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Category: Class 9th

  • Chapter 8 Quadrilaterals Notes for Class 9th Maths

    Chapter 8 Quadrilaterals

    • Angle Sum Property of a Quadrilateral
    • Types of Quadrilaterals
    • Properties of a Parallelogram
    • The Mid-Point Theorem
    1. Sum of the angles of a quadrilateral is 360o
    2. A diagonals of a parallelogram divides it into two congruent triangles.
    3. In a parallelogram
    4. diagonals bisect each other.
    5. opposite angles are equal.
    6. opposite sides are equal
    7. Diagonals of a square bisects each other at right angles and are equal, and vice-versa.
    8. A line through the mid-point of a side of a triangle parallel to another side bisects the third side. (mid-point theorem)
    9. The line through the mid points of sides of a D || to third side and half of it.
    10. A quadrilateral is a parallelogram, if
    11. its opposite angles are equal.
    12. its opposite sides are equal.
    13. its diagonals bisect each other.
    14. a pair of opposite sides is equal and parallel.
    15. Diagonals of a rectangle bisect each other and are equal and vice-versa.
    16. Diagonals of a rhombus bisect each other at right angles and vice-versa.
    17. A line through the mid-point of a side of a triangle parallel to another side bisects the third side.
    18. The line-segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it.

  • Chapter 7 Triangles Notes for Class 9th Maths


    Chapter – 7 Triangles

    1. Congruence of Triangles
    2. Criteria for Congruence of Triangles
    3. Some Properties of a Triangle
    4. Inequalities in a Triangle
    • Triangle- A closed figure formed by three intersecting lines is called a triangle. A triangle has three sides, three angles and three vertices.
    • Congruent figures- Congruent means equal in all respects or figures whose shapes and sizes are both the same for example, two circles of the same radii are congruent. Also two squares of the same sides are congruent.
    • Congruent Triangles- two triangles are congruent if and only if one of them can be made to superpose on the other, so as to cover it exactly.

    • If two triangles ABC and PQR are congruent under the correspondence A « P, B « Q and C « R then symbolically, it is expressed as DABC @ DPQR

    • In congruent triangles corresponding parts are equal and we write ‘CPCT’ for corresponding parts of congruent triangles.

    • SAS congruency rule – Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. For example: DABC and DPQR as shown in the figure satisfy SAS congruent criterion.


    • ASA Congruence Rule- Two triangles are congruent if two angles and the included side of

    one triangle are equal to two angles and the included side of other triangle. For examples

    • AAS Congruence Rule- Two triangle are congruent if any two pairs of angles and one pair of corresponding sides are equal for example DABC and DDEF shown below satisfy AAS
    • Angle opposite to equal sides of a triangle are equal.

    congruence criterion.

    • AAS criterion for congruence of triangles is a particular case of ASA criterion.
    • Isosceles Triangle- A triangle in which two sides are equal is called an isosceles triangle.

    • Sides opposite to equal angles of a triangle are equal.
    • Each angle of an equilateral triangle is 60o.
    • SSS congruence Rule – If three sides of one triangle are equal to the three sides of another triangle then the two triangles are congruent for example DABC and DDEF as shown in

    the figure satisfy SSS congruence criterion.

    • RHS Congruence Rule- If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle then the two triangle are congruent. For example: DABCand DPQR shown below satisfy RHS

    congruence criterion.


    RHS stands for right angle – Hypotenuse side.

    • A point equidistant from two given points lies on the perpendicular bisector of the line segment joining the two points and its converse.
    • A point equidistant from two intersecting lines lies on the bisectors of the angles formed by the two lines.
    • In a triangle, angle opposite to the longer side is larger (greater)
    • In a triangle, side opposite to the large (greater) angle is longer.
    • Sum of any two sides of a triangle is greater than the third side.

  • Chapter 6 Lines and Angles Notes for Class 9th Maths

    Chapter – 6 Lines and Angles

    1. Basic Terms and Definitions
    2. Intersecting Lines and Non-Intersecting Lines
    3. Pairs of Angles
    4. Parallel Lines and a Transversal
    5. Lines Parallel to the same Line
    6. Angle Sum Property of a Triangle
    7. Point- We often represent a point by a fine dot made with a fine sharpened pencil on a piece of paper.
    8. Line- A line is completely known if we are given any two distinct points. Line AB is represented by as AB . A line or a straight line extends indefinitely in both the directions.

    (5) Collinear points- If three or more points lie on the same line, they are called collinear points otherwise they are called non-collinear points.

    Types of Angles-

    1. Acute angle- An acute angle measure between Oo and 90o
    2. Right angle- A right angle is exactly equal to 90o
    3. Obtuse angle- An angle greater than 90o but less than 180o
    4. Straight angle- A straight angle is equal to 180o
    5. Reflex angle- An angle which is greater than 180o but less than 360o is called a reflex angle.
    6. Complementary angles- Two angles whose sum is 90o are called complementary angles.
    7. Supplementary angle- Two angles whose sum is 180o are called supplementary angles.
    8. Adjacent angles- Two angles are adjacent, if they have a common vertex, a common arm and their non-common arms are on different sides of common arm.
    9. Linear pair- Two angles form a linear pair, if their non-common arms form a line.
    10. Vertically opposite angles- Vertically opposite angles are formed when two lines intersect each other at a point.

    TRANSVERSAL:

    1. Corresponding angles
    2. Alternate interior angles
    3. Alternate exterior angles
    4. Interior angles on the same side of the transversal.
    • If a transversal intersects two parallel lines, then
    1. each pair of corresponding angles is equal.
    2. each pair of alternate interior angles is equal.
    3. each pair of interior angle on the same side of the transversal is supplementary.
    • If a transversal interacts two lines such that, either
    1. any one pair of corresponding angles is equal, or
    2. any one pair of alternate interior angles is equal or

    (iii) any one pair of interior angles on the same side of the transversal is supplementary then the lines are parallel.

    • Lines which are parallel to a given line are parallel to each other.
    • The sum of the three angles of a triangle is 180°
    • If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

  • Chapter 5 Introduction to Euclid’s Geometry Notes for Class 9th Maths

    Chapter – 5 Introduction to Euclid’s Geometry

    1. Euclid’s Definitions, Axioms and Postulates
    2. Equivalent Versions of Euclid’s Fifth Postulate

    The Greeks developed geometry is a systematic manner Euclid (300 B.C.) a greek mathematician, father of geometry introduced the method of proving mathematical results by using deductive logical reasoning and the previously proved result. The Geometry of plane figure is known as “Euclidean Geometry”.

    Axioms: The basic facts which are taken for granted without proof are called axioms some Euclid’s axioms are:

    1. Things which are equal to the same thing are equal to one another. i.e. a = b, b = c ^ a = c
    2. If equals are added to equals, the wholes are equal i.e. a = b ^ a + c = b + c
    3. If equals are subtracted from equals, the remainders are equal i.e. a = b ^ a – c = b – c
    4. Things which coincide with one another are equal to one another.
    5. The whole is greater than the part.

    Postulates: Axioms are the general statements, postulates are the axioms relating to a particular field.

    Educlid’s five postulates are.

    1. A straight line may be drawn from any one point to any other point.
    2. A terminated line can be produced indefinitely.
    3. A circle can be drawn with any centre and any radius.
    4. All right angles are equal to one another.
    5. If a straight line falling on two straight lines makes the interior angles on the same side of it

    taken together less than two right angles, then the two straight lines, if produced indefinitely

    meet on that side on which the angles are less than two right angles.

    Statements: A sentence which is either true or false but not both, is called a statement. eg. (i) 4+9=6 If is a false sentence, so it is a statement.

    (ii) Sajnay is tall. This is not a statement because he may be tall for certain persons and may not be taller for others.

    Theorems: A statement that requires a proof is called a theorem. eg. (i) The sum of the angles of triangle is 180°.

    (ii) The angles opposite to equal sides of a triangles are equal.

    Corollary – Result deduced from a theorem is called its corollary.

  • Chapter 4 Linear Equations in Two Variables Notes for Class 9th Maths

    Chapter – 4 Linear Equations in Two Variables

    1. Linear Equations
    2. Solution of a Linear Equation
    3. Graph of a Linear Equation in Two Variables
    4. Equations of Lines Parallel to x-axis and y-axis
    • An equation of the form ax + by + c = 0 where a, b and c are real numbers such that a and b are not both zero is called a linear equation in two variables.
    • A pair of values of x and y which satisfy the equation ax + by + c = 0 is called a solution of the equation.
    • Graph: The graph of every linear equation in two variables is a straight line. Every point on the graph of a linear equation in two variables is two variables is a solution of the linear equation. Conversely, every solution of the linear equation is a point on the graph of the linear equation.
    • A linear equation in two variables has infinitely many solutions.
    • The graph of every linear equation in two variables is a straight line.
    • y = 0 is the equation of x-axis and x = 0 is equation of y-axis.
    • The graph of x = a is a straight line parallel to the y-axis.
    • The graph of y = a is a straight line parallel to the x-axis.
    • An equation of the type y = mx represent a line passing through the origin.

  • Chapter 3 Coordinate Geometry Notes for Class 9th Maths

    Chapter – 3 Coordinate Geometry

    1. Cartesian System
    2. Plotting a Point in the Plane with given Coordinates
    • Coordinate Geometry: The branch of mathematics in which geometric problems are solved

    through algebra by using the coordinate system is known as coordinate geometry.

    • Coordinate System: Coordinate axes: The position of a point in a plane is determined with

    reference to two fixed mutually perpendicular lines, called the coordinate axes.

    In this system, position of a point is described by ordered pair of two numbers.

    Ordered pair: A pair of numbers a and b listed in a specific order with ‘a’ at the first place and ‘b’ at the second place is called an ordered pair (a,b)

    Note that (a,b) ^ (b,a)

    Thus (2,3) is one ordered pair and (3,2) is another ordered pair.

    In given figure O is called origin.

    The horizontal line X1 OX is called the X-axis.

    The vertical line YOY’ is called the Y-axis.

    P(a,b) be any point in the plane. ‘a’ the first number denotes the distance of point from Y-axis and ‘b’ the second number denotes the distance of point from X-axis. a – X – coordinate | abscissa of P. b – Y – coordinate | ordinate of P.

    The coordinates of origin are (0,0)

    Every point on the x-axis is at a distance o unit from the X-axis. So its ordinate is 0.

    Every point on the y-axis is at a distance of unit from the Y-axis. So, its abscissa is 0.

    Note: Any point lying on X – axis or Y – axis Y-axis does not lie in any quadrant.

  • Chapter 2 Polynomials Notes for Class 9th Math

    CHAPTER – 2 POLYNOMIAL

    1. Polynomials in one Variable
    2. Zeroes of a Polynomial
    3. Remainder Theorem
    4. Factorisation of Polynomials
    5. Algebraic Identities
    • Constants: A symbol having a fixed numerical value is called a constant.
    • Variables: A symbol which may be assigned different numerical values is known as variable.
    • Algebraic expressions: A combination of constants and variables. Connected by some or all of the operations +, -, X and is known as algebraic expression.
    • Terms: The several parts of an algebraic expression separated by ‘+’ or ‘-‘ operations are called the terms of the expression.
    • Polynomials: An algebraic expression in which the variables involved have only nonnegative integral powers is called a polynomial.
    1. 5x2 – 4x2 – 6x – 3 is a polynomial in variable x.

    3

    1. (ii) 5 + 8x2 + 4x-2 is an expression but not a polynomial.

    Polynomials are denoted by p(x), q(x) and r(x)etc.

    • Coefficients: In the polynomial x3 + 3x2 + 3x +1, coefficient of x3, x2, x are1,3,3 respectively

    and we also say that +1 is the constant term in it.

    • Degree of a polynomial in one variable: In case of a polynomial in one variable the highest

    power of the variable is called the degree of the polynomial.

    • Classification of polynomials on the basis of degree.

    Degree Polynomial Example

    1. 1 Linear x +1, 2x + 3etc.
    2. 2 Quadratic ax2 + bx + c etc.
    3. 3 Cubic x3 + 3x2 +1 etc. etc.
    4. 4 Biquadratic x4 -1

    Classification of polynomials on the basis of no. of terms

    Polynomial & Examples. Monomial – S3Sx31Yetc.

    3

    No. of terms

    (i) 1

    Binomial – (3 + 6x), (x – 5y) etc.

    (ii) 2

    (iii) 3

    Trinomial- 2x2 + 4x + 2 etc. etc.

    • Constant polynomial: A polynomial containing one term only, consisting a constant term is called a constant polynomial the degree of non-zero constant polynomial is zero.
    • Zero polynomial: A polynomial consisting of one term, namely zero only is called a zero polynomial. The degree of zero polynomial is not defined.
    • Zeroes of a polynomial: Let p(x) be a polynomial. If p(a) =0, then we say that is a zero of the polynomial of p(x).
    • Remark: Finding the zeroes of polynomial p(x) means solving the equation p(x)=0.
    • Remainder theorem: Let f (x) be a polynomial of degree n > I and let a be any real

    number. When f(x) is divided by (x – a) then the remainder is f (a)

    • Factor theorem: Let f(x) be a polynomial of degree n > 1 and let a be any real number.
    1. If f (a) = 0 then (x – a) is factor of f (x)
    2. If (x – a) is factor of f (x)then f (a) = 0
    • Factor: A polynomial p(x) is called factor of q(x) divides q(x) exactly.
    • Factorization: To express a given polynomial as the product of polynomials each of degree less than that of the given polynomial such that no such a factor has a factor of lower degree, is called factorization.

  • Chapter 1 Number Systems Notes for Class 9th Maths

    CHAPTER – 1

    NUMBER SYSTEMS

    1. Rational Numbers
    2. Irrational Numbers
    3. Real Numbers and their Decimal Expansions
    4. Operations on Real Numbers
    5. Laws of Exponents for Real Numbers

  • Mathematics Notes Class 9th

    Notes in Of class 9th Mathematics Presented By ImperialStudy. With Step By Step Math Solution. If you are Getting Problem In Notes So, Here We Provide Full Notes Of Class IX Math Students Also We provide RD Sharam Solution Of Class 9th

    Notes for Class 9 – Maths

  • Improvement in Food Resources Notes Class 9th Science Chapter 15


    Chapter 15: “Improvement in food resources”

    KEY CONCEPTS : [ *rating as per the significance of concept]

    CONCEPTS RATING
    Improvement in crop yield ***
    Crop variety improvement ****
    Crop production management *****
    Crop protection management ***
    Animal Husbandry ****
    1. Food Resources: Cereals (Wheat, rice, maize, millets and sorghum) provide us carbohydrates; Pulses (Grams, pea and lentil) provide us proteins; Oil seeds (Soya bean, ground nut, sesame, and castor) provide us fats; Vegetables, spices and fruits provide us a range of minerals, nucleic acids and vitamins. In addition to these food crops, fodder crops like berseem, oats or sudan grass are raised as food for the livestock are called as fodder crops.
    2. The Kharif crops: The crops grown in rainy season are called as Kharif crops (Paddy, Soya bean, pigeon pea and maize). They are grown from June to October.
    3. The Rabi crops: The crops grown in winter season are called Rabi crops (Wheat, gram, peas, and mustard). They are grown November to April.

    Compare Kharif crops and Rabi crops:

    SN Crop Season Example
    1 Kharif crops June to October ( Rainy Season) Paddy, Soya bean, and maize
    2 Rabi crops November to April ( winter season) Wheat, gram, peas, and mustard
    1. The Green Revolution: Food supplies are generally as proteins, carbohydrates, fats, minerals, nucleic acids and vitamins in all living organisms. Indian population is growing enormously. Green Revolution is the need of the hour to increase food-grain production.
    2. Sustainable Practices: For sustained livelihood, one should undertake mixed farming, intercropping, and integrated farming practices, for example, combining agriculture with livestock/ poultry/ fisheries/bee-keeping. The major group of activities for improving crop yield can be classified as: Crop varietal improvement, Crop production improvement, Crop protection improvement
    3. The Crop varietal improvement:

    a) Hybridization: It refers to crossing between genetically dissimilar plants;It is all to get higher yield, improved quality, biotic and abiotic resistance, change in maturity duration, wider adaptability and desirable agronomic characteristics.

    SN Type Context
    1 Intervarietal Hybridization between different varieties
    2 Interspecific Hybridization between different species
    3 Intergeneric Hybridization between different genera
    4 Genetically Modified Crops (GMC). Another way of improving the crop is by introducing a gene that would provide the desired characteristic.
    1. The Crop production improvement: They include” no cost production”,” low cost production” or “high cost production” practices.
    2. Nutrients( Sixteen elements are required for growth are called as essential elements Carbon, oxygen, hydrogen+ Macronutrients & Micronutrients. They increase the yield):
    SN Macronutrient Micronutrient
    1 Six elements are required in larger quantity Other seven elements are required in small quantity
    2 Ex.Nitrogen, phosphorus, calsium,Postasium, magnisium, sulphur Ex. Iron, manganese, boron, zink, copper, molybdinum, chlorine
    1. Manure & Fertilizers:
    SN Manure Fertilizers
    1 Manure is prepared by the decomposition of animal excreta and plant waste is called as Humus. It decides the texture of the soil. Compost: Farm waste, cow dung etc. Vermi compost: Compost prepared by using earthworms. Fertilizers are commercially produced plant nutrients.

    Excess fertilizers destroy the soil fertility. Organic farming: No use of chemicals fertilizers, herbicides, pesticides etc.( Culturing blue green algae, neem leaves, healthy cropping systems.
    2 It is cheap and prepared in rural homes and fields It is costly and is prepared in factories
    3 It is voluminous and bulky It is compact and concentrated
    4 It is inconvenient to store, transport, handle. It is easy to store, transport, handle.
    5. It is not nutrient specific. It is nuteient specific and can provide specifically nitrogen, phosphorus etc.
    Add great humus to the soil Does not add humus to the soil.
    1. Irrigation: India has variety of water resources: Wells, canals, river lift system, tanks, rainwater harvesting, water shedding management to increase in ground water levels and to check the water flowing away to the sea. Planning to reduce soil erosion.

    4. Cropping patterns:

    SN Mixed cropping Inter-cropping Crop rotation
    1 Two or more crops grown simultaneously on the same piece of land Two or more crops grown simultaneously on the same piece of land in a definite pattern Growing different crops on a piece of land in a preplanned succession
    2 Ex. Wheat+ Gram; Wheat+ Mustard; Wheat+ gram; Groundnut+ sunflower. Soyabean + maize/bajra+Cowpea ((Please refer Fig. 15.2, NCERT Text Book Page- 208). Two or three crops can be grown in a year depending upon the duration.
    3 A type of insurance A few rows of one crop alternate The availability of
    against failure of one with a few rows of a second crop. moisture and
    of the crops. Crops are selected such that their irrigation facilities
    nutrient requirements are decides the choice
    different. This ensures the of the crop to be
    maximum utilization of the cultivated.
    nutrients supplied and prevents
    pests and diseases spreading in the
    crop field.

    8. Crop protection improvement/ management: Field crops are infested by large number

    of weeds, insects pests, diseases & storage of grains

    SN Weeds Insect pests Diseases Storage of grains
    1 Weeds are unwanted plants in the crop field Insect pest is nuisance in the crop field Disease is caused by pathogens in the field Different factors are responsible.
    2 Weeds take up nutrients and reduce the growth Insect pest affect the health of crop and reduce the yield. Diseases alter the physiology of crops and reduce the yield Different factors reduce the quality of stored grains
    3 Ex. Xanthium, Parthenium Ex. Caterpillars, dragonfly Ex. Bacteria, Virus Biotic factors: insects, rodents, fungi

    Abiotic factors: moisture & temperature
    4 Removal of weeds at an early stage is recommended. Spray weedicides Spread of chemicals such as pesticides Spread of chemicals to kill pathogens Systematic management of ware house.
    1. Animal Husbandry: It is a scientific management of animal livestock, includes feeding, breeding and diseases control. Animal-based farming includes cattle farming, Poultry

    farming, fish farming, and bee Keeping.

    SN Content Cattle

    farming

    		 Poultry

    farming

    		 Fish farming Bee Keeping.
    1 Purpose Milk (milch animals) and Meat,

    chicken, egg

    		 Cheep source of animal protein. Honey, wax, medicinal
    draught labor (draught animals) in agriculture. production Fish production is aquaculture. Growing of marine fishes is called

    mariculture.

    		 preparations. Additional income to the farmer.
    2 Cross

    breeding: To get desired qualities

    		 Exotic- quality of lactation Indigenous breeds- quality of disease resistance Exotic &

    Indigenous

    breeds

    		 Both Exotic & Indigenous fishes are used Exotic- high honey collection capacity &stingless. Indigenous bees- are used
    3 Desirable

    maintenance

    		 Good

    ventilation in

    sheds

    Roughage/

    concentrates

    Protection

    from

    parasites & skin diseases Vaccination

    		 Good

    ventilation in

    sheds

    Roughage/

    concentrates

    Protection

    from

    parasites & skin diseases Vaccination

    		 Fish farming/ locating large schools of fish/ use of satellites and echo-sounds In Composite fish culture seed is wild, mixed with other species. Hormonal stimulation to bring desired quality in fish production. Value or quality depends upon the pasturage or the flowers available for the taste of honey.
    4 Example Exotic or foreign breeds ( Jercy, brown Swiss)

    Local breeds (Red sindhi, Sahiwal)

    		 Exotic- Leghorn Indigenous breeds- Aseel Fresh water ( Macrobrachium) & Marine( Peneaus) prawns Fresh water fishes

    Marine fishes( Bombay duck, sardines) Common

    		 Apisceranaindica

    dorsata

    A.florae

    QUESTION BANK

    1. Give two examples of Cereals (Wheat, rice)
    2. Define the Kharif crop and give two examples fThe crops grown in rainy season are called as Kharif crops Ex. Paddy, Soya bean).
    3. Write about the importance of Green Revolution (Indian population is growing enormously. Green Revolution is the need of the hour to increase food-grain production.
    4. Define the term Hybridization(Crossing between genetically dissimilar plants)
    5. What is the importance of Genetically Modified Crops? (It is another way of improving the crop is by introducing a gene that would provide the desired characteristic.)
    6. Define the term mixed cropping and give two examples. (Two or more crops grown simultaneously on the same piece of landEx. Wheat+ Gram; Wheat+ Mustard)
    7. Distinguish between weeds, insects pests(Weeds are unwanted plants in the crop field Insect pest is nuisance in the crop field)
    8. What is Animal Husbandry? It is a scientific management of animal livestock, includes feeding, breeding and diseases control. Animal-based farming includes cattle farming, Poultry farming, fish farming, and bee keeping.
    9. Distinguish between aquaculture and mariculture. (Fish production is aquaculture. Growing of marine fishes is called mariculture.)
    10. What is the importance of Bee Culture? (It is useful for honey, wax, medicinal preparations. And also for additional income to the farmer.)

    QUESTION PAPER:FORMATIVE ASSESSMENT – I (For Practice)

    Marks- 40 Time: 90 minutes

    * General Instructions

    1. Questions 1-5 (1 Mark each) 2. Questions 6-10 (2 Mark each)

    1. Questions 11-15 (3Mark each) 4. . Questions 16-17 (5Mark each)

    Q.1 Maize and Millets are Pulses. Mention True/False

    Q.2 What is the Scientific name of Honey Bee

    Q.2 What led us to improve food grain production?

    Q.3 Which revolution led to the availability of milk for efficient use?

    Q.4 What is the process of injecting semen of desired bull into the vagina of cows is called? Q.5 Name any one exotic breed usually used for variety of improvement programmes.

    Q.6 What is the significance of GMC

    Q.7 Mention the significance of Irrigation in developing agriculture.

    Q.8. What is Pest and give one example.

    Q.9 What is Weed and give one example.

    Q.10 Give two examples for Inter-cropping.

    Q.11 Distinguish between Kharif and Rabi Crops

    Q.12 What is called Sustainable Practice in improvement in food resources.

    Q.13. Mention three techniques of Hybridization used to achieve desirable agronomic characteristics.

    Q.14.Distinguish between Macro Nutrients and Micro Nutrients Q.15 Distinguish between Compost and Vermi Compost.

    Q.16 Distinguish between Cattle farming and Poultry farming.

    Q.17 Distinguish between Fish farming and Bee keeping.