Key points, definitions and digest answers for SSC & CBSE Board
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Mathematics
Chapter 1 — Rational Numbers
📌 Key Points
A rational number is a number that can be written as p/q where p and q are integers and q ≠ 0
Rational numbers are closed under addition, subtraction and multiplication
Division by zero is not defined
Between any two rational numbers there are infinite rational numbers
Zero (0) is the additive identity — a + 0 = a
One (1) is the multiplicative identity — a × 1 = a
Commutative property: a + b = b + a and a × b = b × a
Associative property: (a+b)+c = a+(b+c)
✅ Digest Answers
Q. What is a rational number?
A number that can be expressed in the form p/q where p and q are integers and q is not equal to zero. Example: 3/4, -5/2, 7/1
Q. What is additive inverse?
The additive inverse of a number a is -a, such that a + (-a) = 0. Example: additive inverse of 3/5 is -3/5
Q. What is multiplicative inverse?
The multiplicative inverse of a/b is b/a, such that a/b × b/a = 1. Example: multiplicative inverse of 2/3 is 3/2
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Mathematics
Chapter 2 — Linear Equations in One Variable
📌 Key Points
A linear equation has the form ax + b = 0 where a ≠ 0
It has only one variable with degree 1
The value of variable that satisfies the equation is called its solution or root
To solve: perform same operation on both sides to keep equation balanced
Cross multiplication is used when equation has fractions on both sides
Transposing: moving a term from one side changes its sign
✅ Digest Answers
Q. Solve: 2x + 5 = 11
2x = 11 - 5 = 6 → x = 6/2 = 3
Q. What is transposition?
Moving a term from one side of equation to other side by changing its sign. Example: x + 3 = 7 → x = 7 - 3 = 4
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Mathematics
Chapter 3 — Understanding Quadrilaterals
📌 Key Points
Sum of interior angles of a quadrilateral = 360°
Parallelogram: opposite sides equal and parallel, opposite angles equal
Rectangle: parallelogram with all angles 90°
Rhombus: parallelogram with all sides equal
Square: rectangle with all sides equal
Trapezium: one pair of parallel sides
Diagonals of a parallelogram bisect each other
Diagonals of a rhombus bisect at right angles
✅ Digest Answers
Q. What is a parallelogram?
A quadrilateral in which both pairs of opposite sides are parallel and equal. Its opposite angles are equal and diagonals bisect each other.
Q. Difference between rhombus and square?
Both have all sides equal. But a square has all angles = 90° while a rhombus does not necessarily have right angles.
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Science
Chapter 1 — Crop Production and Management
📌 Key Points
Kharif crops: Sown in June-July, harvested in September-October. Example: Rice, Maize, Cotton
Rabi crops: Sown in October-November, harvested in March-April. Example: Wheat, Mustard, Pea
Irrigation: supply of water to crops at regular intervals
Fertilizers: chemical substances that provide nutrients. Example: Urea, NPK
Manure: natural organic matter from decomposed plant/animal waste
Weeding: removal of unwanted plants (weeds) from fields
Threshing: separating grains from stalks after harvesting
Nitrogen, Phosphorus, Potassium are the three main nutrients for crops
✅ Digest Answers
Q. What is the difference between fertilizer and manure?
Fertilizer is a chemical substance that provides specific nutrients quickly. Manure is organic matter from decomposed waste — it improves soil texture and adds nutrients slowly. Manure is better for long-term soil health.
Q. What is crop rotation?
Growing different crops alternately on the same land. It maintains soil fertility and reduces pests. Example: growing wheat after legumes restores nitrogen in soil.
Q. Name any two Kharif and two Rabi crops.
Kharif: Rice, Maize. Rabi: Wheat, Mustard.
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Science
Chapter 2 — Microorganisms: Friend and Foe
📌 Key Points
Microorganisms are classified into: Bacteria, Fungi, Protozoa, Algae, Viruses
Viruses are not living organisms — they reproduce only inside a host cell
Antibiotics: medicines that kill bacteria. Example: Penicillin (discovered by Alexander Fleming)
Vaccine: weakened germs injected to develop immunity
Fermentation: process by which yeast converts sugar into alcohol and CO₂
Bacteria help in making curd, cheese, vinegar
Nitrogen-fixing bacteria: Rhizobium lives in roots of legume plants
Disease-causing microorganisms are called pathogens
✅ Digest Answers
Q. What are antibiotics? Give an example.
Antibiotics are medicines made from microorganisms that kill or stop the growth of bacteria. Example: Penicillin, Streptomycin. They do NOT work against viruses.
Q. What is fermentation?
The process by which yeast breaks down sugar into alcohol and carbon dioxide in the absence of oxygen. It is used to make bread, wine and beer.
Q. How do vaccines work?
Vaccines contain weakened or dead germs. When injected, they stimulate the body to produce antibodies. These antibodies remain in the body and fight the actual disease in future.
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Science
Chapter 6 — Combustion and Flame
📌 Key Points
Combustion: chemical process in which substance reacts with oxygen to give heat and light
Fuel: substance that burns to produce energy. Types: solid (wood), liquid (petrol), gas (LPG)
Ignition temperature: minimum temperature at which a substance catches fire
Inflammable substances: substances with very low ignition temperature. Example: petrol, alcohol
Fire triangle: Fuel + Oxygen + Heat — all three needed for fire
To extinguish fire: remove any one component of fire triangle
CO₂ is the best fire extinguisher — cuts off oxygen supply
Calorific value: amount of heat produced by complete combustion of 1 kg of fuel
✅ Digest Answers
Q. Why is CO₂ used in fire extinguishers?
CO₂ is heavier than oxygen. It forms a blanket over the burning substance and cuts off the oxygen supply, which stops combustion. It does not harm electrical equipment.
Q. What is ignition temperature?
The minimum temperature at which a substance catches fire and starts burning is called its ignition temperature. Below this temperature, combustion cannot occur even if oxygen is present.
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English Grammar
Parts of Speech — Quick Reference
📌 Key Points
Noun: name of a person, place, thing or idea. Example: Shashikant, Mumbai, book
Pronoun: word used in place of noun. Example: he, she, they, it
Verb: word showing action or state. Example: run, eat, is, was
Adjective: describes a noun. Example: tall boy, red pen
Adverb: describes a verb, adjective or adverb. Example: quickly, very, well
Preposition: shows relation between noun and other words. Example: in, on, at, by
Conjunction: joins words or sentences. Example: and, but, or, because
An adjective is a word that describes or modifies a noun. Examples: beautiful flower, tall building, hot coffee. It answers questions like "which?", "what kind?", "how many?"
Q. Difference between adverb and adjective?
Adjective describes a noun (She is beautiful). Adverb describes a verb, adjective or another adverb (She sings beautifully). Adverbs often end in -ly.
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