Class 6

Students can go through AP Board 6th Class Maths Notes Chapter 2 Whole Numbers to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 2 Whole Numbers

→ Natural numbers: The numbers which we use for counting are called Natural numbers N= {1, 2, 3, 4, 5, 6,…} .

→ Successor: Every natural number has a successor, which is one more than it. Example : Successor of 15 is 15 + 1 = 16

→ Predecessor: Every natural number has a predecessor except 0. Predecessor of a number is one less than it.
Example: Predecessor of 56 is 56 – 1 = 55

→ Whole numbers: The natural numbers along with zero forms the set of Whole numbers.
W = {0, 1, 2, 3, 4, 5, 6,…}

• Every whole number has a successor and every whole number has a predecessor except zero.
• Every natural number is a whole number and every whole number is a natural number except zero.
• The smallest natural number is 1.
• The smallest whole number is 0.
• Addition, subtraction and multiplication can be represented on a number line.

→ Closure property: Sum of any two whole numbers is always a whole number.
Example : 5 + 3 = 8, a whole number.
This is called closure property of whole numbers w.r.t. addition.

→ Closure property: Product of any two whole numbers is always a whole number. Example : 5 × 3 = 15, a whole number.
This is called closure property of whole numbers w.r.t. multiplication.
In other words whole numbers are closed under addition and multiplication.
But whole numbers are not closed under subtraction and division.
Example: 7 – 12, is not a whole number.
9 ÷ 14, is not a whole number.
Division by zero is not defined.
Example: 5 ÷ 0, is not defined

→ Commutative property: Sum of any two whole numbers taken in any order is always same.
Example: 5 + 3 = 3 + 5 = 8
This is called commutative property of whole numbers w.r.t. addition.

→ Commutative property: Product of any two whole numbers taken in any order is always same.
Example: 5 × 3 = 3 × 5 = 15
This is called commutative property of whole numbers w.r.t. addition.
In other words whole numbers are commutative w.r.t. addition and multiplication. But whole numbers are not commutative w.r.t. subtraction and division.
Example: 4 – 9 ≠ 9 – 4 and 8 ÷ 11 ≠ 11 ÷ 8

→ Associative property: The sum of any three whole numbers taken in any or der is always same.
Example : 5 + (8 + 3) = (5 + 8) + 3 =16
This is called associative property of whole numbers w.r.t. addition.

→ Associative property: The product of any three whole numbers taken in any order is always same.
Example : 5 × (8 × 3) = (5 × 8) × 3 = 120
This is called associative property of whole numbers w.r.t. multiplication.
In other words whole numbers are associative w.r.t. addition and multiplication.
But whole numbers are not associative w.r.t. subtraction and division.
Example : 5 – (8 – 3) ≠ (5 – 8) – 3
: 5 ÷ (8 ÷ 3) ≠ (5 ÷ 8) ÷ 3

→ Distributive property of multiplication over addition:
(Example: 5 × (8 + 3) = (5 × 8) + (5 × 3) = 55

→ Additive identity: If zero is added to any whole number, then the result is the number itself.- Here zero is called the additive identity.
Example: 5 + 0 = 5, 7 + 0 = 7, 0 + 9 = 9 and so on.

→ Multiplicative identity: If any whole number is multiplied by 1, then the result is the number itself. Here one is called the multiplicative identity.
Example: 5 × 1 = 5, 7 × 1 = 7, 1 × 9 = 9 and so on.
If we represent the number 1 as a (.) dot, then a whole number can be represented either as an array of a triangle or a square.
The triangular numbers are 3, 6, 10, 15, 21, 28, ……. etc.

The square numbers are 4, 9, 16, 25, 36, …… etc.

→ Multiplication by 9/99/999/9999….etc.
74 × 99 = (74 – 1)/(9 – 7)(10 – 4) = 73/26
256 × 999 = (256 – 1)/(9 – 2)(9 – 5)(10 – 6) = 255/744
4267 × 9999 = (4267 – 1)/(9 – 4)(9 – 2)(9 – 6)(10 – 7) = 4266/5733
Here the number of 9’s in the multiplier is equal to number of digits in the multiplicand.
Answer has two parts: LHS/RHS
LHS: (Multiplicand-1)
RHS: Subtract all digits from 9 but the last digit from 10

Students can go through AP Board 6th Class Maths Notes Chapter 12 Data Handling to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 12 Data Handling

→ Data: Information which is in the shape of numbers or words or pictures which help us in taking decisions is called data.
If data is expressed in numbers it is called numerical data.
Eg: The marks obtained by five students at an examination is 25, 32, 28,14 & 24.
If data is expressed in words it is called data in words.
Eg : The colours liked by some students are Red, black, pink, white, etc.

→ Frequency: Number of times a particular observation occurs in a given data is called its frequency.

→ Frequency distribution table: A table showing the frequency or count of various items is called a frequency distribution table.
A data can be arranged in a tabular form using tally marks. The data arranged in a tally table is easy understood and interpret.

→ Pictograph: If a data is arranged using pictures, then it is called a pictograph.

→ Bar graph: If a data is arranged using rectangles, then it is called a bar graph.
The rectangles can be either vertical or horizontal in a bar graph.

→ Scale: Scale is a convenient way to represent the data. It quantifies what a single unit represents in a given bar graph or pictograph.

Students can go through AP Board 6th Class Maths Notes Chapter 11 Perimeter and Area to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 11 Perimeter and Area

→ Perimeter: The perimeter of a polygon is sum of all its sides.
The perimeter of an equilateral triangle is P = 3 × side
The perimeter of a rectangle P = 2 (length + breadth)
And its area A = length × breadth A = l × b
The perimeter of a square is P = 4 × side And its area A = side × side (or)
A = s × s The circumference of a circle C = 2πr where r is the radius of the circle.

→ Area: The region occupied by a plane figure is called its area.
To find the area of a complex figure, we divide the given shape into the combination of rectangles, squares and triangles where ever necessary.

Students can go through AP Board 6th Class Maths Notes Chapter 10 Practical Geometry to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 10 Practical Geometry

→ The above are the components we see in a geometry box. They are pair of set squares, protractor, graduated ruler, compasses and the divider.

→ Graduated ruler: A scale is used to draw straight edges of given length. It is also used to measure the lengths of the given line segments. A scale is also called a graduated ruler.

→ Compass: A compass is used to draw a circle of given radius. Sometimes we draw only a part of a circle which is called an arc. A compass is used in the construction of a line segment of given length, a perpendicular to a given line, given angle and in many more geometrical shapes.

→ Divider: A divider is used to measure the lengths of straight line segments and curved lines. It is also used to compare the lengths of two line segments.

→ Set squares: The pair of set squares is used to draw the pair of parallel lines.

→ Perpendicular bisector: The perpendicular bisector of a given line segment is the line which divides the given line segment into two equal parts at right angles.

→ Angle bisector: Angle bisector is a ray which divides the given angle into two equal parts.

Students can go through AP Board 6th Class Maths Notes Chapter 9 2D-3D Shapes to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 9 2D-3D Shapes

→ Space: A plane is a set of all points which extends in all directions endlessly in three dimensions.

→ Plane: A plane is a smooth surface which extends in all directions in two dimensions.
Eg: The surfaces of a table, the surface of a blackboard are examples for part of a plane.

→ Polygon: A simple closed figure formed by line segments is called a polygon.

→ Triangles:
A simple closed figure formed by three line segments is called a triangle.
The line segments \(\overline{\mathrm{AB}}\), \(\overline{\mathrm{BC}}\) & \(\overline{\mathrm{CA}}\) are called the sides of the triangle.

A triangle contains three sides.
A triangle contains three interior angles ∠A, ∠B & ∠C and three vertices A, B & C

→ A triangle divides the plane on which it lies into three sets of points.
1. Interior points on the triangle
2. Points on the triangle
3. Points in the exterior of the triangle

→ Quadrilateral:
A simple closed figure bounded by four line segments is called a quadrilateral.

→ Circle: If we draw a boundary along the edge of a round shaped object, then we get the following shape. The shape is called a circle. The length of the curved edge is called circumference. “A” is called the centre of the circle.

→ Chord: A line segment joining any points ‘A’ & ‘B’ on the circumference of the circle is called a chord. DE and FG are chords of the circle.

→ Diameter: The longest chord passing through the centre of the circle is called a diameter. AC & DG are diameters.

→ Arc: A part of the circle is called an arc.

CIRCLE TERMINOLOGY

→ Circumference: The distance around a circle.

→ Radius: The distance from the centre of a circle to the circumference. Half the diameter.

→ Diameter: A straight line passing through the centre of a circle to touch both sides of the circumference. Twice
as long as the radius.

→ Chord: A straight line joining two points on the circumference of a circle. The diameter is a special kind of chord.

→ Arc: A section of the circumference.

→ Sector: A section of a circle, bounded by two radii and an arc.

→ Segment: A section of a circle, bounded by a chord and an arc.

→ Tangent: A straight line touching the circumference once at a given point.

→ A circle divides the plane on which it lies into three parts.

1. Interior points
2. Exterior points
3. Points on the circle

→ BASIC PARTS OF A CIRCLE

• Interior of a Circle
  points A, B, C
• ON the circle
  point D
• Exterior of a Circle
  points E, F, G

→ The region in the interior of a circle enclosed by its boundary is called circular region.

→ Symmetry: Some figures appear beautiful because of their symmetry. Such shapes can be divided into two identical parts along a straight line which is called line of symmetry. A symmetrical figure may have more than one line of symmetry.

→ English alphabet – lines of symmetry:

3-D shapes:
→ NAMES OF 3D SHAPES

→ 3D SHAPES IN REAL – LIFE

→ Cube: A cube is a 3-dimensional figure. It has 6-identical faces. Each face of a cube is a square. All its sides are equal.

→ Cuboid: A cuboid is three a dimensional figure having three measures length, breadth and height.

→ Cylinder: A cylinder has circular faces at its both ends. It has two measures namely radius of the base and height of the cylinder.

→ Cone: A cone is a 3-d figure having curved surface with a circular base.

→ Prism and a Pyramid:

A Prism is a 3-d shape with parallelograms as its lateral surfaces. A Pyramid is a 3-d figure with triangles as its lateral surfaces.
A Prism / Pyramid may have a triangle/ square/rectangle…as its base.
A Prism/Pyramid is named as per its base.

→ Euler’s formula:
The number of faces (F), vertices (V) and edges (E) of a polyhedron are related by this formula: F + V = E + 2

Looking at the box to the right, calculate the number of edges:
Faces = 6
Vertices = 8
F + V = E + 2
6 + 8 = E + 2
14 = E + 2
E = 12

Students can go through AP Board 6th Class Maths Notes Chapter 8 Basic Geometric Concepts to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 8 Basic Geometric Concepts

 

→ Line: A line is a straight edge which extends endlessly on both sides. A line has no width.

Line is a set of infinite points extending in two opposite directions endlessly. A line is represented by any two points lying on it.
The above line is represented by \(\overline{\mathrm{AB}}\)
A line can also be represented by a lower case letter of English alphabet such as l.
A line has no end points.
A line may not be always straight. Sometimes it is curved as shown in the figure.

It is called a curved line.

→ Ray: A ray is a straight edge starting from a point and extends only in one direction endlessly.

A ray has no width.
A ray has only one end point. The end point is called the vertex of the ray. A ray is represented by the initial point and any arbitrary point in the direction in which it extends. Here the ray is \(\overline{\mathrm{AB}}\).

→ Line segment: A part of a line is called a line segment.
A line segment has two ends.

A line segment is represented by its two end points. Line segment \(\overline{\mathrm{AB}}\).
Recall that a small dot made by a shape edged pencil may be treated as a point.

→ History:
Geometry has a long and rich historical nature. The term ‘GEOMETRY’ is derived from the greek word ‘GEOMETRON’. ‘GEO’ means earth and ‘METRON’ means measurement. So, Geometry is the mathematics related to the earth’s measurement.
Early geometry was a collection Of empirically discovered principles concerning lengths, angles, areas and volumes which were developed to meet some practical need in surveying, construction, astronomy and various crafts.
In the ancient India Aryabhatta, Brahmagupta were some of the Indian Mathematicians who contributed their works in geometry.

→ Intersecting lines: Two lines meeting at a single point are called intersecting lines. The point is called the point of intersection. Two lines l & m intersecting at the point A.

→ Concurrent lines: Three or more lines passing through a single point are called concurrent lines and the point is called the point of concurrence.

Here the lines l, m & n are meeting at a single point O and hence are concurrent lines. The point of concurrence is O.

→ Parallel lines: Two lines are said to be parallel, if they never meet each other.

The distance between two parallel lines is constant throughout their length.
Here the lines l & m are parallel to one another.

→ Perpendicular lines: Two lines are said to be perpendicular, if they are straight to one another. Two adjacent sides of a paper are perpendicular to each other.

→ Measuring the length of a line segment: To measure the length of a given line segment we use a graduated scale or a divider in the instrument box.
Adjust the scale along the line segment and find the readings at the two end points. The difference of readings gives us the length of the line segment.
Adjust the two pointed legs of the divider on the two end points of the given line segment. Now measure the width between the legs on a graduated scale.
Measuring line segments in Centimeters

→ Angle: A figure formed by two rays with a common end point is called an angle.

The common end point is called the vertex of the angle. The two rays are called the two arms of the angle.

→ Sexagesimal system : A system related to number sixty is called sexagesimal system. We use this system in measuring angles.

Full angle is also called complete angle.
We use protractor to measure the angle.

Students can go through AP Board 6th Class Maths Notes Chapter 7 Introduction to Algebra to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 7 Introduction to Algebra

→ Expressions: 7 + 14 – 6 & 12 – 8 + 56 +…. such mathematical sentences are called numerical expressions.

When we try to make some general patterns we need to involve some constants and variables in the statements.
Eg: If three line segments are needed to construct a triangle, then the number of line segments needed to construct n-number of triangles is 3 × n.

Here the number of line segments required for a given number of triangles = 3x The value of the numeral is fixed and called a constant and x can take any value from 1, 2, 3, 4, 5, 6,…

So we say that x value is not fixed and varies and hence x is a variable.
If four line segments are needed to construct a square, then the number of line segments needed to construct n-number of squares is 4 × n.

Here the number of line segments required for a given number of triangles = 4x The value of the numeral 4 is fixed and called a constant and x can take any value from 1, 2, 3, 4, 5, 6, ….

So we say that x value is not fixed and varies and hence x is a variable.

→ A variable is an alphabet used to stand for a number.
A variable can like any value; it has no fixed value, but it is a number. We can perform binary operation such as addition, subtraction, multiplication and divisions on them.
Eg: If x is a variable,
then 5 more than x is x + 5
5 less than x is x – 5
5 times x is 5x
One fifth of x is \(\frac{1}{5}\).

→ A variable allows us to express relations in any special situation. Variables allow us to express many common rules of Geometry and Arithmetic in a more general way.
Eg: If the side of a square is s,
then its Area A = s × s
Perimeter = 4 × s
If the length and breadth of a rectangle are l & b, then its
Area A = l × b
Perimeter is P = 2 × (l + b).
The general form of an odd number = 2 × n + 1 = 2n + 1;
Even number = 2 × n = 2n
In the above we have number of line segments required for a given number of triangles is 3 × n.
Suppose the number of triangles is 4, then 4n = 12, this is an equation.
An expression involving the equality (=) symbol is called an equation.
The part l value of the expression on the left of the equality (=), is called LEFT HAND SIDE or L.H.S.
The part l value of the expression on the right of the equality (=), is called RIGHT HAND SIDE or R.H.S.
If the L.H.S. is not equal to R.H.S., then we do not get an equation.
Eg : 8 + 13 ≠ 15
2 + 3 < 9 – 2
56 + 3 > 25 + 5

→ Solution or root of an equation:
Solution of an equation is the value of the variable for which L.H.S and R.H.S are equal. The solution is also called the root of the equation.
Eg : Solution of x – 8 = 4 is x = 12
For the equation x + 3 = 8, x = 7 is not a solution.
We find the solution of an equation by Trial & Error method.
Trial -error method is a process in which the solution of an equation is found by taking some arbitrary values for the variable.

Students can go through AP Board 6th Class Maths Notes Chapter 6 Basic Arithmetic to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 6 Basic Arithmetic

→ If a comparison is made by finding the difference between two quantities, it is called comparison by difference.
Eg: Age of Harshita is 11 years and age of Srija is 8 years. Harshita is (11 – 8 = 3) 3 years older than Srija or Srija is 3 years younger than Harshita.

→ If a comparison is made by division it makes more sense than the comparison made by taking the difference.
Eg: If cost a key pad cell phone is Rs. 3000 and another smart phone is Rs. 15000, then the cost of the second phone is five times the cost of the first phone.

→ Ratio: Comparison of two quantities of the same type by virtue of division is called ratio. Eg: The weight of Ramu is 24 kg and the weight of the Gopi is 36 kg., then the ratio of weights is 24/36. It can also be written as 24:36 and read as 24 is to 36.
The ratio of two numbers ‘a’ and ‘b’ (b ≠ 0) is a ÷ b or a/b or \(\frac{a}{b}\) and is denoted as a : b and is read as a is to b.
In the ratio a : b the quantities a and b are called the terms of the ratio.
In the ratio a : b the quantity a is called the first term or antecedent and b is called the second term or the consequent of the ratio.
The value of a fraction remains the same if the numerator and the denominators are multiplied or divided by the same non-zero number so is the ratio.
That is if the first term and the second term of a ratio are multiplied or divided by . the same non-zero number.
3 : 4 = 3 × 5 : 4 × 5 = 15 : 20
Also 36 : 24 = 36 – 4 : 24 – 4 = 9 : 6.

→ Ratio in the simplest form or in the lowest terms:
A ratio a : b is said to be in its simplest form if its terms have no factors in common other than 1. A ratio in the simplest form is also called the ratio in its lowest terms. Generally ratios are expressed in their lowest terms.
To express a given ratio in its simplest term, we cancel H.C.F. from both its terms. To find the ratio of two terms, we express the both terms in the same units.
Eg: Ratio of 3 hours and 120 minutes is 3 : 2 (as 120 minutes = 2 hours) or 180 : 120 (as 3 hours = 180 minutes)
A ratio has no units or it is independent of units used in the quantities compared. The order of terms in a ratio a : b is important a : b ≠ b : a.

→ Equivalent ratio:
A ratio obtained by multiplying or dividing the antecedent and consequent of a given ratio by the same number is called its equivalent ratio.
Eg: 3 : 4 = 3 × 5 : 4 × 5 = 15 : 20. Here 3 : 4 & 15 : 20 are called equivalent ratios.
Also 36 : 24 = 36 ÷ 4 : 24 ÷ 4 = 9 : 6. Here 36 : 24 & 9 : 6 are called equivalent ratios.

→ Comparison of ratios: To compare two ratios
a) First express them as fractions
b) Now convert them to like fractions
c) Compare the like fractions

→ Proportion:
If two ratios are equal, then the four terms of these ratios are said to be in proportion. If a : b = c : d, then a, b, c and d are said to be in proportion.
This is represented as a : b :: c : d and read as a is b is as c is d.
The equality of ratios is called proportion.
Conversely in the proportion a : b :: c : d , the terms a and d are called extremes and b and c are called means.
If four quantities are in proportion, then
Product of extremes = Product of means .
If a : b :: c : d, then a × d = b × c
From this we have

→ Unitary method:
The method in which first we find the value of one unit and then the value of required number of units is known as unitary method.
Eg: If the cost of 8 books Rs.96, then find the cost of 15 books.
Cost of one book = 96/8 = 12 Cost of 15 books = 12 × 15 = 180
Distance travelled in a given time = speed × time From this we have

→ Percentage:
The word per cent means for every hundred or out of hundred. The word percentage is derived from the Latin language. The % symbol is uses to represent percent.
Eg: 5% is read as five percent
5% = \(\frac{5}{100}\) = 0.05
38% = \(\frac{38}{100}\) = 0.38

→ To convert a percentage into a fraction:
a) Drop the % symbol
b) Divide the number by 100
Eg: 25% = \(\frac{25}{100}\) = 0.25 = \(\frac{1}{4}\)

→ To convert a fraction into percentage:
a) Assign the percentage symbol %
b) Multiply the given fraction with 100
Eg: \(\frac{3}{4}\) = \(\frac{3}{4}\) × 100% = 75% = 0.75

Students can go through AP Board 6th Class Maths Notes Chapter 1 Numbers All Around us to understand and remember the concepts easily.

AP State Board Syllabus 6th Class Maths Notes Chapter 1 Numbers All Around us

HISTORICAL NOTES:
INDIA
→ Zero: Ancient Indians invented zero. The ancient Indian Bhakshali manuscript depicts zero, which is the recorded evidence of zero which we use today. We can also find the circular symbol ‘o’ to represent zero, the earliest epigraphical evidence at Chaturbhuj temple, Gwalior, Madhya Pradesh.

→ Number system:
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called digits. Every number is written using these digits. We can write infinitely many numbers using these digits.

→ Reading numbers:
There are two commonly used methods of numeration.
i) Indian system of numeration also called Hindu-Arabic system of numeration.
ii) International system of numeration. ‘
We read numbers using place value of digits. The place values enable us to read numbers easily and clearly.

→ Indian system:


The digits in a number are separated by commas as per the above table i.e., starting from right we place a comma after three digits and thereafter we place a comma after every two digits.

In other words, to read numbers in the Hindu-Arabic system of numeration digits are divided into periods namely units/thousands/lakhs/crores and so on .from right to left.

The value of each digit in a number depends upon its place in the given number.
As we move from right to left the place value increases by 10 times to its previous place.

Example: 75698425
Placing commas at correct positions we have
7, 56, 98, 425: 7 crores 56 lakhs 98 thousand 4 hundred and twenty five : Seven crores fifty six lakhs ninety eight thousand four hundred and twenty five

Example: 600540283
Placing commas at correct positions we have
60, 05, 40, 283: 60 crores 05 lakhs 40 thousand 2 hundred and eighty three : Sixty crores five lakhs forty thousand two hundred and eighty three

→ International system of numeration:
The digits in a number are separated by commas as per the table below i.e., starting from right we place a comma after three digits.
In other words, to read numbers in the International system of numeration digits are divided into periods namely units/thousands/millions/billions and so on from right to left.

Example: 52463801221
Placing commas at correct positions we have
52, 463, 801, 221: 52 billions 463 millions 801 thousands 2 hundred and twenty one: Fifty two billions four hundred sixty three millions eight hundred one thousands two hundred and twenty one

Example: 956785020412
Placing commas at correct positions we have
956, 785, 020, 412: 956 billions 785 millions 020 thousands 4 hundred and twelve : Nine hundred fifty six billions seven hundred eighty five millions twenty thousands four hundred and twelve

→ Comparison between Hindu-Arabic & International systems of numeration:

Indian	international
1 lakh	100 thousands
10 lakhs	1 million
1 crore.	10 millions
10 crores	100 millions
100 crores	1 billion

Also we have higher place values mentioned in Vedic numbering system.
Eka/dasa/sata/sahasra/ayuta/laksa/niyuta/koti/sanku/mahasanku/vrnda/mahavrnda/padma/mahapadma/kharva/mahakharva/samudra/ogha/mahaugha…etc

→ Large numbers used in daily life situations:

• Areas of large countries when expressed in sq.km
• To measure water flow at dams
• To measure the weights of products like food grains
• To measure the population

Face value: The face value of a digit in a number is the digit itself.
Place value of digits:The place value of a digit in a number is the product of its face, value and the place value in which it is written in the number.
Example: Face value and the place value of 5 in the number 485796 is Face value = 5
Place value = 5 x 1000 = 5000

→ Comparison of numbers:
To compare two numbers
i) Align the digits by place value
ii) Compare the digits in each place, starting from the greatest place Ascending order : Ascending order means arrangement of numbers from the smallest to the greatest.
Descending order : Descending order means the arrangement of numbers from the greatest to the smallest.
Example : 52, 235; 75, 222 ; 86, 412 ; 1, 25, 896 ; 18, 259 ; 35, 986
Ascending order: 18, 259 ; 35,986 ; 52,235 ; 75, 222 ; 86,412 & 1,25,896 Descending order: 1, 25, 896 ; 86,412 ; 75,222 ; 52,235 ; 35,986 & 18,259

→ Rounding off and Estimation of numbers:
Rules to round off a number to a given place:

Example:
Round off 6879124 to its nearest tens, hundreds, thousands, ten thousands and lakhs.
68,79,124 when rounded off to tens: 68, 79, 120
68,79,124 when rounded off to hundreds: 68, 79, 100
68,79,124 when rounded off to thousands: 68, 79, 000
68,79,124 when rounded off to ten thousands: 68, 80, 000
68,79,124 when rounded off to lakhs: 69, 00, 000
68,79,124 when rounded off to ten lakhs: 70, 00, 000

Students can go through Andhra Pradesh SCERT AP State Board Syllabus 6th Class Maths Notes Pdf in English Medium and Telugu Medium to understand and remember the concepts easily. Besides, with our AP State 6th Class Maths Notes students can have a complete revision of the subject effectively while focusing on the important chapters and topics. Students can also read AP Board 6th Class Maths Solutions for exam preparation.

AP State Board Syllabus 6th Class Maths Notes

• Chapter 1 Numbers All Around us Notes
• Chapter 2 Whole Numbers Notes
• Chapter 3 HCF & LCM Notes
• Chapter 4 Integers Notes
• Chapter 5 Fractions and Decimals Notes
• Chapter 6 Basic Arithmetic Notes
• Chapter 7 Introduction to Algebra Notes
• Chapter 8 Basic Geometric Concepts Notes
• Chapter 9 2D-3D Shapes Notes
• Chapter 10 Practical Geometry Notes
• Chapter 11 Perimeter and Area Notes
• Chapter 12 Data Handling Notes

These AP State Board Syllabus 6th Class Maths Notes provide an extra edge and help students to boost their self-confidence before appearing for their final examinations.

Regular practice with TS 6th Class Social Bits with Answers 21th Lesson Greenery in Telangana improves students’ confidence and readiness for assessments and examinations.

TS 6th Class Social Bits 20th Lesson Greenery in Telangana

Objective Type Questions

I. Choose the correct answer and write its letter in the bracket.

1. Telangana lies between these latitudes.
A) 15°46′ and 18°15′ N
B) 14°45′ and 19°47’ N
C) 15°46′ and 19°47′ N
D) 15°46′ and 19°47’ S
Answer:
C) 15°46′ and 19°47′ N

2. Telangana is situated in this plaleau
A) Malwa
B) Chota Nagpur
C) Deccan
D) Mysore
Answer:
C) Deccan

3. The rainfall of Telangana is ……….
A) Heavy
B) Scanty
C) Average
D) Vulnerable
Answer:
B) Scanty

4. The total geographical area under the forest cover should be a minimum of
A) 33%
B) 28%
C) 36%
D) 24%
Answer:
A) 33%

5. Present tree cover area of Telangana state is ……….
A) 29%
B) 24%
C) 31%
D) 22%
Answer:
B) 24%

6. Telangana State Government initiating massive plantation programme in
A) notified forest areas
B) areas outside the notified areas
C) both A & B
D) none of them
Answer:
C) both A & B

7. Massive planting activities are taken up in these areas
A) road-side avenues
B) river and canal bank
C) schools and colleges
D) all the above
Answer:
D) all the above

8. …………… seedlings are proposed to be planted in Telangana state,
A) 200 crores
B) 230 crores
C) 250 crores
D) 210 crores
Answer:
B) 230 crores

9. The number of nurseries established by the forest and other government departments
A) more than 4000
B) more than 5000
C) more than 3000
D) more than 3500
Answer:
A) more than 4000

10. These plants are being planted in the Greenery Programme
A) Medicinal plants
B) Fruit and nut bearing
C) Flowering plants
D) above all
Answer:
D) above all

11. Growing more plants and trees is useful in
A) getting rainfall
B) improving ground water level
C) reducing pollution
D) all are correct
Answer:
D) all are correct

12. This forest produce is available from forests
A) bamboo
B) honey
C) timber
D) all are correct
Answer:
D) all are correct

13. The real problem is
A) planting the sapplings
B) protecting the sapplings
C) both of them
D) none of them
Answer:
B) protecting the sapplings

14. Jadav Molai Payeng belongs to
A) Assom
B) Bihar
C) Manipur
D) Jharkhand
Answer:
A) Assom

15. Jadav Molai Payeng is called as
A) Iron man of India
B) Iron man of Assom
C) The Forest Man of India
D) The Forest Man of Assom
Answer:
C) The Forest Man of India

16. Greenery programme by the schools is being encouraged by state government by giving
A) awards
B) rewards
C) punishments
D) above all
Answer:
B) rewards

17. “Each one, plant one” programme is related to
A) Schools
B) Offices
C) Factories
D) Villages
Answer:
A) Schools

18. The massive programme of planting is achieved by involving
A) Teachers and students
B) Parents
C) Community
D) Above all
Answer:
D) Above all

19. Daripalli Ramaiah is popularly known as
A) Dhanyajeevi
B) Vanajeevi
C) Raithu mitra
D) Raithu bandhu
Answer:
B) Vanajeevi

20. Who transformed the slogan ‘Plant a tree and save a life’ ?
A) Rangaiah
B) Ramaiah
C) Kotaiah
D) None of above
Answer:
B) Ramaiah

21. Vanajeevi Ramaiah won the prestigious award
A) Padma Bhushan
B) Padma Vibhushan
C) Padma Shree
D) Nobel
Answer:
C) Padma Shree

22. Longitudinal extent of Telangana state is
A) 77° 16′ and 18°43′ E
B) 88°16’ and 19° 35′ E
C) 77° 16′ and 81°43’ E
D) 88° 16’ and 90°35′ N
Answer:
C) 77° 16′ and 81°43’ E

23. Daripalli Ramaiah is popularly known as
A) Vana Ramaiah
B) veera Ramaiah
C) Jeevi Ramaiah
D) Venajeevi Ramaiah
Answer:
D) Venajeevi Ramaiah

24. The climate of Telangana is
A) Hot and dry
B) Very cool
C) Temperate
D) None
Answer:
A) Hot and dry

25. Telangana state is situated in zone.
A) Arid
B) Semi-arid
C) Dry-humid
D) Moist
Answer:
B) Semi-arid

26. In Assom social forestry program was held in
A) 1976
B) 1978
C) 1979
D) 1980
Answer:
C) 1979

27. Who is known as “The Forest Man of India” ?
A) K.C.R,
B) K.T.R.
C) Jadav Molai Payeng
D) Subrahmanyam
Answer:
C) Jadav Molai Payeng

28. Jadav Molai Payeng received this Award
A) Padma Bhushan
B) Padma Shree
C) Bharat Ratna
D) None
Answer:
B) Padma Shree

29. This programme is initiated by schools in Telangana for greenery.
A) Each one teach one
B) Each one plant one
C) Each one save one
D) None
Answer:
B) Each one plant one

30. The famous slogan “Plant a tree and save a life” given by
A) Daripalli Ramaiah
B) Rama Rao
C) Subbamma
D) Rajendra
Answer:
A) Daripalli Ramaiah

31. He is popularly known as Vanajeevi
A) D. Ramaiah
B) Rajendra
C) K.C.R.
D) K.T.R.
Answer:
A) D. Ramaiah

Regular practice with TS 6th Class Social Bits with Answers 20th Lesson Sculptures and Buildings improves students’ confidence and readiness for assessments and examinations.

TS 6th Class Social Bits 20th Lesson Sculptures and Buildings

Objective Type Questions

I. Choose the correct answer and write its letter in the bracket.

1. Archaeologists have found remains of Stupas from
A) Uttar Pradesh
B) Maharashtra
C) Andhra Pradesh
D) Assom
Answer:
C) Andhra Pradesh

2. ……… was the famous Buddhist monastery at that time.
A) Takshasila
B) Patna
C) Varanasi
D) Naianda
Answer:
D) Naianda

3. ………….. is the capital city of Ikshvaku Kings.
A) Vijayapuri
B) Nagarjunakonda
C) Vijayawada
D) Amaravathi
Answer:
A) Vijayapuri

4. Sanchi stupa is in ……………
A) Madhya Pradesh
B) Maharashtra
C) Andhra Pradesh
D) Assom
Answer:
A) Madhya Pradesh

5. Karle chaitya was built about …………. years ago.
A) 2100
B) 2000
C) 2200
D) 2300
Answer:
A) 2100

6. It was only 10,000 years ago that people began agriculture and animal herding in modem …………
A) Syria and Palestine
B) Israel and Palestine
C) Arabia and Palestine
D) Baluchistan
Answer:
A) Syria and Palestine

7. 5000 years ago, in Indian subcontinent in north – western areas of this regions people began agriculture and adopted village life.
A) Baluchistan
B) Sindh & Punjab.
C) Gujarat
D) All the above
Answer:
D) All the above

8. The famous old cities in Indian sub-continent
A) Harappa-Mohenjodaro
B) Kalibhangan
C) Lothal
D) All the above
Answer:
D) All the above

9. In India, this culture is called as most of the important sites of this culture were situated in the plains watered by River Indus and its tributaries.
A) Harappan civilisation
B) Mohenjodaro culture
C) Indus valley civilisation
D) All the above
Answer:
C) Indus valley civilisation

10. By ………….. we mean a place, where a large number of people live who do not depend on either agriculture or hunting or gathering for their liveihood
A) villages
B) janapadas
C) towns
D) cities
Answer:
C) towns

11. The fecial feature of Harappan buildings
A) They used good baked bricks of a standard size and shape
B) They used stones
C) They used lime bhattis
D) None
Answer:
A) They used good baked bricks of a standard size and shape

12. The Harappan people used tools made of these material for their daily needs.
A) stone and wood
B) stone and copper
C) copper and iron
D) gold and silver
Answer:
A) stone and wood

13. The Harappan people used very fine and long stone blades for cutting, finely carved …………. for trading, beautiful and’ colourful polished stone beads for
oranamants weights etc.
A) stone seals
B) stone toys
C) stone paths
D) none
Answer:
A) stone seals

14. They also used …………. to make objects of daily use like ladles, spoons and bangles.
A) sea shells
B) sea saws
C) both A & B
D) none
Answer:
C) both A & B

15. Even though inscriptions of Harappa people are available, they are not known
A) how to read
B) how to write
C) how to understand
D) None
Answer:
A) how to read

16. It appears that some ………….. years after the great Harappan cities were, the towns declined. Trade and artisanal production declined and people moved out of these cities to villages.
A) 500
B) 700
C) 800
D) 900
Answer:
B) 700

17. In olden days, in many regions large and polished pillars were set up by this emperor.
A) Ashoka
B) Chandragupta.
C) Kanishka
D) Bimbisara
Answer:
A) Ashoka

18. The first one of the royal symbol
A) Sanchi
B) Saranath
C) Kausambi
D) Lahore
Answer:
B) Saranath

19. Hemisphere constructed on a platform is ……..
A) Vihara
B) Pillar
C) Picture
D) Pit
Answer:
B) Pillar

20. The stupas in Ashoka period were made of …..
A) Mud
B) Brick
C) Wood
D) All of the above
Answer:
D) All of the above

21. The pillar above the stupa is called as
A) A bridge between earth and heaven
B) A bridge between earth and sky
C) A bridge between earth and hell
D) A bridge between earth and native
Answer:
A) A bridge between earth and heaven

22. The remains of stupas in Andhra Pradesh were found at
A) Amaravathi, Bhattiprolu
B) Ramathirtham, Salihundam
C) Both A & B
D) None
Answer:
C) Both A & B

23. It is believed the dome of the stupa represents the
A) heaven
B) earth
C) universe
D) bridge
Answer:
C) universe

24. In A.P, a crystal box with the relic of Buddha near this stupa.
A) Bhattiprolu
B) Ramathirtham
C) Salihundam
D) Amaravathi
Answer:
A) Bhattiprolu

25. The famous stupa in Andhra Pradesh
A) Amaravatl
B) Ramathirtham
C) Salihundam
D) Bhattiprolu
Answer:
A) Amaravatl

26. 1900 years ago this was very excellent with silpa thoranas.
A) Amaravathi
B) Bhattiprolu
C) Ramathirtham
D) Salihundam
A) Amaravathi

27. …………. used in the construction of chaityas.
A) Mud
B) Wood
C) Stone
D) All the above
Answer:
B) Wood

28. The old stone temple was safe here in Madhaya Pradesh
A) Sanchi
B) Saranath
C) Kanheri
D) Karle
Answer:
D) Karle

29. These are best examples for ancient sculptures in south India.
A) Nagarjuna Hill
B) Amaravathi
C) Both A & B
D) Salihundam
Answer:
A) Nagarjuna Hill

30. This Barber got permission to enter in Buddhist Sangha
A) Upali
B) Amrapali
C) Thadhagath
D) Thadhatmakar
Answer:
B) Amrapali

31. The sculpture like Gandhara, Mathura, Saranath can be seen here.
A) Amaravathi
B) Nagarjuna Hill
C) Bhattiprolu
D) Salihundam
Answer:
C) Bhattiprolu

32. The Chaitya that was constructed 2100 years ago
A) Karle
B) Bhaja
C) Kanheri
D) Nasik
Answer:
A) Karle

33. These viharas were constructed with bricks or stones.
A) Takshasila
B) Nagarjuna Hill
C) Nalanda
D) All the above
Answer:
D) All the above

34. These Chinese travellers visited India to visit the areas related to Buddha and famous Buddhist vidya pheets.
A) Fa-hi-an
B) Itsing
C) Hu-en-Tsang
D) All the above
Answer:
D) All the above

35. We can see viharas curved from stone here.
A) Karle Bhaja
B) Kanheri
C) Nasik
D) All the above
Answer:
A) Karle Bhaja

36. Match the following
1) Girl standing ( ) A) Bronze statue
2) A bull ( ) B) Terracota
3) Mother ( ) C) Harappan goddess sea

A) A – 1, B – 2, C – 3
B) A – 3, B – 1, C – 2
C) A – 1, B – 3, C – 2
D) A – 3,B – 2, C – 1
Answer:
C) A – 1, B – 3, C – 2

37.
At present lion capital is in
A) Sanchi
B) Gaya
C) Saranath
D) Delhi
Answer:
C) Saranath

38.
Whose potrait is this?
A) Ashoka
B) Kanishka
C) Harsha
D) Guptas
Answer:
A) Ashoka

39.
Karle chaitya was built ….. years ago
A) 2100
B) 3100
C) 2500
D) 2000
Answer:
A) 2100

40. Viharas and Chaityas are belongs to
A) Buddism
B) Sikkism
C) Jainism
D) Hinduism
Answer:
A) Buddism

41. Fa-hi-an, Itsing belonged to
A) Japan
B) Tibet
C) China
D) India
Answer:
C) China

42. Nalanda in ……… is the most famous Buddhist monastery.
A) Andhra Pradesh
B) Karnataka
C) Kerala
D) Bihar
Answer:
D) Bihar

43. Vijayapuri is the capital city of kings.
A) Chola
B) Mauryan
C) Chera
D) Ikshvaku
Answer:
D) Ikshvaku

44. A usually had small rooms around an open courtyard.
A) Stupa
B) Chaitya
C) Vihara
D) Pillar
Answer:
C) Vihara

45. The pillars and the Lion Capital represent the power and majesty of the …… emperors.
A) Mauryan
B) Satavahanas
C) Ikshvaku
D) Magadha
Answer:
C) Ikshvaku