Angles
  3.1 Adjacent angles: Two angles in a plane are called adjacent angles, if
 (i) they have a common vertex,
 (ii) they have a common arm, and
  (iii) their other arms lie on the opposite sides of the common arm.
3.2 Linear Pair: Two adjacent angles are said to form a linear pair of angles, if their non- common arms are two opposite rays.
3.3 Vertically opposite angles: Two angles formed by two intersecting lines having no common arm are called vertically opposite angles.
3.4 Angles at a point: Angles formed by a number of rays having a common initial point are called angles at a point.

3.5 Complementary angles: If the sum of the measures of two angles is 90o, then the angles are called complementary angles.
3.6 Supplementary angles: Two angles are said to be supplementary angles if the sum of their measures is 180o, and each of them is called a supplement of the other.
4. Parallel Lines: If two lines lie in the same plane and do not intersect when produced on either side then such lines are said to be parallel to each other.
5. Transversal: A straight line which cuts two or more straight lines at distinct points is called a transversal.
6. The angles formed when a transversal cuts two parallel lines
6.1 Interior angles
6.2 Exterior angles
6.3 Pair of Alternate interior angles (Alternate angles)
6.4 Pair of Alternate Exterior angles
6.5 Pair of Corresponding angles
6.6 Pair of interior angles on same side of transversal (Co-interior angles)

7. Construction of a line parallel to a given line through a point not on the line.
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Introduction
2. Lines and Angles
3. Complementary angles and Supplementary angles
4. Adjacent angles
5. Linear Pair
6. Vertically opposite angles
7. Angles made by Transversal
MAIN TEACHING
Online oral explanation and some written work
1. INTRODUCTION (PAIRS OF ANGLES)
2. Types of Angles
3. Pairs of Angles
4. Parallel Lines
5. Perpendicular Lines
6. Angles Formed by a Transversal
STUDENTS TAKE  AWAY
Complete all questions of Exercise 9(A), 9(B), 9(C), 9(D), 9(E), 9(F), 9(G) and 9(H) from given link of chapter.


ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.

 R/10                                                          
 22/09/2021 
REVISION
LINKS
Click on the chapter’s name to download the chapter name in PDF form.
TOPIC: Introduction, Variable, Constant, Algebraic Expressions, Terms, Coefficient, Like and Unlike Terms, Types of Algebraic expressions, Degree of Polynomials, Addition and Subtraction of Algebraic expressions

EXPLAINED
1. Introduction (Algebraic expressions)
2. Variable: A symbol which takes various numerical values is called a variable.
3. Constant: A symbol having a fixed numerical value is called a constant.
4.  Algebraic expressions: A combination of constants and variables connected by the signs of fundamental operations of addition (+), subtraction (-), multiplication (×), and division ( ÷) is called an algebraic expression.

5. Parts of an Algebraic expression
5.1 Terms: Various parts of an algebraic expression which are separated by the signs of   ‘+’ or ‘ ─’ are called the terms of the expression.
5.2 Factors: Each term in an algebraic expression is a product of one or more number(s) and / or literal number(s). These number(s) and / or literal number(s) are known as the factors of that term.
5.3 Coefficient: In a term of an algebraic expression, any of the factors with the signs of  the term is called the coefficient of the product of the other factors.
6. Like Terms: The terms having the same literal factors are called like or similar.
7. Unlike Terms: The terms not having same literal factors are called unlike or dissimilar terms.

8. Types of Algebraic expressions
8.1 Monomials: An algebraic expression containing only one term is called a monomial. Example:-  3, 2x, 5x2y, -6abc, 3ab2c3
8.2 Binomials: An algebraic expression containing two terms is called a binomial. Example:- x +3, 5 – 2x, a2 – 2abc, x3 + 3
8.3 Trinomials: An algebraic expression containing three terms is called a trinomial. Example:-  2x – y + 3, x2 + y2 + z2, 3 + xyz + x3.
8.4 Polynomials: An algebraic expression containing two or more terms is called a polynomial. x +3, 2x – y + 3, 4x3 – x2 + 6x +3, 7y3 + 5y2 – 8y +9.

5. Degree of Polynomials
6. Standard form of  a Polynomials
7. Addition of Algebraic expressions
8. Subtraction of Algebraic expressions
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1.  Introduction (Algebraic expressions)
2. Parts of an Algebraic expression
2.1 TERMS
2.2 FACTORS
3. Like and Unlike Terms
4.  Types of Algebraic expressions
5. Addition of Algebraic expressions
6. Subtraction of Algebraic expressions
MAIN TEACHING
Oral and Explanation Online with some written work.

STUDENTS TAKE  AWAY
Complete all questions of Exercise 5(A), 5(B), and 5(C) from given link of chapter.

ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.

 R/09                                                          
 14/09/2021, 15/09/2021, 21/09/2021 
CONTINUATION OF CHAPTER- 02
LINKS
Click on the chapter’s name to download the chapter in PDF form.
TOPIC: Introduction,  Like and Unlike Decimals, Addition and Subtraction of Decimals, Multiplication of Decimals, Division of Decimals

EXPLAINED
1. Introduction (Decimals)
6. Like and Unlike Decimals: Decimals having the same number of digits on the right of the decimal point are known as like decimals. Otherwise, the decimals are unlike  decimals.

For example, 5.25, 15.04, 273.89 are like decimals and 9.5, 18.235, 20.0254 etc are unlike decimals.

7. Addition and Subtraction of Decimals
~ In order to add or subtract decimals, we may use the following steps:
Step I Convert the given decimals to like decimals.
Step II Write the decimals in columns with their decimal points directly below each other so that tenths come under tenths, hundredths come under hundredths and so on.
Step III Add or subtract as we add or subtract whole numbers.
Step IV Place the decimal point, in the answer, directly below the other decimal points.

For example,  Add: 15.44, 7.524 and 25
Solution: Converting the given decimals to like decimals, we have 15.440, 7.524 and 25.000.
8. Multiplication of Decimals
8.1 Multiplication of a Decimal by 10, 100, 1000 etc.
We follow the following rules to multiply a decimal by 10, 100, 1000 etc.
Rule I On multiplying a decimal by 10, the decimal point is shifted to the right by one place.
Rule II On multiplying a decimal by 100, the decimal point is shifted to the right by two place.
Rule III On multiplying a decimal by 1000, the decimal point is shifted to the right by three place, and so on.

ILLUSTRATION: Find the following products:
(i) 27.05 x 10                 (ii) 429.7 x 100              (iii) 31.09 x 1000
Solution:     We have,
                   (i) 27.05 x 10 = 270.5
                   (ii) 429.7 x 100 = 429.70 x 100 = 42970
                   (iii) 31.09 x 1000 = 31.090 x 1000 = 31090

8.2 Multiplication of a Decimal by a Whole number
~ In order to multiply a decimal by a whole number, we follow the following steps:
Step I Multiply the decimal without the decimal point by the given whole number.
Step II Mark the decimal point in the product to have as many places of decimal as are there in the given decimal.

ILLUSTRATION: Find each of the following products:
(i) 3.25 x 12                   (ii) 0.524 x 15                (iii) 0.0275 x 17
Solution:      We have,
                             (i) 3.25 x 12 = 39.00
                             (ii) 0.524 x 15 = 7.860
                             (iii) 0.0275 x 17 = 0.4675

9. Division of Decimals
9.1 Dividing a decimal by 10, 100, 1000 etc.
~ In order to divide a decimal by 10, 100, 1000 etc., we follow the following rules:
Rule I When a decimal is divided by 10, the decimal point is shifted to the left by one place.
Rule II When a decimal is divided by 100, the decimal point is shifted to the left by two place.
Rule III When a decimal is divided by 1000, the decimal point is shifted to the left by three place.

ILLUSTRATION    Divide:
                   (i) 12.75 by 10     (ii) 127.5 by 100            (iii) 1275.7 by 1000
                   (iv) 0.58 by 10     (v) 3.52 by 100              (v) 6.25 by 1000
Solution:      We have
                   (i) 12.75 ÷ 10 = 12.75/10 = 1.275
                   (ii) 127.5 ÷ 100 = 127.5/100 = 1.275
                   (iii) 1275.7 ÷ 1000 = 1275.7/1000 = 1.2757
                   (iv) 0.58 ÷ 10 = 0.58/10 = 0.058
                   (v)  3.52 ÷ 100 = 3.52/100 = 0.0352
                   (vi) 6.25 ÷ 1000 = 6.25/ 1000 = 0.00625

9.2 Dividing a decimal by a Whole number
~ In order to divide a decimal by a whole number, we follow the following steps:
Step I Check the whole number part of the dividend.
Step II If the whole number part of the dividend is less than the divisor, then place 0 in the ones place in the quotient. Otherwise, go to step III.
Step III Divide the whole number part of the dividend.
Step IV Place the decimal point to the right of ones place in the quotient obtained in Step I.
Step V Divide the decimal part of the dividend by the divisor. If the digits of the dividend are exhausted, then place zeros to the right of dividend and remainder each time and continue the process.

Example:    Divide 93.45 by 15
93.45/ 15 = 6.23
9.3 Dividing a decimal by a decimal
~ In order to divide a decimal by another decimal, we follow the following steps:
Step I Multiple the dividend and divisor by 10, 100, 1000 etc to convert the divisor into a whole number.
Step II Divide the new dividend by the whole number obtained in step I.

MUST WATCH VIDEOS FOR BETTER UNDERSTANDING
7. Decimal Numbers
VIDEO 7
8. Comparing decimal numbers
9. Adding decimal numbers
10. Multiply decimal numbers
11. Divide decimal numbers
MAIN TEACHING
Online oral explanation and some written work

STUDENTS TAKE AWAY
Complete all questions of Exercise  2(G), 2(H), 2(I), 2(J), 2(K), 2(L) and 2(M) from given link of chapter.

ASSIGNMENT
I. Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.

 R/8                                                          
 31/08/2021, 01/09/2021, 03/09/2021, 07/09/2021, 08/09/2021 
LINKS
Click on the chapter’s name to download the chapter in PDF form.
TOPIC: Introduction, Fraction, Proper Fraction, Improper Fraction, Mixed Fraction, Equivalent Fractions, Like Fractions, Unlike Fractions, Addition and Subtraction of Fractions, Multiplication of Fractions, Division of Fractions, Like and Unlike Decimals, Addition and Subtraction of Decimals, Multiplication of Decimals, Division of Decimals

EXPLAINED
1. Introduction (Fractions AND Decimals)
1.1 Fraction: A fraction is a number representing a part of a whole. The whole may be a single object or a group of objects.

2. Types of Fractions
2.1 Proper Fraction: A fraction whose numerator is less than the denominator, is called a proper fraction.

2.2 Improper Fraction: A fraction whose numerator is more than or equal to the denominator, is called an improper fraction.

2.3 Mixed Fraction: A combination of a whole number and a proper fraction is called a mixed fraction.

2.4 Equivalent Fractions: A given fraction and various fractions obtained by multiplying (or dividing) its numerator and denominator by the same non-zero number, are called equivalent fractions.

2.5 Like Fractions: Fractions having the same denominators are called like fractions.

2.6 Unlike Fractions: Fractions with different denominators are called unlike fractions.

2.7 Fraction in lowest terms: A fraction is in its lowest terms if its numerator and denominator have no common factor other than 1.

3. Addition and Subtraction of Fractions
~ In order to add or subtract like fractions, we add or subtract their numerators and retain the common denominator.

For example,
~ In order to add or subtract unlike fractions, we follow the following steps:
Step I:  Obtain the fractions and their denominators.
Step II:  Find the LCM of the denominators.
Step III:  Convert each fraction into an equivalent fraction having its denominator equal to the LCM obtain in step II.
Step IV: Add or Subtract like fractions obtained in Step III.

For example,
Solution: LCM of 10 and 15 is (5 x 2 x 3) = 30
So, we convert the given fractions into equivalent fractions with denominator 30.
4. Multiplication of Fractions
 5. Division of Fractions
~ The division of a fraction a/b by a non- zero fraction c/d is defined as the product of a/b with multiplicative inverse or reciprocal of c/d.
6. Like and Unlike Decimals: Decimals having the same number of digits on the right of the decimal point are known as like decimals. Otherwise, the decimals are unlike decimals.
For example, 5.25, 15.04, 273.89 are like decimals and 9.5, 18.235, 20.0254 etc are unlike decimals.

7. Addition and Subtraction of Decimals
~ In order to add or subtract decimals, we may use the following steps:
Step I Convert the given decimals to like decimals.
Step II Write the decimals in columns with their decimal points directly below  each other so that tenths come under tenths, hundredths come under hundredths and so on.
Step III Add or subtract as we add or subtract whole numbers.
Step IV Place the decimal point, in the answer, directly below the other decimal points.

For example,  Add: 15.44, 7.524 and 25
Solution: Converting the given decimals to like decimals, we have 15.440, 7.524 and 25.000.
8. Multiplication of Decimals
8.1 Multiplication of a Decimal by 10, 100, 1000 etc.
We follow the following rules to multiply a decimal by 10, 100, 1000 etc.
Rule I On multiplying a decimal by 10, the decimal point is shifted to the right  by one place.
Rule II On multiplying a decimal by 100, the decimal point is shifted to the right by two place.
Rule III On multiplying a decimal by 1000, the decimal point is shifted to the right by three place, and so on.

ILLUSTRATION: Find the following products:
(i) 27.05 x 10                 (ii) 429.7 x 100              (iii) 31.09 x 1000
Solution:     We have,
(i) 27.05 x 10 = 270.5
(ii) 429.7 x 100 = 429.70 x 100 = 42970
(iii) 31.09 x 1000 = 31.090 x 1000 = 31090

8.2 Multiplication of a Decimal by a Whole number
~ In order to multiply a decimal by a whole number, we follow the following steps:
Step I Multiply the decimal without the decimal point by the given whole number.
Step II Mark the decimal point in the product to have as many places of decimal as are there in the given decimal.

ILLUSTRATION: Find each of the following products:
(i) 3.25 x 12                   (ii) 0.524 x 15                (iii) 0.0275 x 17
Solution:      We have,
(i) 3.25 x 12 = 39.00
(ii) 0.524 x 15 = 7.860
(iii) 0.0275 x 17 = 0.4675

9. Division of Decimals
9.1 Dividing a decimal by 10, 100, 1000 etc.
~ In order to divide a decimal by 10, 100, 1000 etc., we follow the following rules:
Rule I When a decimal is divided by 10, the decimal point is shifted to the left by one place.
Rule II When a decimal is divided by 100, the decimal point is shifted to the left by two place.
Rule III When a decimal is divided by 1000, the decimal point is shifted to the left by three place.

ILLUSTRATION    Divide:
(i) 12.75 by 10     (ii) 127.5 by 100            (iii) 1275.7 by 1000
(iv) 0.58 by 10     (v) 3.52 by 100              (v) 6.25 by 1000
Solution:      We have
(i) 12.75 ÷ 10 = 12.75/10 = 1.275
(ii) 127.5 ÷ 100 = 127.5/100 = 1.275
(iii) 1275.7 ÷ 1000 = 1275.7/1000 = 1.2757
(iv) 0.58 ÷ 10 = 0.58/10 = 0.058
(v)  3.52 ÷ 100 = 3.52/100 = 0.0352
(vi) 6.25 ÷ 1000 = 6.25/ 1000 = 0.00625

9.2 Dividing a decimal by a Whole number
~ In order to divide a decimal by a whole number, we follow the following steps:
Step I Check the whole number part of the dividend.
Step II If the whole number part of the dividend is less than the divisor, then place 0 in the ones place in the quotient. Otherwise, go to step III.
Step III Divide the whole number part of the dividend.
Step IV Place the decimal point to the right of ones place in the quotient obtained in Step I.
Step V Divide the decimal part of the dividend by the divisor. If the digits of the dividend are exhausted, then place zeros to the right of dividend and remainder each time and continue the process.

Example:    Divide 93.45 by 15
          93.45/ 15 = 6.23
9.3 Dividing a decimal by a decimal
~ In order to divide a decimal by another decimal, we follow the following steps:
Step I Multiple the dividend and divisor by 10, 100, 1000 etc to convert the divisor into a whole number.
Step II Divide the new dividend by the whole number obtained in step I.
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Introduction
2. Types of Fractions
3. Addition of Fractions
4. Multiplication of Fractions
5. Reducing to fractions to lowest form
6. Division of Fractions
7. Decimal Numbers
8. Comparing decimal numbers
9. Adding decimal numbers
10. Multiply decimal numbers
11. Divide decimal numbers
MAIN TEACHING
Online oral explanation and some written work

STUDENTS TAKE AWAY
Complete all questions of Exercise 2(A), 2(B), 2(C), 2(D), 2(E), 2(F), 2(G), 2(H), 2(I), 2(J), 2(K), 2(L), 2(M) from given link of chapter.

ASSIGNMENT
I.Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.

 R/7                                                          
 24/08/2021, 25/08/2021, 27/08/2021 
CONTINUATION OF CHAPTER- 14
LINKS
Click on the chapter’s name to download the chapter in PDF form.
TOPIC:  Circumference of a Circle, Area of a Circle
5. Introduction (Circle)
6. Terms Related to a Circle
6.1 Radius
6.2 Diameter
6.3 Chord
6.4  Circumference
6.5 Concentric Circles
6.6 Semicircle
7. Formulae for Circumference of a Circle
8.  Area of a Circle
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Circumference of a Circle
2. Area of a Circle
MAIN TEACHING
Online oral explanation and some written work

STUDENTS TAKE AWAY
Complete all questions of Exercise  14(E) and 14(F) from given link of chapter.


ASSIGNMENT
I. Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.
II. Choose the correct alternative in each of the following:
1. Find the area of a circle having radius 14 cm.
(a) 196cm2            (b) 308cm2            (c) 616cm2            (d) None of these

2. Find the breadth of a rectangular plot of land, if its area is 440m2 and the length is 22m.
(a) 20m                 (b) 5m                  (c) 15m                     (d) 10m

3. One of the sides and the corresponding height of a parallelogram are 4cm and 3cm respectively. Find the area of the parallelogram.
(a) 12cm2              (b) 7cm2                (c) 6cm2                    (d) None of these

4. Find the area of a verandah 2.25m wide constructed outside a room 5.5m long and 4m wide.
(a) 36sq.m              (b) 63sq.m                (c) 64sq.m                 (d) 84sq.m

5. When the circumference and area of a circle are numerically equal, what is the diameter numerically equal to?
(a) Area                (b) Circumference          (c) 271                  (d) 4

6. A gardener wants to fence a circular garden of diameter 14m. Find the length of the rope he needs to purchase.
(a) 44m                 (b) 28m                            (c) 88m                (d) None of these

7. If the area of a circle is 2464m2, find its diameter.
(a) 56m                 (b) 154m                          (c) 176m               (d) 206m

8. What is the circumference of a circle of radius 7cm?
(a) 44cm               (b) 49cm                           (c) 14cm               (d) None of these

9. Ayush made his picture on a rectangular sheet of length 60cm and breadth 20cm wide. Area of picture is:
(a) 1200cm2                   (b) 1250cm2             (c) 1100cm2        (d) None of these

10. If a side of a square is 4cm then its perimeter is:
(a) 16cm               (b) 8cm                 (c) 12cm               (d) None of these

11. The area of triangle is
(a) (½) x base x height                       (b) (½) x (base + height)         
(c) Base x height                                (d) None of these

12. Find radius of a circle of diameter 9.8m.
(a) 4.9m                (b) 19.6m             (c) 10m                 (d) None of these

13. What is the circumference of a circle of diameter 10cm?
(a) 35cm               (b) 30cm               (c) 31.4cm            (d) None of these

14. Find the perimeter of a triangle with sides 4cm, 6cm and 10cm.
(a) 20cm               (b) 24cm               (c) 9cm                 (d) 18cm

15. The area of a rectangular sheet is 500cm2. If the length of the sheet is 25cm. What is its width?
(a) 20cm               (b) 25cm               (c) 50cm               (d) None of these

16. Find the area of a square park whose perimeter is 320cm?
(a) 6400m2           (b) 6000m2           (c) 1280m2            (d) None of these

17. The area of parallelogram is
(a) height x height          (b) base x height   (c) base + height   (d) base x base

18. If a side of a square is 5cm then its area is:
(a) 20cm2              (b) 25cm2              (c) 10cm2              (d) None of these

19. Find the area of a triangle with a base of 20cm and a height of 30cm.
(a) 300cm2            (b) 100cm2            (c) 400cm2            (d) 600cm2

20. Find the height x, if the area of the parallelogram is 24cm2 and the base is 4cm.
(a) 4cm                 (b) 6cm                 (c) 5cm                 (d) None of these

 R/6                                                          
 10/08/2021, 11/08/2021
 CONTINUATION OF CHAPTER- 14 
LINKS
Click on the chapter’s name to download the chapter in PDF form.
CH:- 14 Perimeter and Area
TOPIC: Area of a Triangle, Circumference of a Circle, Area of a Circle

EXPLAINED
4.4 The Area of a Triangle
5. Introduction (Circle)
6. Terms Related to a Circle
6.1 Radius
6.2 Diameter
6.3 Chord
6.4  Circumference
6.5 Concentric Circles
6.6 Semicircle
7. Formulae for Circumference of a Circle
8.  Area of a Circle
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Area of a Triangle
2. Circumference of a Circle
3. Area of a Circle
MAIN TEACHING
Online oral explanation and some written work

STUDENTS TAKE AWAY
Complete all questions of Exercise  14(D), 14(E) and 14(F) from given link of chapter.

ASSIGNMENT
I. Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.

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 27/07/2021, 28/07/2021, 30/07/2021, 03/08/2021, 04/08/2021, 06/08/2021 
LINKS
Click on the chapter’s name to download the chapter in PDF form.
CH:- 14 Perimeter and Area
TOPIC: Introduction, Perimeter and area, Perimeter and Area of a Square, Perimeter and Area of a Rectangle, Area of Parallelogram, Area of a Triangle, Circumference of a Circle, Area of a Circle, Unit’s Conversion.

EXPLAINED
1. Introduction (Perimeter and Area)
2. Perimeter Formulae
2.1 The Perimeter of a Square
2.2 The Perimeter of a Rectangle
2.3 The Perimeter of a Parallelogram
2.4 The Perimeter of a Triangle
3. Unit’s Conversions
4. Area Formulae
4.1 The Area of a Square
4.2 The Area of a Rectangle
4.3 The Area of a Parallelogram
4.4 The Area of a Triangle
5. Introduction (Circle)
6. Terms Related to a Circle
6.1 Radius
6.2 Diameter
6.3 Chord
6.4  Circumference
6.5 Concentric Circles
6.6 Semicircle
7. Formulae for Circumference of a Circle
8. Area of a Circle
MUST WATCH THE VIDEOS FOR BETTER UNDERSTANDING
1. Introduction (Perimeter and Area)
2. Perimeter and Area of a Square
3. Perimeter and Area of a Rectangle
4. Area of Parallelogram
5. Area of a Triangle
6. Circumference of a Circle
7. Area of a Circle
8. Unit’s Conversion
MAIN TEACHING
Online oral explanation and some written work
1. Introduction (Perimeter and Area)
2. Perimeter, Circumference and Area Formulas
3. What is a Circle?
STUDENTS TAKE AWAY
Complete all questions of Exercise 14(A), 14(B), 14(C), 14(D), 14(E) and 14(F) from the given link of the chapter below.


 ASSIGNMENT
I. Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.
II. Choose the correct alternative in each of the following:
1. Find the area of a circle having radius 14 cm.
(a) 196cm2            (b) 308cm2            (c) 616cm2            (d) None of these
2. Find the breadth of a rectangular plot of land, if its area is 440m2 and the length is 22m.
(a) 20m                 (b) 5m                   (c) 15m                  (d) 10m
3. One of the sides and the corresponding height of a parallelogram are 4cm and 3cm respectively. Find the area of the parallelogram.
(a) 12cm2             (b) 7cm2                (c) 6cm2                (d) None of these
4. Find the area of a verandah 2.25m wide constructed outside a room 5.5m long and 4m wide.
(a) 36sq.m           (b) 63sq.m             (c) 64sq.m             (d) 84sq.m
5. When the circumference and area of a circle are numerically equal, what is the diameter numerically equal to?
(a) Area               (b) Circumference          (c) 271                  (d) 4
6. A gardener wants to fence a circular garden of diameter 14m. Find the length of the rope he needs to purchase.
(a) 44m                (b) 28m                 (c) 88m                  (d) None of these
7. If the area of a circle is 2464m2, find its diameter.
(a) 56m               (b) 154m                (c) 176m                (d) 206m
8. What is the circumference of a circle of radius 7cm?
(a) 44cm             (b) 49cm                (c) 14cm                 (d) None of these
9. Ayush made his picture on a rectangular sheet of length 60cm and breadth 20cm wide. Area of picture is:
(a) 1200cm2       (b) 1250cm2          (c) 1100cm2            (d) None of these
10. If a side of a square is 4cm then its perimeter is:
(a) 16cm             (b) 8cm                 (c) 12cm                 (d) None of these
11. The area of triangle is
(a) (½) x base x height                       (b) (½) x (base + height)         
(c) Base x height                                (d) None of these
12. Find radius of a circle of diameter 9.8m.
(a) 4.9m             (b) 19.6m             (c) 10m                 (d) None of these
13. What is the circumference of a circle of diameter 10cm?
(a) 35cm            (b) 30cm               (c) 31.4cm            (d) None of these
14. Find the perimeter of a triangle with sides 4cm, 6cm and 10cm.
(a) 20cm            (b) 24cm               (c) 9cm                 (d) 18cm
15. The area of a rectangular sheet is 500cm2. If the length of the sheet is 25cm. What is its width?
(a) 20cm            (b) 25cm               (c) 50cm               (d) None of these
16. Find the area of a square park whose perimeter is 320cm?
(a) 6400m2        (b) 6000m2           (c) 1280m2            (d) None of these
17. The area of parallelogram is
(a) height x height   (b) base x height   (c) base + height   (d) base x base
18. If a side of a square is 5cm then its area is:
(a) 20cm2          (b) 25cm2              (c) 10cm2              (d) None of these
19. Find the area of a triangle with a base of 20cm and a height of 30cm.
(a) 300cm2        (b) 100cm2            (c) 400cm2            (d) 600cm2
20. Find the height x, if the area of the parallelogram is 24cm2 and the base is 4cm.
(a) 4cm             (b) 6cm                  (c) 5cm                 (d) None of these

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 06/07/2021, 07/07/2021, 09/07/2021, 13/07/2021, 14/07/2021, 16/07/2021, 20/07/2021, 23/07/2021 
LINKS
Click on the chapter’s name to download the chapter in PDF form.
CH:- 9 PAIRS OF ANGLES

TOPIC: : Introduction, Types of Angles, Pairs of Angles, Angles formed by a Transversal, Parallel Lines, Angles formed by Parallel lines and Transversals, Construction.

EXPLAINED
1. Introduction (Lines and Angles)
1.1 POINT
1.2 LINE
1.3 LINE SEGMENT
1.4 RAY
2. Types of Angles

2.1 Acute angle: An angle whose measure is more than 0o but less than 90o is called an acute angle.
2.2 Right angle: An angle whose measure is 900 is called a right angle.
2.3 Obtuse angle: An angle whose measure is more than 90o but less than 180o is called an obtuse angle.
2.4 Straight angle: An angle whose measure is 180o is called a straight angle.
2.5 Reflex angle: An angle whose measure is more than 180o but less than 360o is                                 called a reflex angle.
2.6 Complete angle: An angle whose measure is 360o is called a complete angle.
3. Pairs of Angles
3.1 Adjacent angles: Two angles in a plane are called adjacent angles, if
(i)   they have a common vertex,
(ii)  they have a common arm, and
(iii) their other arms lie on the opposite sides of the common arm.
3.2 Linear Pair: Two adjacent angles are said to form a linear pair of angles, if their non- common arms are two opposite rays.
3.3 Vertically opposite angles: Two angles formed by two intersecting lines having no common arm are called vertically opposite angles.
3.4 Angles at a point: Angles formed by a number of rays having a common                                             initial point are called angles at a point.
3.5 Complementary angles: If the sum of the measures of two angles is 90o, then the angles are called complementary angles.
3.6 Supplementary angles: Two angles are said to be supplementary angles if the sum of their measures is 180o, and each of them is called a supplement of the other.
4. Parallel Lines: If two lines lie in the same plane and do not intersect when produced on either side then such lines are said to be parallel to each other.
5. Transversal: A straight line which cuts two or more straight lines at distinct points is called a transversal.
6. The angles formed when a transversal cuts two parallel lines
6.1 Interior angles
6.2 Exterior angles
6.3 Pair of Alternate interior angles (Alternate angles)
6.4 Pair of Alternate Exterior angles
6.5 Pair of Corresponding angles
6.6 Pair of interior angles on same side of transversal (Co-interior angles)

7. Construction of a line parallel to a given line through a point not on the line.

MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Introduction
2. Lines and Angles
3. Complementary angles and Supplementary angles
4. Adjacent angles
5. Linear Pair
6. Vertically opposite angles
7. Angles made by Transversal
MAIN TEACHING 
Online oral explanation and some written work
1. INTRODUCTION (PAIRS OF ANGLES)
2. Types of Angles
3. Pairs of Angles
4. Parallel Lines
5. Perpendicular Lines
6. Angles Formed by a Transversal
STUDENTS TAKE  AWAY
Complete all questions of Exercise 9(A), 9(B), 9(C), 9(D), 9(E), 9(F), 9(G) and 9(H) from given link of chapter.

ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in your OCB.

 R/3                                                          
 02/07/2021
 CONTINUATION OF CHAPTER - 05 
LINKS
Click on the chapter's name to download the chapter in PDF form.
CH:-5 ALGEBRAIC EXPRESSIONS
TOPIC: Subtraction of Algebraic expressions

EXPLAINED
1. Subtraction of Algebraic expressions
MUST WATCH THE VIDEO FOR BETTER UNDERSTANDING
1. Subtraction of Algebraic expressions
    VIDEO 1
MAIN TEACHING
Oral and Explanation Online with some written work.

STUDENTS TAKE  AWAY
Complete all questions of Exercise 5(C) from given link of chapter.
Chapter's Link

ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


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 04/06/2021, 08/06/2021, 09/06/2021, 11/06/2021, 15/06/2021, 16/06/2021 
LINKS
Click on the chapter's name to download the chapter's name in PDF form.
CH:-5 ALGEBRAIC EXPRESSIONS
TOPIC: Introduction, Variable, Constant, Algebraic Expressions, Terms, Coefficient, Like and Unlike Terms, Types of Algebraic expressions, Degree of Polynomials, Addition and Subtraction of Algebraic expressions

EXPLAINED
1. Introduction (Algebraic expressions)
2. Variable: A symbol which takes various numerical values is called a variable.
3. Constant: A symbol having a fixed numerical value is called a constant.
4.  Algebraic expressions: A combination of constants and variables connected by the signs of fundamental operations of addition (+), subtraction (-), multiplication (×), and division ( ÷) is called an algebraic expression.
5. Parts of an Algebraic expression
5.1 Terms: Various parts of an algebraic expression which are separated by the signs of   ‘+’ or ‘ ─’ are called the terms of the expression.
5.2 Factors: Each term in an algebraic expression is a product of one or more number(s) and / or literal number(s). These number(s) and / or literal number(s) are known as the factors of that term.
5.3 Coefficient: In a term of an algebraic expression, any of the factors with the signs of the term is called the coefficient of the product of the other factors. 
6. Like Terms: The terms having the same literal factors are called like or similar.
7. Unlike Terms: The terms not having same literal factors are called unlike or dissimilar terms.
8. Types of Algebraic expressions
8.1 Monomials: An algebraic expression containing only one term is called a monomial. Example:-  3, 2x, 5x2y, -6abc, 3ab2c3
8.2 Binomials: An algebraic expression containing two terms is called a binomial. Example:- x +3, 5 – 2x, a2 – 2abc, x3 + 3
8.3 Trinomials: An algebraic expression containing three terms is called a trinomial. Example:-  2x – y + 3, x2 + y2 + z2, 3 + xyz + x3.
8.4 Polynomials: An algebraic expression containing two or more terms is called a polynomial. x +3, 2x – y + 3, 4x3 – x2 + 6x +3, 7y3 + 5y2 – 8y +9.
5. Degree of Polynomials
6. Standard form of  a Polynomials
7. Addition of Algebraic expressions
8. Subtraction of Algebraic expressions

MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Introduction (Algebraic expressions)
          VIDEO 1
2. Parts of an Algebraic expression
    2.1 TERMS
    2.2 FACTORS
    2.3 Coefficients
3. Like and Unlike Terms
          VIDEO 3
4. Types of Algebraic expressions
          VIDEO 4
5. Addition of Algebraic expressions
          VIDEO 5
6. Subtraction of Algebraic expressions
          VIDEO 6

MAIN TEACHING
Oral and Explanation Online with some written work.

STUDENTS TAKE  AWAY
Complete all questions of Exercise 5(A), 5(B), and 5(C) from given link of chapter.

Chapter's Link
ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.

 R/1                                                          
 04 / 05 / 2021 - 02 / 06 / 2021 
Click on the chapter name to download chapter in PDF form.
TOPIC: Introduction, Recall, Properties of addition and subtraction of integers , Commutative Property, Associative Property, Additive Identity Multiplication of a Positive and a Negative Integer Commutative of Multiplication

EXPLAINED
1. Introduction
2.  Properties of addition and subtraction of integers,
3. Properties of multiplication
4. Properties of division
5. Operator precedence
6. Use of brackets
7. Removal of brackets

MUST WATCH THE VIDEOS FOR BETTER UNDERSTANDING
Video 01
Video 02
Video 03
Video 04
Video 05

MAIN TEACHING
Oral and explanation with some written work
1. Properties of addition and subtraction of integers
2. Properties of multiplication
  2.1 Closure property
  2.2 Commutativity property
  2.3 Associativity property
  2.4 Distributivity of multiplication over addition
  2.5 Existence of multiplicative identity
  2.6 Property of zero
3. Use of brackets
4. Removal of brackets

STUDENTS TAKE AWAY
Complete all examples and Exercise 1(A), 1(B), 1(C), 1(D) and 1(E) from given link of chapter.

ASSIGNMENT
Complete the questions given in Chapter Assessment in OCB.

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