R/12
04/10/2021, 05/10/2021, 06/10/2021, 07/10/2021, 08/10/2021, 09/10/2021
LINKS
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REVISION
TOPIC: Introduction, Sides, Angles and Diagonals of a Quadrilateral, Adjacent Sides and Opposite Sides, Angle Sum Property of a Quadrilateral, interior and Exterior Angles of a quadrilateral, Exterior Angles Sum property.
EXPLAINED
1. Introduction, Sides, Angles and Diagonals of a Quadrilateral,
2. Adjacent Sides and Opposite Sides,
3. Angle Sum Property of a Quadrilateral,
4. Interior and Exterior Angles of a quadrilateral,
5. Exterior Angles Sum property.
1. Introduction, Sides, Angles and Diagonals of a Quadrilateral,
2. Adjacent Sides and Opposite Sides,
3. Angle Sum Property of a Quadrilateral,
4. Interior and Exterior Angles of a quadrilateral,
5. Exterior Angles Sum property.
MAIN TEACHING
1. Introduction, Sides, Angles and Diagonals of a Quadrilateral,
2. Adjacent Sides and Opposite Sides,
3. Angle Sum Property of a Quadrilateral,
4. Interior and Exterior Angles of a quadrilateral,
5. Exterior Angles Sum property.
WATCH THE VIDEOS FOR YOUR BETTER UNDERSTANDING
STUDENTS TAKE AWAY
Complete all examples and Exercise 12 from given link of chapter.
ASSIGNMENT
Complete the questions given in Chapter Assessment in OCB
R/11
24/09/2021, 25/09/2021, 27/09/2021, 28/09/2021, 29/09/2021, 30/09/2021, 01/10/2021
LINKS
Click on the chapter's name to download the chapter in PDF form.
REVISION
TOPIC: Introduction, Review of concepts and Definitions, Classification of polynomials, Addition of algebraic expressions, Subtraction of algebraic expressions, Multiplication of algebraic expressions, Division of algebraic expressions, Special products of Binomials (IDENTITIES).
EXPLAINED
1. Introduction
2. Review of concepts and Definitions
2.1 Constant: A symbol having a fixed numerical value is called a constant.
2.2 Variable: A symbol which takes various numerical values is called a variable.
2.3 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.
2.4 Terms: Various parts of an algebraic expression which are separated by the signs of ‘+’ or ‘ ─’ are called the terms of the expression
2.5 Like Terms: The terms having the same literal factors are called like or similar.
2.6 Unlike terms: The terms not having same literal factors are called unlike or dissimilar terms
2.7 Coefficients: 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.
2.8 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.
3. Classification of polynomials
3.1 Monomial: An algebraic expression containing only one term is called a monomial. Example:- 3, 2x, 5x2y, -6abc, 3ab2c3
3.2 Binomial: An algebraic expression containing two terms is called a binomial. Example:- x +3, 5 – 2x, a2 – 2abc, x3 + 3
3.3 Trinomial: An algebraic expression containing three terms is called a trinomial. Example:- 2x – y + 3, x2 + y2 + z2, 3 + xyz + x3.
4. Addition of algebraic expressions
5. Subtraction of algebraic expressions
6. Multiplication of algebraic expressions
7. Division of algebraic expressions
8. Special products of Binomials (IDENTITIES).
6. Multiplication of algebraic expressions
7. Division of algebraic expressions
8. Special products of Binomials (IDENTITIES).
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Introduction (Algebraic Expression)
2. Parts of an Algebraic expression: Factors
3. Parts of an Algebraic expression: Coefficients
4. Like and Unlike terms
5. Types of Algebraic Expressions
6. Addition of algebraic expressions
7. Subtraction of algebraic expressions
8. Multiplication of algebraic expressions
9. . Special products of Binomials (IDENTITIES)
MAIN TEACHING
Oral and Explanation Online with some written work.
1. Introduction
2. What are Expressions?
3. Monomials, Binomials and Polynomials
4. Addition and Subtraction of algebraic expressions
5. Multiplication of algebraic expressions and Identity
STUDENTS TAKE AWAY
Complete all questions of Exercise 5(A), 5(B), 5(C), 5(D), 5(E), 5(F), 5(G), and 5(H) from given link of chapter.
R/10
13/09/2021, 14/09/2021, 20/09/2021, 21/09/2021
LINKS
Click on the chapter’s name to download the chapter in PDF form.
CH-14 PROBABILITY
Click on the chapter’s name to download the chapter in PDF form.
CH-14 PROBABILITY
TOPIC: Introduction, Conditional Probability, Multiplication Theorem on Probability, Independent Events, Baye’s Theorem, Random variables and its Probability, Distributions, Bernoulli Trials and Binomial Distribution.
EXPLAINED
1. Introduction (Probability)
1.1 Probability: Probability is a branch of mathematics that deals with calculating the likelihood of a given event’s occurrence.
2. Some terms related to Probability
2.1 Experiment: An operation which can produce some well-defined outcomes, is called an experiment.
2.2 Random Experiment: An experiment in which all possible outcomes are known and the exact outcome cannot be predicted in advance, is called a random experiment.
2.3 Trial: By a trial, we mean performing a random experiment.
2.4 Event: Outcome associated with an experiment is called an event.
2.5 Sure events: The events whose probability is one are called sure events.
2.6 Impossible events: The events whose probability is zero are called impossible events.
2.7 Elementary event: An event with only one possible outcome is called an elementary event.
3. Probability of an event E, denoted as P(E), is given by
MUST WATCH THE VIDEO FOR BETTER UNDERSTANDING
1. Probability
1. Definition of Probability
STUDENTS TAKE AWAY
Complete all questions of Exercise- 14 from given link of chapter.
ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.
R/9
31/08/21, 03/09/21, 06/09/21, 07/09/21, 10/09/21
LINKSClick on the chapter’s name to download the chapter in PDF form.
TOPIC: Introduction, A review of work done earlier, Finding a Percentage of a number, Percent Increase and Decrease, Profit and Loss, Simple Interest, Compound Interest, Discount
EXPLAINED
1. Introduction (Percentage)
Percent: The word percent is an abbreviation of the Latin phrase ‘per centum’ which means per hundred or hundredths. The Symbol % is used for the term percent.
2. A review of work done earlier
2.1 Ratio
2.2 Proportion
2.3 Percent as a Ratio
2.4 Percent in Decimal Form
3. Finding a Percentage of a Number
To find a percent of a given number, we proceed as follows:
Step I: Obtain the number, say x.
Step II: Obtain the required percent, say P %.
Step III: Multiply x by P and divide by 100 to obtain the required P % of x
i.e. P % of x = P/100 × x
Example: Find: (i) 12% of Rs 1200
Solution: 12% of Rs 1200 = Rs 12/100 × 1200
= 144
4. Percent Increase and Decrease
5. Discount
6. Review of Concepts
6.1 Cost Price: The amount paid to purchase an article or the price at which an article is made is known as its cost price.
The cost price is abbreviated as C.P.
6.2 Selling Price: The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.
6.3 Profit: If the selling price (S.P.) of an article is greater than the cost price (C.P.), the difference between the selling price and cost price is called profit.
Thus, if S.P. > C.P., then
Profit = S.P. – C.P.
6.4 Profit Percentage: The profit percent is the profit that would be obtained for a C.P. of Rs 100 i.e.,
6.5 Loss: If the selling price (S.P.) of an article is less than the cost price (C.P.), the difference between the cost price (C.P.) and the selling price (S.P.) is called loss.
Thus, if S.P. < C.P., then
Loss = C.P. – S.P.
6.6 Loss Percentage: The loss percent is the loss that would be made for a C.P. of Rs 100. i.e.,
7. Simple Interest
8. Compound Interest
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Introduction
2. Ratio
3. Convert Ratio to Percentages
4. Convert Decimal number into Percentage
5. Profit and Loss Percentage
6. Simple Interest
7. Compound Interest
8. Use of Compound Interest Formula
MAIN TEACHING
Online oral explanation and some written work
1. What is Percentage?
2. Ratio
3. Definition
4. Formulae
5. Compound Interest
STUDENTS TAKE AWAY
Complete all questions of Exercise 8(A), 8(B), 8(C), 8(D) and 8(E) from given link of chapter.
ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.
R/8
23/08/21, 24/08/21, 27/08/21
CONTINUATION OF CH:- 12
LINKS
Click on the chapter’s name to download the chapter in PDF form.
TOPIC: Volume of a Cuboid and a Cube, Volume of a Cylinder.
EXPLAINED
2.3 Cylinder
2.5 Sphere
6. Volume and surface area of a Cylinder
Let us consider a cylinder whose height is h units and the radius of whose base is r units. Then we have
6.1 Volume of the cylinder = (pr2h) cubic units.
6.2 Curved surface area of the cylinder = (2prh) sq units.
6.3 Total surface area of the cylinder = 2pr( h + r) sq units.
Example:
~ Find the volume, curved surface area, and total surface area of a cylinder having radius of the base 14 cm and height 30 cm.
Solution: Here, r = 14 cm and h = 30 cm.
(i) Volume of the cylinder = (pr2h) cubic units
= (22/7 x 14 x 14 x 30) cm3
= 18480 cm3.
= 18480 cm3.
(ii) Curved surface area of the cylinder = (2prh) sq units
= (2 x 22/7 x 14 x 30) cm2
= 2640 cm2.
= 2640 cm2.
(iii) Total surface area of the cylinder = 2pr( h + r) sq units
= [2 x 22/7 x 14 x ( 14 + 30)] cm2
= 3872 cm2.
= 3872 cm2.
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Surface area of a Cylinder
2. Volume of a cube
3. Volume of Cuboid and Cylinder
MAIN TEACHING
Online oral explanation and some written work
1. What is Mensuration?
2. Area and Perimeter of 2-D figures
3. Volume, Total surface area and Curved surface area of 3-D Figures
STUDENTS TAKE AWAY
Complete all questions of Exercise 12(E) and 12(F) from given link of chapter.
ASSIGNMENT
I. Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.
R/7
02/08/21, 03/08/21, 06/08/21, 10/08/21
LINKS
Click on the chapter’s name to download the chapter in PDF form.
TOPIC: Introduction, Area of Plane Shapes, Area of Trapezium, Area of a Polygon, Surface Area of a Cuboid, Surface Area of a Cube, Cylinder, Area of curved surface of Cylinder, Volume of a Cuboid and a Cube, Volume of a Cylinder.
Click on the chapter’s name to download the chapter in PDF form.
EXPLAINED
1. Introduction (Mensuration)
The word “Mensuration” is derived from the Greek word “Mensuration” meaning “to measure” and refers to that branch of mathematics and deals with the measurement of geometric magnitudes, such as areas of surfaces and volumes of solids. It is a practical branch of mathematics.
It is categorized in two parts:
1. Mensuration of 2-D figures
Some of 2-D shapes in mensuration
1.1 Square
1.2 Rectangle
1.3 Parallelogram
1.4 Rhombus
1.5 Triangle
1.6 Trapezoid
1.7 Circle
2. Mensuration of 3-D figures
Some of 3-D shapes in Mensuration
2.1 Cuboid
2.2 Cube
2.3 Cylinder
2.4 Cone
2.5 Sphere
3. Introduction (TSA, LSA and Volume)
3.1 Total Surface Area (TSA): Total surface area is the sum of the areas of all the sides of three dimensional figure.
3.2 Lateral surface area (LSA): Lateral surface area is the sum of the areas of all sides of a 3D object except its top and bottom bases.
3.3 Volume: The space occupied by a solid body is called its volume.
4. Area of a Trapezium
Area of Trapezium = ½ x (Sum of the parallel sides) x (Distance between parallel sides)
= ½ x ( a + b) x h sq units.
Example:
~ Find the area of a trapezium whose parallel sides are of lengths 10 cm and 12 cm and the distance between them is 4 cm.
Solution: Here, Sum of the parallel sides (a = 10 cm, b = 12 cm). Distance between parallel sides (h) = 4 cm.
Area of the trapezium = ½ x ( a + b) x h sq units
= [½ x (10 + 12) x 4] cm2
= [½ x 22 x 4] cm2
= 44 cm2.
= [½ x 22 x 4] cm2
= 44 cm2.
4. Volume and Surface Area of a Cuboid
Formulae:
Let us consider a Cuboid of length = l units, breadth = b units, and height =h units. Then, we have
4.1 Total surface area of the Cuboid = 2(lb + bh + lh) sq units.
4.2 Lateral surface area of the Cuboid = [2(l + b) x h] sq units.
4.3 Volume of the Cuboid = (l x b x h) cubic units.
Example:
~ Find the volume, the total surface area and the lateral surface area of a Cuboid
which is 15 m long, 12 m wide and 4.5 m high.
Solution:
Here, l = 15 m, b = 12 m and h = 4.5 m
Volume of the Cuboid = (l x b x h) cu units.
= (15 x 12 x 4.5) m3
= 810 m3
= 810 m3
Total surface area of the Cuboid = 2(lb + bh + lh) sq units
= 2(15 x 12 + 12 x 4.5 + 15 x 4.5) m2
= 603 m2.
= 603 m2.
Lateral surface area of the Cuboid = [2(l + b) x h] sq units
= [2(15 + 12) x 4.5] m2
= 243 m3.
= 243 m3.
5. Volume and Surface Area of a Cube
Formulae:
Let us consider a cube of edge = a units. Then we have
5.1 Volume of the cube = a3 cubic units.
5.2 Total surface area of the cube = 6a2 sq units.
5.3 Lateral surface area of the cube = 4a2 sq units.
Example:
~ Find the volume, total surface area and lateral surface area of a cube, each of
whose edges measures 20 cm.
Solution: Here, a = 20 cm.
Volume of the cube = a3 cubic units
= (20 x 20 x 20) cm3
= 8000 cm3.
= 8000 cm3.
Total surface area of the cube = 6a2 sq units
= (6 x 20 x 20) cm2
= 2400 cm2.
= 2400 cm2.
Lateral surface area of the cube = 4a2 sq units
= (4 x 20 x 20) cm2
= 1600 cm2.
= 1600 cm2.
6. Volume and surface area of a Cylinder
Formulae:
Let us consider a cylinder whose height is h units and the radius of whose base is r units. Then we have
6.1 Volume of the cylinder = (pr2h) cubic units.
6.2 Curved surface area of the cylinder = (2prh) sq units.
6.3 Total surface area of the cylinder = 2pr( h + r) sq units.
Example:
~ Find the volume, curved surface area, and total surface area of a cylinder
having radius of the base 14 cm and height 30 cm.
Solution: Here, r = 14 cm and h = 30 cm.
(i) Volume of the cylinder = (pr2h) cubic units
= (22/7 x 14 x 14 x 30) cm3
= 18480 cm3.
= 18480 cm3.
(ii) Curved surface area of the cylinder = (2prh) sq units
= (2 x 22/7 x 14 x 30) cm2
= 2640 cm2.
= 2640 cm2.
(iii) Total surface area of the cylinder = 2pr( h + r) sq units
= [2 x 22/7 x 14 x ( 14 + 30)] cm2
= 3872 cm2.
= 3872 cm2.
MUST WATCH THE VIDEOS FOR BETTER UNDERSTANDING
1. Introduction (Area of Plane Shapes)
2. Area of Trapezium
3. Area of a Polygon
4. Surface Area of a Cuboid, and a Cube
5. Surface area of a Cylinder
6. Volume of a cube
7. Volume of Cuboid and Cylinder
MAIN TEACHING
Online oral explanation and some written work
1. What is Mensuration?
1. What is Mensuration?
2. Area and Perimeter of 2-D figures
3. Volume, Total surface area and Curved surface area of 3-D Figures
STUDENTS TAKE AWAY
Complete all questions of Exercise 12(A), 12(B), 12(C), 12(D), 12(E) and 12(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. The formula for lateral surface area of Cuboid is
(a) 2h (l + b) (b) 2l (h + b) (c) 2b(l + h) (d) 2(lb + bh + hl)
2. The cost of papering the wall of a room, 12m long, at the rate of Rs.1.35 per square meter is Rs.340.20. The cost of matting the floor at Re.0.85 per square meter is Rs.91.80. Find the height of the room.
(a) 12m (b) 8m (c) 6m (d) 10m
3. The length of parallel sides of trapezium is 14cm and 6cm and its height is 5cm. Its area will be
(a) 50cm2 (b) 100cm2 (c) 210cm2 (d) 10cm2
4. Two dimensional figure is a
(a) solid figure (b) plane figure (c) cylinder figure (d) None of these
5. Surface area of a Cuboid = ___________.
(a) 2h (l + b) (b) 2lbh (c) 2 (lb + bh + hl)) (d) None of these
6. A rectangular paper of width 7cm is rolled along its width and a cylinder of radius 20cm is formed. Find the volume of the cylinder.
(a) 8800cm3 (b) 8800cm (c) 8800cm2 (d) None of these
7. The formula for finding lateral surface area of cylinder is
(a) 2prh (b) ) pr2 (c) ) 2pr(r + h) (d) ) 2pr
8. Which of the following is an example of two dimensions?
(a) Cuboid (b) ) cone (c) ) sphere (d) ) circle
9. Find the volume of a Cuboid whose length = 8cm, breadth= 6cm and height = 3.5cm.
(a) 168cm2 (b) 168cm3 (c) 215cm3 (d) 150cm3
10. In a quadrilateral, half of the product of the sum of the lengths of parallel sides and the parallel distance between them gives the area of
(a) rectangle (b) parallelogram (c) triangle (d) trapezium
11. Diagonals of rhombus are
(a) equal (b) half of one diagonal
(c) different length (d) none of above
12. The area of four walls of the room is
(a) 2(lb + bh + hl))) (b) 2l (h + b)
(c) 2(lb x bh x hl)) (d) 2h (l + b)
13. Find the height of Cuboid whose volume is 490cm3 and base area is 35cm2.
(a) 12cm (b) 14cm (c) 10cm (d) 16cm
14. The amount of space occupied by a three dimensional objects is called its
(a) area (b) surface area
(c) volume (d) lateral surface area
15. A cylindrical tank has a capacity of 5632m3, if the diameter of its base is 16m, find its depth.
(a) 66m (b) 30m (c) 26m (d) 28m
16. Find the total surface area of a cube whose volume is 343cm3.
(a) 350cm2 (b) 294cm2 (c) 494cm2 (d) 200cm2
17. Solid figures are
(a) 2D (b) 3D (c) 1D (d) 4D
18. The area of a trapezium is
(a) ½ (sum of parallel sides) x h (b) 2 (sum of parallel sides) x h
(c) (sum of parallel sides) x h (d) ½ (sum of parallel sides) + h
19. The formula for finding total surface area of Cuboid is
(a) 2(lb x bh x hl))) (b) 2(lb + bh + hl)
(c) 2lb (bh + hl) (d) 2h (l + b)
20. Find the volume of a Cuboid whose length is 8cm, breadth 6cm and height 3.5cm.
(a) 215cm3 (b) 168cm3 (c) 172cm3 (d) 150cm3
R/6
23/07/21, 26/07/21, 27/07/21, 30/07/21
LINKS
Click on the chapter’s name to download chapter name in PDF form.
CH:- 02 POWERS(EXPONENTS)
CH:- 02 POWERS(EXPONENTS)
TOPIC: Introduction, Negative integral exponents, Decimal number system, Zero exponent, Laws of exponents for integral powers, Use of exponents to express small numbers in standard form.
EXPLAINED
1. Introduction (EXPONENTS)
1. Introduction (EXPONENTS)
3. Negative Integral Exponents: For any non-zero rational number ‘a’ and a positive integer, we define
Examples:
5. Laws of exponents for integral powers
5.2 Dividing Powers with the same Base
Law II: If 'a' is any non-zero rational number and m and n are natural numbers, such that m > n, then
5.1 Multiplying Powers with the same Base
Law I: If 'a' is a non-zero rational number and m, n are natural numbers, then
Examples:
(i) 52 x 53 = 52+3 = 55
(ii) 32 x 34 x 38 = 32+4+8 = 314
(iii) 7x x 72 = 7x+2
(ii) 32 x 34 x 38 = 32+4+8 = 314
(iii) 7x x 72 = 7x+2
5.2 Dividing Powers with the same Base
Law II: If 'a' is any non-zero rational number and m and n are natural numbers, such that m > n, then
Examples:
(i) 911 ÷ 97 = 911 – 7 = 94
(ii) (-7)13 ÷ (-7)9 = (-7)13 – 9 = (-7)4
(i) 911 ÷ 97 = 911 – 7 = 94
(ii) (-7)13 ÷ (-7)9 = (-7)13 – 9 = (-7)4
5.3 Power of a Power
Law III: If 'a' is any rational number different from zero and m, n are natural numbers, then
Examples:
(i) (23)4 = 23x4 = 212
(ii) (-3)5 )3 = (-3)5x3 = (-3)15
5.4 Multiplying Powers with the same Exponents
Law IV: If 'a, b' are non-zero rational numbers and m is a natural number, then
Law IV: If 'a, b' are non-zero rational numbers and m is a natural number, then
Examples:
(i) 25 x 35 = (2 x 3)5 = 65
(ii) (-4)3 x (-2)3 = { (-4) x (-2) }3 = 83
(i) 25 x 35 = (2 x 3)5 = 65
(ii) (-4)3 x (-2)3 = { (-4) x (-2) }3 = 83
5.5 Dividing Powers with the same Exponents
Law V: If 'a and b' are non-zero rational numbers and n is a natural number, then
Law V: If 'a and b' are non-zero rational numbers and n is a natural number, then
Examples:
6. Use of exponents to express small numbers in standard form.
MUST WATCH THE VIDEOS FOR BETTER UNDERSTANDING
1. Introduction
VIDEO 1
2. Exponent
VIDEO 2
3. Powers with Negative exponents
VIDEO 3
4. Decimal number system
VIDEO 4
5. Laws of Exponents
VIDEO 5
6. Use of exponents to express small numbers in standard form
VIDEO 6
VIDEO 1
2. Exponent
VIDEO 2
3. Powers with Negative exponents
VIDEO 3
4. Decimal number system
VIDEO 4
5. Laws of Exponents
VIDEO 5
6. Use of exponents to express small numbers in standard form
VIDEO 6
MAIN TEACHING
Online oral Explanation and some Written work.
1. Introduction (EXPONENTS)
2. Zero Exponent
3. Laws of exponents for integral powers
4. Use of exponents to express small numbers in standard form
STUDENTS TAKE AWAY
Complete all questions of Exercise 2(A) and 2(B) 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. The value of 72 is
(a) 7 (b) 49 (c) 2 (d) 14
2. 16 is the multiplicative inverse of
(a) 2-4 (b) 28 (c) 82 (d) 24
3. In 102 the base is
(a) 1 (b) 0 (c) 10 (d) 100
4. Change of an electron is 0.000,000,000,000,000,000,16 coulomb and in exponential form it can be written as
(a) 16 x 10-18 coulomb (b) 1.6 x 10-21 coulomb
(c) 1.6 x 10-19 coulomb (d) 16 x 10-21 coulomb
5. Evaluate the exponential expression (–n)4 x (-n)2, for n = 5.
(a) 25 (b) 15625 (c) 3125 (d) 625
6. Value of (30 + 20) x 50 is
(a) 1 (b) 25 (c) 2 (d) 0
7. When we have to add numbers in standard form, we convert them into numbers with the ___________ exponents.
(a) same (b) different (c) not equal (d) None of these
8. Very small numbers can be expressed in standard form using _____ exponents
(a) equal (b) negative (c) positive (d) None of these
9. Multiplicative inverse of 7-2 is __________.
(a) 49 (b) 5 (c) 7 (d) ─14
10. The value of 10000 is
(a) 0 (b) 1000 (c) 1 (d) None of these
11. The standard form of 9030000000 is given by
(a) 9.03 x 109 (b) 90.3 x 107 (c) 903 x 106 (d) 9.03 x 10-9
12. The multiplicative inverse of 2-3 is
(a) 2 (b) 3 (c) 3 (d) 23
13. Find the value of the expression a2 for a = 10.
(a) 100 (b) 1 (c) 10 (d) None of these
14. Evaluate exponential expression -25.
(a) 15 (b) -32 (c) 16 (d) None of these
15. In exponential form 149,600, 000,000m is given by
(a) 1.496 x 1011m (b) 1.496 x 108
(c) 14.96 x 108m (d) 14.96 x 1011m
16. The value of 30 is __________.
(a) 0 (b) 3 (c) 1 (d) None of these
17. The value of 32 is equal to
(a) 9 (b) 1 (c) -6 (d) 5
18. The base in the expression 1024 is______________.
(a) 1 (b) 10 (c) 0 (d) 24
19. (am)n is equal to
(a) am+n (b) am-n (c) amn (d) an-m
20. For a non zero rational number a, (a3)-2 is equal to
(a) a6 (b) a-6 (c) a-9 (d) a1
R/5
12/07/21, 13/07/21, 16/07/21, 19/07/21, 20/07/21
LINKS
Click on the chapter's name to download the chapter in PDF form.
CH:- 10 QUADRILATERALS
Click on the chapter's name to download the chapter in PDF form.
CH:- 10 QUADRILATERALS
TOPIC: Introduction (Quadrilateral), Sides, Angles and Diagonals of a Quadrilateral, Adjacent Sides and Opposite Sides, Adjacent Sides and opposite Angles, Angle Sum Property of a Quadrilateral, interior and Exterior Angles of a quadrilateral, Exterior Angles Sum property, Various types of Quadrilaterals, Properties of Parallelograms, Properties of Rectangle , Square and Rhombus.
EXPLAINED
1. Introduction (Quadrilateral)
1. Introduction (Quadrilateral)
Quadrilateral: A plane figure bounded by four line segments AB, BC, CD, and DA is called a quadrilateral.
1.1 Vertices: The points A, B, C, D are called the vertices of quad. ABCD.
1.2 Sides: The line segments AB, BC, CD, and DA are called the sides of quad. ABCD.
1.3 Diagonals: The line segments AC and BD are called the diagonals of quad. ABCD.
1.4 Adjacent Sides: Two sides of a quadrilateral having a common end point are called its adjacent sides.
(AB, BC), (BC, CD), (CD, DA) and (DA, AB) are four pairs of adjacent sides of quad. ABCD.
1.5 Opposite Sides: Two sides of a quadrilateral having no common end point are called its opposite sides.
(AB, CD) and (AD, BC) are two pairs of opposite sides of quad. ABCD.
1.6 Adjacent Angles: Two angles of a quadrilateral having a common arm are called its adjacent angles.
(ÐA, ÐB), (ÐB, ÐC), (ÐC, ÐD) and (ÐD, ÐA) are four pairs of adjacent angles.
1.7 Opposite Angles: Two angles of a quadrilateral having no common arm are called its opposite angles.
(ÐA, ÐC) and (ÐB, ÐD) are two pairs of opposite angles of quad. ABCD.
2. Angle Sum Property of a Quadrilateral
3. Exterior Angles Sum property
4. Types of Quadrilaterals
4.1 Trapezium: A quadrilateral having one pair of opposite sides parallel is called a trapezium.
4.2 Isosceles trapezium: If the two non- parallel sides of a trapezium are equal then it is called an isosceles trapezium.
4.3 Parallelogram: A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram.
4.4 Rhombus: A parallelogram having all sides equal, is called a rhombus.
4.5 Square: A parallelogram whose all sides are equal and one of whose angles is 90o is called a square.
4.6 Rectangle: A parallelogram one of whose angles is 90o, is called a rectangle.
4.7 Kite: A quadrilateral in which two pairs of adjacent sides are equal is known as a kite.
8. Properties of a Parallelogram
9. Properties of a Rhombus
10. Properties of a Rectangle
11. Properties of a Square
12. Properties of a Trapezium
13. Properties of a Kite
MUST WATCH VIDEO FOR BETTER UNDERSTANDING
1. Introduction (Quadrilateral)
2. Angle Sum Property of a Quadrilateral
3. Angle Sum Property of other Polygons
4. Sum of Exterior Angles of a Polygon
5. Types of Quadrilaterals
6. Properties of a Parallelogram
7. Properties of a Rectangle
8. Properties of a Square
9. Properties of a Rhombus
MAIN TEACHING
Online oral Explanation and some Written work.
1. Introduction (Quadrilateral)
2. What is Quadrilateral?
3. Types of Quadrilaterals
4. Properties of Quadrilaterals
STUDENTS TAKE AWAY
Complete all questions of Exercise 10(A), 10(B), 10(C), and 10(D) from given link of chapter.
Chapter's Link
Chapter's Link
R/4
02/07/21, 05/07/21, 06/07/21, 09/07/21
CONTINUATION OF CHAPTER - 05
LINKS
Click on the chapter's name to download the chapter in PDF form.
Click on the chapter's name to download the chapter in PDF form.
1. Division of algebraic expressions
1.1 Dividing a Polynomial by a Monomial
1.2 Dividing a Polynomial by a Polynomial
2. Special products of Binomials (IDENTITIES).
2.1 Identity 1
(a – b)2 = a2 – 2ab + b2
2.3 Identity 3
(a + b) (a – b) = (a2 – b2)
(a – b)2 = a2 – 2ab + b2
2.3 Identity 3
(a + b) (a – b) = (a2 – b2)
MUST WATCH THE VIDEOS FOR BETTER UNDERSTANDING
1. Division of algebraic expressions
2. Special products of Binomials (IDENTITIES)
MAIN TEACHING
Oral and Explanation Online with some written work.
STUDENTS TAKE AWAY
Complete all questions of Exercise 5(F), 5(G), and 5(H) from given link of chapter.
ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.
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R/3
07/06/21, 08/06/21, 11/06/21, 14/06/21, 15/06/21, 18/06/21
LINKS
Click on the chapter's name to download the chapter in PDF form.
TOPIC: Introduction, Review of concepts and Definitions, Classification of polynomials, Addition of algebraic expressions, Subtraction of algebraic expressions, Multiplication of algebraic expressions, Division of algebraic expressions, Special products of Binomials (IDENTITIES).
EXPLAINED
1. Introduction
2. Review of concepts and Definitions
2.1 Constant: A symbol having a fixed numerical value is called a constant.
2.2 Variable: A symbol which takes various numerical values is called a variable.
2.3 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.
2.4 Terms: Various parts of an algebraic expression which are separated by the signs of ‘+’ or ‘ ─’ are called the terms of the expression
2.5 Like Terms: The terms having the same literal factors are called like or similar.
2.6 Unlike terms: The terms not having same literal factors are called unlike or dissimilar terms.
2.7 Coefficients: 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.
2.8 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.
3. Classification of polynomials
3.1 Monomial: An algebraic expression containing only one term is called a monomial. Example:- 3, 2x, 5x2y, -6abc, 3ab2c3
3.2 Binomial: An algebraic expression containing two terms is called a binomial.
Example:- x +3, 5 – 2x, a2 – 2abc, x3 + 3
3.3 Trinomial: An algebraic expression containing three terms is called a trinomial.
Example:- 2x – y + 3, x2 + y2 + z2, 3 + xyz + x3.
4. Addition of algebraic expressions
5. Subtraction of algebraic expressions
6. Multiplication of algebraic expressions
7. Division of algebraic expressions
8. Special products of Binomials (IDENTITIES).
MUST WATCH THE VIDEOS FOR BETTER UNDERSTANDING
1. Introduction (Algebraic Expression)
2. Parts of an Algebraic expression: Factors
3. Parts of an Algebraic expression: Coefficients
4. Like and Unlike terms
5. Types of Algebraic Expressions
6. Addition of algebraic expressions
7. Subtraction of algebraic expressions
8. Multiplication of algebraic expressions
9. . Special products of Binomials (IDENTITIES)
MAIN TEACHING
Oral and Explanation Online with some written work.
1. Introduction
2. What are Expressions?
3. Monomials, Binomials and Polynomials
4. Addition and Subtraction of algebraic expressions
5. Multiplication of algebraic expressions and Identity
STUDENTS TAKE AWAY
Complete all questions of Exercise 5(A), 5(B), 5(C), 5(D), 5(E), 5(F), 5(G), and 5(H) from given link of chapter.
ASSIGNMENT
Complete the questions given in Mental Maths and Multiple Choice Questions in OCB.
R/2
11 / 05 / 2021, 04 / 06 / 2021
LINKS
Click on the chapter's name to download the chapter in PDF form.
TOPIC: Introduction, Rational number, Properties of addition of rational numbers, Subtraction of rational numbers, Properties of subtraction, Multiplication of rational numbers, Properties of multiplication of rational numbers, Division of rational numbers, Properties of division of rational numbers, Representation of rational numbers on the number line.
EXPLAINED
1. Introduction (Rational number).
2. Properties of addition of rational numbers.
2.1 Closure property
2.2 Commutativity
2.3 Associativity
2.4 Existence of additive identity (Zero)
3. Properties of subtraction
3.1 Closure property
3.2 Commutativity
3.3 Associativity
4. Properties of multiplication of rational numbers
4.1 Closure property
4.2 Commutativity
4.3 Associativity
4.4 Existence of multiplicative identity
4.5 Multiplication by 0
4.6 Distributivity of multiplication over addition
5. Representation of rational numbers on the number line.
MUST WATCH THE VIDEOS FOR BETTER UNDERSTANDING
1. Introduction (Rational number).
2. Closure property.
3. Commutative property for rational numbers.
4. Associative property for rational numbers.
5. Distributive property for rational numbers.
6. Representation of rational numbers on the number line.
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 the Chapter's Assessment in your OCB.
R/1
04 / 05 / 2021, 07 / 05 / 2021
LINKS
Click on the chapter's name to download the chapter in PDF form.
Ch 12. Quadrilaterals
TOPIC: Introduction, Sides, Angles and Diagonals of a Quadrilateral, Adjacent Sides and Opposite Sides, Angle Sum Property of a Quadrilateral, interior and Exterior Angles of a quadrilateral, Exterior Angles Sum property.
Click on the chapter's name to download the chapter in PDF form.
Ch 12. Quadrilaterals
TOPIC: Introduction, Sides, Angles and Diagonals of a Quadrilateral, Adjacent Sides and Opposite Sides, Angle Sum Property of a Quadrilateral, interior and Exterior Angles of a quadrilateral, Exterior Angles Sum property.
1. Introduction, Sides, Angles and Diagonals of a Quadrilateral,
2. Adjacent Sides and Opposite Sides,
3. Angle Sum Property of a Quadrilateral,
4. Interior and Exterior Angles of a quadrilateral,
5. Exterior Angles Sum property.
MAIN TEACHING
1. Introduction, Sides, Angles and Diagonals of a Quadrilateral,
2. Adjacent Sides and Opposite Sides,
3. Angle Sum Property of a Quadrilateral,
4. Interior and Exterior Angles of a quadrilateral,
5. Exterior Angles Sum property.
WATCH THE VIDEOS FOR YOUR BETTER UNDERSTANDING
Video 01. Introduction to Quadrilateral
Video 02. Adjacent Sides and Opposite Sides
Video 03. Angle Sum Property
Video 04. Sum of Exterior Angles
STUDENTS TAKE AWAY
Complete all examples and Exercise 12 from given link of chapter.
Complete the questions given in the Chapter's Assessment in your OCB
