245 Questions
What is the collection of numbers represented by the symbol N?
Natural numbers
What happens to the collection of numbers when you add zero to the natural numbers?
It becomes a collection of whole numbers
What is the symbol used to denote the collection of whole numbers?
W
What type of numbers stretch in front of you on the number line?
Negative integers
What is true about the list of natural numbers?
It is an infinite list
What is the starting point on the number line?
0
What happens when you walk all the way back on the number line?
You reach zero
What is the purpose of the bag in the context of collecting numbers?
To store any type of number
What is the value of (5 + 7) (2 + 5)?
72
What is the result of simplifying (5 + 5) (5 - 5)?
20
What is the value of (3 + 7) (11 - 7)?
38
What is the purpose of rationalizing the denominator in an expression?
To make the denominator a rational number
What is the definition of 'simplifying' an expression in the context of the example above?
Writing the expression as the sum of a rational and an irrational number
What is the value of (11 - 7) (11 + 7)?
4
What is the identity involving square roots used to rationalize the denominator?
Not specified in the content
What is the purpose of using the number line to visualize the expression ⋅ ?
To determine if the expression is rational or irrational
What is the purpose of rationalising the denominator?
To make the denominator a rational number
What is the correct implementation of the identity (iv) to rationalise the denominator of 1/(2+3)?
Multiply and divide by (2+3)
What is the equivalent expression of 1/2 in which the denominator is a rational number?
1/(2) × (2/2)
What is the value of the expression 1/2 + 1/2?
1
Why do we multiply by 2/2 to rationalise the denominator of 1/2?
Because 2/2 is equal to 1
What is the correct rationalisation of the denominator of 1/(3-5)?
Multiply and divide by (3+5)
What is the purpose of using the identities (iii) and (iv) in rationalising the denominator?
To make the denominator a rational number
Why do we rationalise the denominator of an expression?
To make it easier to work with the expression
What is the characteristic of the decimal expansion of the rational number 10/3?
Non-terminating recurring
What is the purpose of the bar above the digits in the decimal expansion of a rational number?
To indicate the block of digits that repeats
What can be concluded about the decimal expansion of a number like 3.142678?
It is a terminating decimal expansion
What is the general form of a rational number with a terminating decimal expansion?
p/q where q is not equal to 0
What is the characteristic of the decimal expansion of the rational number 1/7?
Non-terminating recurring
What is the general form of a rational number with a non-terminating recurring decimal expansion?
p/q where q is not equal to 0
What can be concluded about a number like 1.272727...?
It is a rational number
What is the purpose of expressing a rational number in the form p/q?
To show that the number is a rational number
What is the simplified form of the expression (3 + 3) (2 + 2)?
24
Why does the definition of π as a ratio of circumference to diameter seem to contradict the fact that π is irrational?
The definition of π is only an approximation.
What is the value of the expression (52)7?
514
How do you rationalize the denominator of the expression 1/√(7 - 6)?
Multiply the numerator and denominator by √(7 - 6)
What is the value of the expression 73 × 93?
633
What is the law of exponents that states a^m × a^n = a^(m + n)?
The law of exponents for multiplication
What is the value of the expression 2310/237?
233
What is the purpose of rationalizing the denominator of an algebraic expression?
To simplify the expression
What is the main issue with the histogram prepared by the student?
The areas of the rectangles are not proportional to the frequencies
What is the minimum class-size in the given table?
10
Why do we need to modify the lengths of the rectangles in the histogram?
To make the areas of the rectangles proportional to the frequencies
What should be the lengths of the rectangles modified to be proportional to?
The class-size
What is the purpose of selecting a class interval with the minimum class-size?
To modify the lengths of the rectangles
What is the mistake in the histogram prepared by the student?
The widths of the rectangles are varying
What is the correct representation of the data from the table?
A histogram with modified lengths of the rectangles
Why does the histogram give a misleading picture of the data?
Because the areas of the rectangles are not proportional to the frequencies
What is the purpose of representing the data in a histogram?
To represent the data in a more detailed and precise manner
Why is a kink or break marked on the horizontal axis in the histogram?
Because the first class interval starts from 30.5 and not zero
What is the purpose of choosing a suitable scale for the vertical axis?
To accommodate the maximum frequency
What is the difference between a bar graph and a histogram?
A bar graph is used for discrete class intervals, while a histogram is used for continuous class intervals
What is the advantage of using a histogram over a tabular form?
It provides a better visual representation of the data
What is the purpose of representing the weights on the horizontal axis?
To represent the data in a more detailed and precise manner
Why is the scale of the horizontal axis chosen as 1 cm = 5 kg?
To suit the data range
What is the purpose of marking the total frequency at the top of the histogram?
There is no mention of marking the total frequency at the top of the histogram
What is the purpose of plotting the point A(135, 0) in constructing a frequency polygon?
To indicate the zero frequency of the class 130-140
What is the advantage of using a frequency polygon to compare two sets of data?
It allows us to compare the performance of two different sections of the same class
What is the characteristic of the data for which a frequency polygon is used?
The data is continuous and very large
What is the correct order of the points plotted in the frequency polygon?
A, B, C, D, E, F, G, H
What is the purpose of joining the points plotted in the frequency polygon by line segments?
To form a continuous curve representing the distribution
What is the value of the frequency corresponding to the class-mark 185?
6
What is the total frequency of the distribution?
52
What is the class-mark of the class 160-170?
165
What is the purpose of making the class intervals continuous in the histogram of the given data?
To make the histogram more informative
What is the advantage of using a histogram to represent the data on the length of leaves?
It shows the distribution of the data more clearly
What is the number of lamps that have a life time of more than 700 hours?
146
What is the main disadvantage of concluding that the maximum number of leaves are 153 mm long?
It is not supported by the given data
What is the purpose of using a histogram to represent the data on the life times of neon lamps?
To show the distribution of the data
What is the limitation of using a histogram to represent the data on the length of leaves?
It does not provide information about individual data points
What is the advantage of using a histogram to compare the data on the length of leaves and the life times of neon lamps?
It allows for a direct comparison of the data
What is the purpose of modifying the lengths of the rectangles in the histogram?
To adjust for the different class sizes
What is the purpose of finding the mid-point of the class preceding 0-10 in the given frequency distribution table?
To mark the end point of the frequency polygon on the negative direction of the horizontal axis
What is the term used to describe the mid-points of the class-intervals used in the data?
Class-marks
What is the advantage of drawing a frequency polygon independently without drawing a histogram?
It requires only the mid-points of the class-intervals
What is the point where the line segment meets the vertical axis marked as in the frequency polygon?
A
What is the purpose of extending the horizontal axis in the negative direction?
To find the class preceding 0-10
What is the sequence of points in the frequency polygon?
OABCDEFGHIJKL
Why is the mid-point of the class succeeding the last class of the given data found?
To find the end point of the frequency polygon on the positive direction of the horizontal axis
What is the purpose of marking the mid-points of the tops of the rectangles as B, C, D, E, F, G, H, I, J, K?
To draw the histogram for the given data
What is the main reason for plotting the point A(135, 0) in the frequency polygon?
To maintain continuity of the polygon
What is the primary use of frequency polygons in statistics?
To analyze continuous large data sets
What is the purpose of joining the points A, B, C, D, E, F, and G by line segments in the frequency polygon?
To create a visual representation of the data
Why is the point H(205, 0) plotted in the frequency polygon?
To maintain continuity of the polygon
What is the advantage of using frequency polygons over other graphical representations?
They are useful for comparing large continuous data sets
What is the relationship between the class-marks and the frequencies in the frequency polygon?
The frequencies are proportional to the class-marks
How many points are plotted to construct the frequency polygon?
8
Why do we add class intervals with zero frequency at the beginning and end of the frequency polygon?
To ensure the area of the polygon is the same as the area of the histogram
What is the purpose of joining the mid-points of the upper sides of the adjacent rectangles of a histogram?
To create a polygon
What is the scale used to plot the frequencies in the frequency polygon?
Vertical axis
What is the condition required to make the area of the frequency polygon the same as the area of the histogram?
Addition of class intervals with zero frequency
Why do we assume a class interval with frequency zero before the lowest class and one after the highest class?
To ensure the area of the polygon is the same as the area of the histogram
What is the purpose of using line segments to join the mid-points of the upper sides of the adjacent rectangles of a histogram?
To create a polygon
What is the property of congruent triangles used to prove that the area of the frequency polygon is the same as the area of the histogram?
Area is equal
What is the condition required to complete the frequency polygon when there is no class preceding the first class?
Addition of class intervals with zero frequency
What is the purpose of using a frequency polygon to represent quantitative data and its frequencies?
To provide a more visual representation of the data
What is the most suitable graphical representation for the data of the length of 40 leaves of a plant?
Histogram
What is the correct conclusion about the maximum number of leaves?
The maximum number of leaves are within the range of 145-153 mm.
What is the total number of lamps with a life time of more than 600 hours?
148
Why is it necessary to make the class intervals continuous in the histogram?
To ensure that the data is represented accurately
What is the purpose of modifying the lengths of the rectangles in the histogram?
To make the lengths of the rectangles proportional to the frequencies
What is the mistake in the histogram prepared by the student?
The lengths of the rectangles are not proportional to the frequencies
Why does the histogram give a misleading picture of the data?
The frequencies are not accurately represented
What is the purpose of representing the data in a histogram?
To visualize the distribution of the data
What is the approximate percentage of female fatality rate due to reproductive health conditions?
31.8%
What is the relation between the number of girls and boys in different sections of Indian society?
The number of girls is proportional to the number of boys
Which condition is the second leading cause of women's ill health and death worldwide?
Neuropsychiatric conditions
What is the approximate percentage of female fatality rate due to 'Other causes'?
22%
What is the major cause of women's ill health and death worldwide?
Reproductive health conditions
What is the approximate percentage of female fatality rate due to Cardiovascular conditions and Respiratory conditions combined?
8.4%
What is the most suitable graph to represent the data of runs scored by two teams A and B on the first 60 balls in a cricket match?
Frequency polygon
What is the advantage of representing the marks of the students of both sections on the same graph by two frequency polygons?
To compare the performance of the two sections
What is the main difference between the frequency polygons of the two teams A and B?
The frequency of the runs scored
What can be inferred about the performance of the students in Section A from the frequency polygon?
The students performed poorly in the higher marks range
What is the purpose of using frequency polygons to represent the data of the students' marks?
To compare the performance of the two sections
What is the advantage of using frequency polygons to represent the data of the runs scored by the two teams?
It allows for the comparison of the performance of the two teams
What can be inferred about the performance of Team A from the frequency polygon?
Team A performed poorly in the initial overs
What is the similarity between the frequency polygons of the two teams A and B?
The number of intervals
What is the velocity of an object if it travels 96 m in 2 s?
20 m/s
What is the force required to produce an acceleration of 1.944 m/s² on a mass of 35000 kg?
68000 N
What is the maximum height reached by a ball thrown upwards with an initial velocity of 29.4 m/s?
44.1 m
What is the change in kinetic energy of an object that moves from rest to a velocity of 3.07 km/s?
4000 J
What is the gravitational force between two objects of mass 500 kg and 800 kg, separated by a distance of 1.944 m?
3000 N
What is the weight of an object on the moon if its weight on earth is 98 N?
16.3 N
What is the total time taken by an object to travel from the ground to a maximum height of 122.5 m and back to the ground?
10 s
What is the acceleration of an object that experiences a force of 240 N and has a mass of 10 kg?
6 m/s²
What is the formula for the compound formed by the reaction of magnesium and chlorine?
MgCl2
What is the mass of calcium carbonate (CaCO3) required to produce 26 g of calcium oxide (CaO)?
39 g
What is the valency of the element lithium?
1
What is the relationship between the elements X and Y if the mass number of X is 12 and the mass number of Y is 14?
Isotopes
What is the atomic number of the element fluorine?
9
What is the average speed of an object that travels 2400 m in 100 s?
24 m/s
What is the displacement of an object that travels from a point 2000 m east to a point 2200 m east?
200 m
What is the average velocity of an object that travels 2400 m in 100 s with a displacement of 200 m?
2.00 m/s
What is the correct formula of Calcium Carbonate?
CaCO3
What is the mass of Calcium Oxide?
26 g
What is the atomic mass number of Fluorine?
19
What is the correct description of the species with atomic number 12?
Magnesium
What is the average speed of an object?
24 km h
What is the correct displacement of an object?
200 m^-1
What is the correct atomic mass number of Sulphur?
32
What is the correct relationship between X and Y if their mass numbers are 12 and 14 respectively?
Isotopes
What is the velocity of an object if it travels 96 meters in 2 seconds?
20 m/s
A force of 2500 N is applied to an object. What is the resulting acceleration?
5 m/s
An object is projected upwards with an initial velocity of 29.4 m/s. What is its maximum height?
44.1 m
A packet is submerged in water. What will happen to the packet?
It will sink
A body is moving with a constant velocity. What is the net force acting on the body?
Zero
What is the gravitational force between two objects of mass 500 kg and 800 kg, separated by a distance of 2 m?
6000 N
A car is moving with a velocity of 3.07 km/s. What is its acceleration if it is subjected to a force of 2550 N?
5 m/s
What is the total energy of an object of mass 10 kg moving with a velocity of 10 m/s?
1000 J
What is the molecular formula of magnesium chloride?
MgCl2
What is the mass of calcium carbonate (CaCO3) if the mass of calcium is 26 g?
124 g
What is the relationship between X and Y if the mass number of X is 12 and Y is 14?
Isotopes
What is the valency of lithium?
1
What is the symbol of the element with atomic number 9 and mass number 19?
Fluorine
What is the average speed of an object if it travels a distance of 2200 m in a certain time and its displacement is 200 m?
2.00 m/s
What is the atomic number of sulphur if its mass number is 32?
16
What is the name of the element with atomic number 12 and mass number 24?
Magnesium
What is the velocity of the object if it travels 96 m in 2 s?
20 m/s
What is the net force acting on an object if it experiences a force of 2550 N in the direction of motion and a force of 200 N in the opposite direction?
2350 N
What is the weight of an object on the moon if it weighs 98 N on earth?
16.3 N
What is the total energy of an object if it has a kinetic energy of 2000 J and a potential energy of 1000 J?
3000 J
What is the period of a pendulum if it completes 22,600 oscillations in one hour?
0.5 s
What is the acceleration of an object if it experiences a force of 500 N and its mass is 10 kg?
5 m/s^2
What is the gravitational force between two objects if one object has a mass of 10 kg and the other object has a mass of 20 kg, and the distance between them is 0.5 m?
39.2 N
What is the maximum height reached by a projectile if it is thrown with an initial velocity of 29.4 m/s and the acceleration due to gravity is 9.8 m/s^2?
44.1 m
What is the main reason for the pressure exerted by a gas on the walls of its container?
The random movement of gas particles
What can be inferred about the motion of particles in the gaseous state?
The particles move randomly at high speed
What is the effect of compressing a gas on the motion of its particles?
The particles collide more frequently
What is the arrangement of particles in a gas?
Particles are far apart
What happens to the density of a substance when it changes from a solid to a gas?
Density decreases
What is the correct order of increasing density?
air, exhaust from chimneys, cotton, honey, water, chalk, iron
What is the purpose of applying vaseline on the pistons before inserting them into the syringes?
To decrease the friction
What can be observed when trying to compress the content by pushing the piston in each syringe?
The piston is easily pushed in the gaseous state
What is the state of matter where the forces of attraction between particles are minimum?
Gas
Which process involves the change of solid state directly to gaseous state without going through liquid state?
Sublimation
What is the characteristic of the arrangement of particles in gases?
Randomly arranged
What is the term for the change of gaseous state directly to solid state without going through liquid state?
Deposition
Which process is a surface phenomenon?
Evaporation
What is the characteristic of the spaces in between the constituent particles in gases?
Maximum
What is the term for the change of state from liquid to vapour that occurs in bulk?
Boiling
What is the general term for the change of state from one phase to another?
Interconversion
What is the primary reason why solid carbon dioxide is also known as dry ice?
It changes directly from solid to gas without changing into liquid state
What does the experiment with camphor and an inverted funnel demonstrate?
Sublimation of camphor
What is the location of the Publication Division mentioned in the publication?
New Delhi
What is the primary factor that determines the state of a substance?
Pressure and temperature
Who is the Head of the Publication Division?
Anup Kumar Rajput
What is the term for the change of state from solid to gas without changing into liquid?
Sublimation
What is the price of the publication?
₹ 155.00
What is the term for the change of state from gas to solid without changing into liquid?
Deposition
What is the recommended approach to education according to the National Curriculum Framework (NCF) 2005?
Linking school life to life outside school
What is the reason why solid carbon dioxide changes directly into gas on decrease of pressure to 1 atmosphere?
It is stored under high pressure
What is the primary difference between the various states of matter?
The difference in the distances between the constituent particles
Where is the publication printed?
SDA Print ‘N’ Pack, Loni, Ghaziabad
What is the effect of applying pressure and reducing temperature on a gas?
It gets liquefied
What is the type of paper used for printing the publication?
80 GSM paper with NCERT watermark
Who is the Chief Business Manager (In charge) of the publication?
Amitabh Kumar
What is the phone number of the Publication Division in Kolkata?
033-25530454
What is the name of the scientist after whom the phenomenon of scattering of light is named?
Tyndall
What is the characteristic of a suspension?
Heterogeneous mixture
What is the reason for the Tyndall effect observed when sunlight passes through the canopy of a dense forest?
Presence of water droplets in the mist
What is the characteristic of the particles in a suspension?
They are visible to the naked eye
What is the name of the phenomenon observed when a fine beam of light enters a room through a small hole?
Tyndall effect
What is the type of mixture in which the solute particles do not dissolve but remain suspended throughout the bulk of the medium?
Suspension
What is the reason for the Tyndall effect observed in a mixture of water and milk?
Presence of particles of milk in water
What is the characteristic of colloids?
They are big enough to scatter a beam of light
What is the primary difference between a mixture and a solution?
A mixture is a heterogeneous mixture, while a solution is a homogeneous mixture
What is the term for the particles in a suspension that are visible to the naked eye?
Dispersed phase
What is the characteristic of a colloid?
Particles are not visible to the naked eye, but can scatter light
What is the definition of an element?
A form of matter that cannot be broken down by chemical reactions into simpler substances
What is the term for the major component of a solution?
Solvent
What is the characteristic of a pure substance?
It has a fixed composition
What is the term for the amount of solute present per unit volume or per unit mass of a solution?
Concentration
What is the main difference between a compound and a mixture?
A compound has a fixed composition, while a mixture has a variable composition
What is the main characteristic of matter that is discussed in the chapter?
It is made up of particles
What is the concept used to explain the spread of salt or sugar throughout the water in the experiment?
The concept of matter being made up of particles
What is the significance of the experiment where salt or sugar is dissolved in water?
It shows that matter is made up of particles
What is the common classification of matter discussed in the chapter?
The five basic elements of ancient Indian philosophers
What is the main idea behind the concept of the five basic elements of ancient Indian philosophers?
That everything is made up of five basic elements
What is the significance of the statement 'everything is made up of matter'?
It means that everything is made up of particles
What is the main idea behind the discussion of the five basic elements of ancient Indian philosophers and the similar classification of matter by ancient Greek philosophers?
To show that ancient philosophers had a similar understanding of matter
What is the purpose of discussing the concept of matter in the chapter?
To understand the surroundings and the concept of unity of the nation
What is the primary reason why the shape of each individual sugar or salt crystal remains fixed?
Because of the fixed arrangement of particles in the crystal
What is the primary goal of the National Policy on Education (1986) in the context of the child-centred system of education?
To encourage children to reflect on their own learning and pursue imaginative activities
What is the characteristic of the particles of matter that enables a diver to cut through water in a swimming pool?
The particles can change shape easily
What happens to the air trapped in the minute holes of a sponge when it is pressed?
The air is released
What is the main reason for not treating the prescribed textbook as the sole basis of examination?
To give importance to other resources and sites of learning
What is the role of school principals and teachers in implementing the National Policy on Education (1986)?
To take steps to encourage children to reflect on their own learning and pursue imaginative activities
What is the primary reason why the three human chains are able to withstand the force of the fourth group of students?
The students are touching each other with only their finger tips
What is the significance of flexibility in the daily time-table in schools?
It is necessary for effective implementation of the annual calendar
What is the characteristic of the particles of matter that enables the fourth group of students to break the human chains?
The particles can change shape easily
What is the primary reason why cold food does not have a strong smell?
The particles of matter are not moving quickly
What is the primary aim of the syllabi and textbooks developed on the basis of NCF?
To implement the basic idea of a child-centred system of education
What is the consequence of treating children as receivers of a fixed body of knowledge?
It promotes rote learning and sharp boundaries between different subject areas
What is the characteristic of the particles of matter that enables us to observe different types of matter around us?
The particles have different characteristics
What is the primary reason why the human chains are formed by touching each other with only their finger tips?
To make the chains stronger
What is the significance of recognizing children as participants in learning?
It encourages children to pursue imaginative activities
What is the purpose of restructuring and reorienting knowledge at different stages in the syllabi and textbooks developed on the basis of NCF?
To address the problem of curricular burden
What is the primary reason why a colloidal solution appears to be homogeneous?
Because of the uniform distribution of colloidal particles
What is the main difference between a suspension and a colloidal solution?
Particulate size
Why can't we see colloidal particles with our naked eyes?
Because they are too small
What is the concentration of the solution in terms of mass percentage?
11.11%
Why do colloidal particles scatter light?
Because they are too small
What is true about a colloidal solution?
It is a heterogeneous mixture
What happens to a suspension when the particles settle down?
It breaks and does not scatter light anymore
Study Notes
Number Systems
- The number line is a visual representation of numbers, and it extends infinitely in both positive and negative directions.
- Natural numbers (N) are a set of numbers that start from 1 and go on forever, represented by the symbol N.
- Whole numbers (W) are a set of numbers that include natural numbers and 0, represented by the symbol W.
- Negative integers are a set of numbers that extend infinitely in the negative direction.
Rational Numbers
- Rational numbers are numbers that can be expressed as a fraction (p/q), where p and q are integers and q ≠ 0.
- Examples of rational numbers include 3.142678, 0.142857, and 1.272727...
- Terminating decimals are decimals that end after a finite number of digits, whereas non-terminating recurring decimals are decimals that go on indefinitely but have a repeating pattern.
- Rational numbers can be expressed as a finite decimal or a non-terminating recurring decimal.
Irrational Numbers
- Irrational numbers are numbers that cannot be expressed as a fraction (p/q), where p and q are integers and q ≠ 0.
- Examples of irrational numbers include π and √2.
- Irrational numbers can be represented on the number line, but they cannot be expressed as a finite decimal or a non-terminating recurring decimal.
Simplifying Expressions
- Simplifying expressions involves combining like terms and using the rules of algebra to simplify the expression.
- Examples of simplifying expressions include (5 + 7)(2 + 5) and (3 + 7)(11 - 7).
Rationalizing Denominators
- Rationalizing denominators involves multiplying the numerator and denominator of a fraction by a suitable number to make the denominator a rational number.
- Examples of rationalizing denominators include rationalizing the denominator of √2 and 1/(2 + √3).
Laws of Exponents
- The laws of exponents are rules for simplifying expressions involving exponents, such as a^m × a^n = a^(m+n).
- Examples of using the laws of exponents include simplifying 17^2 × 17^5 and (5^2)^7.
Visualizing Data
- Data can be visualized using bar graphs, which are better representations of data than tables
- Bar graphs can be used to easily compare data at a glance
Histograms
- Histograms are a form of representation used for continuous class intervals
- They are similar to bar graphs, but are used for continuous data
- The widths of the rectangles in a histogram are proportional to the class sizes, and the areas of the rectangles are proportional to the frequencies
- When the widths of the rectangles are varying, the histogram may not give a correct picture, and modifications need to be made to the lengths of the rectangles
Frequency Distribution Tables
- Frequency distribution tables can be represented graphically using histograms
- The weights of 36 students are represented in a frequency distribution table, which can be graphically represented as a histogram
- The horizontal axis represents the weights, and the vertical axis represents the number of students
Drawbacks of Histograms
- Histograms can give a misleading picture if the widths of the rectangles are varying
- In such cases, modifications need to be made to the lengths of the rectangles to ensure that the areas are proportional to the frequencies
Frequency Polygons
- Frequency polygons are used to represent continuous data
- They can be drawn independently without drawing histograms
- The mid-points of the class-intervals are called class-marks, and are used to draw the frequency polygon
- Frequency polygons are useful for comparing two different sets of data of the same nature
Drawing Frequency Polygons
- To draw a frequency polygon, the class-marks are plotted along the horizontal axis, and the frequencies along the vertical axis
- The points are then joined by line segments to form the frequency polygon
- The points corresponding to the class-marks of the classes preceding and succeeding the given data are also plotted with zero frequency
Histograms and Frequency Polygons
- A frequency polygon is a visual way of representing quantitative data and its frequencies
- To create a frequency polygon, join the mid-points of the upper sides of adjacent rectangles in a histogram by line segments
- The frequency polygon can be completed by assuming two class intervals with zero frequency, one before the lowest class and one after the highest class
- The area of the frequency polygon is the same as the area of the histogram due to the properties of congruent triangles
Drawing Frequency Polygons
- Frequency polygons are used when the data is continuous and very large
- To draw a frequency polygon, plot class-marks on the horizontal axis, frequencies on the vertical axis, and then join the points by line segments
- The points corresponding to class-marks with zero frequency should also be plotted
Example of Drawing a Frequency Polygon
- Example 4: drawing a frequency polygon for the marks obtained by 51 students in a test
- The class-marks are plotted along the horizontal axis, frequencies along the vertical axis, and the points are joined by line segments
- The points corresponding to class-marks with zero frequency are also plotted
Other Graphical Representations
- Histograms can be used to represent data graphically
- Frequency polygons can be used to compare two different sets of data of the same nature
- Other graphical representations, such as frequency polygons, can be used depending on the nature of the data
Chapter 3: Compounds and Molecules
- MgCl2 is a compound.
- CaO is a compound.
- Cu(NO3)2 is a compound.
- AlCl3 is a compound.
- CaCO3 is a compound.
- Calcium and oxygen are components of a compound.
- Hydrogen and bromine are components of a compound.
- Sodium, hydrogen, carbon, and oxygen are components of a compound.
- Potassium, sulfur, and oxygen are components of a compound.
- The mass of a substance can be calculated (e.g., 26 g, 256 g, 124 g, 36.5 g, 63 g).
Chapter 4: Atomic Structure
- Atomic mass of an element is 80.006.
- Valency of an element can be 1 (e.g., lithium).
- Isotopes have different mass numbers (e.g., X = 12, Y = 14).
- True or false statements about atomic structure can be evaluated.
Chapter 7: Motion
- Distance and displacement can be calculated (e.g., distance = 2200 m, displacement = 200 m).
- Average speed and average velocity can be calculated (e.g., 2.00 m/s, 1.90 m/s).
- Distance traveled and velocity can be calculated (e.g., 96 m, 20 m/s).
Chapter 8: Forces
- Force and acceleration can be calculated (e.g., 2 m/s², 14000 N).
- Frictional force can be calculated (e.g., 4N).
- Force and mass can be calculated (e.g., 35000 N, 3 kg).
- Momentum can be calculated (e.g., 10 kg m/s, 500 kg m/s).
Chapter 9: Gravity
- Weight on earth and moon can be calculated (e.g., 98 N, 16.3 N).
- Maximum height and total time of a projectile can be calculated (e.g., 122.5 m, 10 s).
- Gravitational force can be calculated (e.g., 3.56 × 10²² N).
- Initial velocity and height of a projectile can be calculated (e.g., 29.4 m/s, 44.1 m).
Chapter 10: Energy
- Energy can be calculated (e.g., 0 J, -210 J, 2000 J).
- Energy transfer can be described (e.g., 9 × 10⁸ J).
- Energy conversion can be described (e.g., 5.4 × 10⁷ J).
Chapter 11: Waves and Sound
- Wavelength and frequency can be calculated (e.g., 17.2 m, 0.0172 m, 22,600 Hz).
- Time period of a wave can be calculated (e.g., 11.47 s).
- Speed of a wave can be calculated (e.g., 6000 m/s).
Chapter 3: Compounds and Molecules
- MgCl2 is a compound.
- CaO is a compound.
- Cu(NO3)2 is a compound.
- AlCl3 is a compound.
- CaCO3 is a compound.
- Calcium and oxygen are components of a compound.
- Hydrogen and bromine are components of a compound.
- Sodium, hydrogen, carbon, and oxygen are components of a compound.
- Potassium, sulfur, and oxygen are components of a compound.
- The mass of a substance can be calculated (e.g., 26 g, 256 g, 124 g, 36.5 g, 63 g).
Chapter 4: Atomic Structure
- Atomic mass of an element is 80.006.
- Valency of an element can be 1 (e.g., lithium).
- Isotopes have different mass numbers (e.g., X = 12, Y = 14).
- True or false statements about atomic structure can be evaluated.
Chapter 7: Motion
- Distance and displacement can be calculated (e.g., distance = 2200 m, displacement = 200 m).
- Average speed and average velocity can be calculated (e.g., 2.00 m/s, 1.90 m/s).
- Distance traveled and velocity can be calculated (e.g., 96 m, 20 m/s).
Chapter 8: Forces
- Force and acceleration can be calculated (e.g., 2 m/s², 14000 N).
- Frictional force can be calculated (e.g., 4N).
- Force and mass can be calculated (e.g., 35000 N, 3 kg).
- Momentum can be calculated (e.g., 10 kg m/s, 500 kg m/s).
Chapter 9: Gravity
- Weight on earth and moon can be calculated (e.g., 98 N, 16.3 N).
- Maximum height and total time of a projectile can be calculated (e.g., 122.5 m, 10 s).
- Gravitational force can be calculated (e.g., 3.56 × 10²² N).
- Initial velocity and height of a projectile can be calculated (e.g., 29.4 m/s, 44.1 m).
Chapter 10: Energy
- Energy can be calculated (e.g., 0 J, -210 J, 2000 J).
- Energy transfer can be described (e.g., 9 × 10⁸ J).
- Energy conversion can be described (e.g., 5.4 × 10⁷ J).
Chapter 11: Waves and Sound
- Wavelength and frequency can be calculated (e.g., 17.2 m, 0.0172 m, 22,600 Hz).
- Time period of a wave can be calculated (e.g., 11.47 s).
- Speed of a wave can be calculated (e.g., 6000 m/s).
Chapter 3: Compounds and Molecules
- MgCl2 is a compound.
- CaO is a compound.
- Cu(NO3)2 is a compound.
- AlCl3 is a compound.
- CaCO3 is a compound.
- Calcium and oxygen are components of a compound.
- Hydrogen and bromine are components of a compound.
- Sodium, hydrogen, carbon, and oxygen are components of a compound.
- Potassium, sulfur, and oxygen are components of a compound.
- The mass of a substance can be calculated (e.g., 26 g, 256 g, 124 g, 36.5 g, 63 g).
Chapter 4: Atomic Structure
- Atomic mass of an element is 80.006.
- Valency of an element can be 1 (e.g., lithium).
- Isotopes have different mass numbers (e.g., X = 12, Y = 14).
- True or false statements about atomic structure can be evaluated.
Chapter 7: Motion
- Distance and displacement can be calculated (e.g., distance = 2200 m, displacement = 200 m).
- Average speed and average velocity can be calculated (e.g., 2.00 m/s, 1.90 m/s).
- Distance traveled and velocity can be calculated (e.g., 96 m, 20 m/s).
Chapter 8: Forces
- Force and acceleration can be calculated (e.g., 2 m/s², 14000 N).
- Frictional force can be calculated (e.g., 4N).
- Force and mass can be calculated (e.g., 35000 N, 3 kg).
- Momentum can be calculated (e.g., 10 kg m/s, 500 kg m/s).
Chapter 9: Gravity
- Weight on earth and moon can be calculated (e.g., 98 N, 16.3 N).
- Maximum height and total time of a projectile can be calculated (e.g., 122.5 m, 10 s).
- Gravitational force can be calculated (e.g., 3.56 × 10²² N).
- Initial velocity and height of a projectile can be calculated (e.g., 29.4 m/s, 44.1 m).
Chapter 10: Energy
- Energy can be calculated (e.g., 0 J, -210 J, 2000 J).
- Energy transfer can be described (e.g., 9 × 10⁸ J).
- Energy conversion can be described (e.g., 5.4 × 10⁷ J).
Chapter 11: Waves and Sound
- Wavelength and frequency can be calculated (e.g., 17.2 m, 0.0172 m, 22,600 Hz).
- Time period of a wave can be calculated (e.g., 11.47 s).
- Speed of a wave can be calculated (e.g., 6000 m/s).
Matter and Its Properties
- The National Curriculum Framework (NCF) 2005 recommends that children's life at school must be linked to their life outside the school.
- In the gaseous state, particles move randomly at high speed, exerting pressure on the walls of the container due to their random movement.
Characteristics of Particles in Different States
- Solids: particles have minimum kinetic energy, forces of attraction between particles are maximum, and arrangement of particles is most ordered.
- Liquids: particles have intermediate kinetic energy, forces of attraction between particles are intermediate, and layers of particles can slip and slide over each other.
- Gases: particles have maximum kinetic energy, forces of attraction between particles are minimum, and particles move randomly with no order.
Inter-Convertible States of Matter
- States of matter can be changed by changing temperature or pressure.
- Sublimation: change of solid state directly to gaseous state without going through liquid state.
- Deposition: change of gaseous state directly to solid state without going through liquid state.
- Boiling: bulk phenomenon where particles from the bulk of the liquid change into vapor state.
- Evaporation: surface phenomenon where particles from the surface gain enough energy to overcome the forces of attraction present in the liquid and change into the vapor state.
Suspensions and Colloids
- Suspension: a heterogeneous mixture in which the solute particles do not dissolve but remain suspended throughout the bulk of the medium.
- Properties of a suspension:
- Is a heterogeneous mixture
- Particles can be seen by the naked eye
- Colloids: big enough to scatter a beam of light passing through it and make its path visible, but do not settle down when left undisturbed.
- Tyndall effect: scattering of a beam of light by particles of dust and smoke in the air, or by particles of a colloid or suspension.
Education Reform
- The National Policy on Education (1986) aims to shift from a bookish learning approach to a child-centered system of education.
- The new syllabi and textbooks are designed to discourage rote learning and encourage creativity and imagination in children.
- The success of this effort depends on teachers and principals taking steps to allow children to reflect on their own learning and pursue imaginative activities.
- Recognizing children as active participants in learning, rather than just receivers of knowledge, is crucial for this approach.
Matter in Our Surroundings
- Matter is the material that makes up everything in the universe, including living and non-living things.
- Matter occupies space and has mass, which means it has both volume and weight.
- The concept of particles is essential to understanding matter and its properties.
- Early Indian philosophers and ancient Greek philosophers classified matter into five basic elements: air, earth, fire, sky, and water.
States of Matter
- Matter exists in three main states: solid, liquid, and gas, due to variations in the characteristics of its particles.
- The properties of each state of matter, such as shape and volume, are different.
- Solids have a fixed shape and volume, liquids take the shape of their container and have a fixed volume, and gases have neither a fixed shape nor a fixed volume.
Solutions, Suspensions, and Colloids
- A solution is a homogeneous mixture of two or more substances, where the solvent is the major component and the solute is the minor component.
- The concentration of a solution is the amount of solute present per unit volume or per unit mass of the solution.
- A suspension is a heterogeneous mixture where the particles are visible to the naked eye.
- Colloids are heterogeneous mixtures with particle sizes too small to be seen with the naked eye, but big enough to scatter light.
- Colloids are useful in industry and daily life, with examples including milk and sponges.
Characteristics of Matter
- The particles of matter have mass, volume, and occupy space.
- Matter can exist in different states (solid, liquid, gas) depending on the characteristics of its particles.
- Matter can be classified into pure substances, which can be elements or compounds, and mixtures, which can be separated into pure substances using appropriate techniques.
Pure Substances
- Pure substances can be elements or compounds.
- Elements are forms of matter that cannot be broken down by chemical reactions into simpler substances.
- Compounds are substances composed of two or more different types of elements, chemically combined in a fixed proportion.
Learn about number systems, number lines, and representation of various types of numbers. Start with the basics and explore the concept of number systems.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
