CLASS9............MATHS....SA1

First Term Marks: 90 Units Marks I NUMBER SYSTEMS 17 II ALGEBRA 25 III GEOMETRY 37 IV COORDINATE GEOMETRY 11 V MENSURATION Total (Theory) 90

 UNIT I: NUMBER SYSTEMS 1. REAL NUMBERS (18 Periods) 1. Review of representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification. Rational numbers as recurring/terminating decimals. 2. Examples of non-recurring / non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number. 3. Existence of √ݔ for a given positive real number x (visual proof to be emphasized). 4. Definition of nth root of a real number. 5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.) 6. Rationalization (with precise meaning) of real numbers of the type (and their combinations) 1 a bx &, 1 x y where x and y are natural number and a and b are integers.
UNIT II: ALGEBRA 1. POLYNOMIALS (23) Periods Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Further verification of identities of the type (x+y+z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx, (x ± y)3 = x3 ± y3 ± 3xy (x ± y), x3 ± y3 = (x ± y) (x2 B xy + y2 ), x3 + y3 + z3 — 3xyz = (x + y + z) (x2 + y2 +z2 — xy — yz — zx) and their use in factorization of polymonials. Simple expressions reducible to these polynomials.


 UNIT III : GEOMETRY 1. INTRODUCTION TO EUCLID'S GEOMETRY (6) Periods History - Geometry in India and Euclid's geometry. Euclid's method of formalizing observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example: (Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common

2. LINES AND ANGLES (13) Periods 1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180o and the converse. 2. (Prove) If two lines intersect, vertically opposite angles are equal. 3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines. 4. (Motivate) Lines which are parallel to a given line are parallel. 5. (Prove) The sum of the angles of a triangle is 180o . 6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

3. TRIANGLES (20) Periods 1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). 2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence). 3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruene). 4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle

 5. (Prove) The angles opposite to equal sides of a triangle are equal. 6. (Motivate) The sides opposite to equal angles of a triangle are equal. 7. (Motivate) Triangle inequalities and relation between 'angle and facing side' inequalities in triangles.
UNIT IV: COORDINATE GEOMETRY 1. COORDINATE GEOMETRY (6) Periods The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane. UNIT V: MENSURATION 1. AREAS (4) Periods Area of a triangle using Heron's formula (without proof) and its application in finding the area of a quadrilateral.

UNNN...............IVERSE

The Universe

The Universe is everything we can touch, feel, sense, measure or detect. It includes living things, planets, stars, galaxies, dust clouds, light, and even time. Before the birth of the Universe, time, space and matter did not exist.

The Universe contains billions of galaxies, each containing millions or billions of stars. The space between the stars and galaxies is largely empty. However, even places far from stars and planets contain scattered particles of dust or a few hydrogen atoms per cubic centimeter. Space is also filled with radiation (e.g. light and heat), magnetic fields and high energy particles (e.g. cosmic rays).

The Universe is incredibly huge. It would take a modern jet fighter more than a million years to reach the nearest star to the Sun. Travelling at the speed of light (300,000 km per second), it would take 100,000 years to cross our Milky Way galaxy alone.

No one knows the exact size of the Universe, because we cannot see the edge – if there is one. All we do know is that the visible Universe is at least 93 billion light years across. (A light year is the distance light travels in one year – about 9 trillion km.)

The Universe has not always been the same size. Scientists believe it began in a Big Bang, which took place nearly 14 billion years ago. Since then, the Universe has been expanding outward at very high speed. So the area of space we now see is billions of times bigger than it was when the Universe was very young. The galaxies are also moving further apart as the space between them expands.

The birth of galaxies

We cannot see anything that happened during the first 300  000 years of the Universe. Scientists try to work it out from their knowledge of atomic particles and from computer models.

The only direct evidence of the Big Bang itself is a faint glow in space. Spacecraft and telescopes on balloons see this as a patchy pattern of slightly warmer and cooler gas all around us. These ripples also show where the hydrogen clouds were slightly denser.

As millions of years passed, the dense areas pulled in material because they had more gravity. Finally, about 100 million years after the Big Bang, the gas became hot and dense enough for the first stars to form.

New stars were being born at a rate 10 times higher than in the present-day Universe. Large clusters of stars soon became the first galaxies.

Hubble's newest camera eyes hotbed of star formation

The Hubble Space Telescope and powerful ground-based telescopes are now beginning to find galaxies that were created about one billion years after the Big Bang. These small galaxies were much closer together than galaxies are today. Collisions were common. Like two flames moving towards each other, they merged into bigger galaxies. Our Milky Way galaxy came together in this way.

BING BANG THEORY

The Big Bang

Most astronomers believe the Universe began in a Big Bang about 14 billion years ago. At that time, the entire Universe was inside a bubble that was thousands of times smaller than a pinhead. It was hotter and denser than anything we can imagine.

Then it suddenly exploded. The Universe that we know was born. Time, space and matter all began with the Big Bang. In a fraction of a second, the Universe grew from smaller than a single atom to bigger than a galaxy. And it kept on growing at a fantastic rate. It is still expanding today.

As the Universe expanded and cooled, energy changed into particles of matter and antimatter. These two opposite types of particles largely destroyed each other. But some matter survived. More stable particles called protons and neutrons started to form when the Universe was one second old.

Over the next three minutes, the temperature dropped below 1 billion degrees Celsius. It was now cool enough for the protons and neutrons to come together, forming hydrogen and helium nuclei.

After 300 000 years, the Universe had cooled to about 3000 degrees. Atomic nuclei could finally capture electrons to form atoms. The Universe filled with clouds of hydrogen and helium gas.

VII....Tracing Changes Through A Years

Q1: Who was considered a ‘foreigner’ in the past?

Ans:A person who was a stranger or who was not a part of the society or culture was considered as a ‘foreigner’ or ‘pardeshi’ or ‘ajnabi’.

2: State whether True or False: –

1. We do not find inscriptions for the period after 700.
2. The Marathas asserted their political importance during this period.
3. Forest-dwellers were sometimes pushed out of their lands with the spread of agricultural settlements.
4. Sultan Ghiyasuddin Balban controlled Assam, Manipur and Kashmir

Ans:(a) T (b) T (c) T (d) F

Q3: Fill in the blanks:

1. Archives are places where ___________ are kept.
2. _______ was a fourteenth century chronicler.
3. _____ ______ _____ _____ and ______ were some of the new crops introduced into the subcontinent during this period

Ans:(a) manuscripts / records / documents (b) Ziyauddin Barani (c) Potatoes, corn, chillies, tea and coffee.

Q4: List some of the technological changes associated with this period.

Ans:Some of the technological changes associated with this period:

• Persian wheel in irrigation.
• Fire arms in combat.
• Spinning wheel in weaving.
• New foods and brewages like potato, corn, chillies, tea and coffee.

Q5: In what ways has the meaning of the term “Hindustan” changed over the centuries?

Ans:The meaning of the term ‘Hindustan’ changed over the centuries in various ways. In the 13th century Muihaj-i-Siraj used the term ‘Hindustan’ to mean the areas of Punjab, Haryana and the area lying between Ganga and Yamuna. He used this term in a political sense that was a part of the dominion of Delhi Sultan.
In the 16th century Babar used the same term to describe the geography, the fauna and the culture of the inhabitants of this subcontinent. In 14th century Amir Khusaru used the erm ‘Hind’ in the same sense as Babar did in 16thcentury.
But the term ‘Hindustan’ never carried the political and national meanings as the term ‘India’ does today.

Q6: How were the affairs of Jatis regulated?

Ans:The affairs of jatis were regulated in the following ways –

• Jatis formed their own rules and regulations.
• There was an assembly of elders called Jati panchayat which used to enforce the rules etc.
• Jatis were also directed to follow the rules of the village.
• Several villages were governed by a chieftain.

CLASS.....VII...Towns Trades And Craft Persons

Q1: Fill in the blanks: –

1. The Rajarajeshvara Temple was built in _______.
2. Ajmer is associated with the Sufi Saint ________.
3. Hampi was the capital of the _____ Empire.
4. The Dutch established a settlement at ______ in Andhra Pradesh.

Ans:

(a) Thanjavur (TN) (b) Moinuddin Chishti (c) Vijayanagara (d) Masulipatnam.

Q2: State whether True or False: –

1. We know the name of the architect of the Rajarajeshvara Temple from an inscription.
2. Merchants preferred to travel individually rather than in caravans.
3. Kabul was a major center for trade in elephants.
4. Surat was an important trading port on the Bay of Benga

Ans:(a)-T (b)-F (c)-F (d)-F

Q3: How was water supplied to the city of Thanjavur?

Ans:Water from wells and tanks was supplied to the city of Thanjavur through channels.

Q3: How was water supplied to the city of Thanjav

Ans:Water from wells and tanks was supplied to the city of Thanjavur through channels.

Q4: Who lived in the ‘Black Towns’ in cities such as Madras?

Ans:‘Black Towns’ were established by the European rulers. The ‘Blacks’ of the native traders, artisans and crafts persons like weavers were confined in ‘Black Towns’ in the citieslike Madras by the white rulers.

Q5: Why do you think towns grew around temples?

Ans:Towns grew around temples because of the following reasons:

• Priests, workers, artisans, crafts persons settled around temples.
• Several shops came up around temple to cater to the needs of pilgrims and the priests etc.

Q6: How important were crafts persons for the building and maintenance of temples?

Ans:Crafts persons were very important for the building and maintenance of temples because of the following reasons:

• They carried in play work in copper and silver. Crafts persons from Bidar were well known for Bidri work.
• Goldsmiths, Bronze smiths, Blacksmiths, Masons, Carpenters built temples.
• They also maintained them
• Weavers also played an important role in cotton textiles.
• Thus they made delighted crafts in buildings and temples which looked beautiful and als

Q7: Why did people from distant lands visit Surat?

Ans:People from distant parts used to visit Surat during those days because –

• It was the gate-way to west Asia.
• They came here to purchase cotton textiles, textiles with their gold less border.

Q8: In what ways craft productions in cities like Calcutta different from that in cities like Thanjavur?

Ans:Craft production in Thanjavur was different from that of Kolkata in the following manner:

• Craft production in Thanjavur was in the form of inlays work in copper and silver.
• In Kolkata it was in the form of cotton textiles, jute textiles and silk textiles.

Q9: What were the problems encountered by merchants? Do you think some of these problems persist today?

Ans:During earlier times and medieval period merchants had to face lot of problems, most of which however, don’t persist today. Merchants had to pass through many kingdoms and forests. They had to travel in caravans, which are not required now-a-days. They had to carry goods on the back of camels, donkeys and horses as then there were no transport facilities like today. Their goods were looted frequently since there was no proper security as it is now. They had to face competition with European traders and work in a limited environment. Harsh climate and routes killed several merchants on the way or in the middle of their journey during those days since weather forecasting was not advanced as it is now.