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Mathematics

Free sample CBSE/NCERT Class 9 Mathematics animated/multimedia lesson videos and tests

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Tupoints class 9 lessons have been designed to build a sound foundation of learning for future exam performance in such a way that the lessons and practice tests follow a symmetrical approach to exam preparation right from class 9. At the core of lessons and tests lies the philosophy of orienting the students towards real exam ways and methods to learn and prepare smartly for best exam results and score.

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Tupoints software is designed as per the guidelines of NCERT and the other State Boards of India. With the help of Subject MatterExperts, Instruction Designers & Online Tutors and path-breaking technology, we have developed an all-inclusive knowledge repositorythat is updated with the latest syllabus .Tupoints software is designed as per the guidelines of NCERT and the other State Boardsof India. With the help of Subject Matter Experts, Instruction Designers & Online Tutors and path-breaking technology, we havedeveloped an all-inclusive knowledge repository that is updated with the latest syllabus .Tupoints software is designed as per theguidelines of NCERT and the other State Boards of India. With the help of Subject Matter Experts, Instruction Designers & OnlineTutors and path-breaking technology, we have developed an all-inclusive knowledge repository that is updated with the latest syllabus.Tupoints software is designed as per the guidelines of NCERT and the other State Boards of India. With the help of SubjectMatter Experts, Instruction Designers & Online Tutors and path-breaking technology, we have developed an all-inclusive knowledgerepository that is updated with the latest syllabus .Tupoints software is designed as per the guidelines of NCERT and the other StateBoards of India. With the help of Subject Matter Experts, Instruction Designers & Online Tutors and path-breaking technology, wehave developed an all-inclusive knowledge repository that is updated with the latest syllabus .Tupoints software is designed as perthe guidelines of NCERT and the other State Boards of India. With the help of Subject Matter Experts, Instruction Designers & Online.

,Sl.No

Chapter name

Number of Animated lessons

Total duration,1

Number system

13

37m,2

Polynomials

11

43m,3

Coordinate Geometry

8

13m,4

Linear equation in two variables

8

15m,5

Introduction to Euclid’s Geometry

7

16m,6

Lines and angles

9

22m,7

Triangles

8

20m,8

Quadrilaterals

8

19m,9

Areas of parallelograms and triangles

6

11m,10

Circles

10

27m,11

Constructions

5

11m,12

Heron’s formula

5

16m,13

Surface areas and volumes

15

37m,14

Statistics

8

27m,15

Probability

8

10m, Tupoints videos and tests are simple to learn and practice and are self explanatory.

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,Mathematics Course Structure Class IX

,Units

Chapter name

Marks,1

Number System

11,2

Algebra

21,4

Geometry

29,4

Trigonometry

7,Total

90,

First Term Syllabus

1. REAL NUMBERS

1. Review of representation of natural numbers, integers, rational numbers on thenumber line. Representation of terminating / non-terminating recurring decimals,on the number line through successive magnification. Rational numbers as recurring/terminatingdecimals.2. Examples of non-recurring / non-terminating decimals. Existence of non-rationalnumbers (irrational numbers) such as √2, √3 and their representation on the numberline. Explaining that every real number is represented by a unique point on thenumber line and conversely, every point on the number line represents a unique realnumber.3. Existence of √x 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 positivereal bases (to be done by particular cases, allowing learner to arrive at the generallaws.)6. Rationalization (with precise meaning) of real numbers of the type (and theircombinations) of rational numbers in terms of terminating/non-terminating recurringdecimals.

UNIT II: ALGEBRA

1. POLYNOMIALS

Definition of a polynomial in one variable, its coefficients, with examples andcounter examples, its terms, zero polynomial. Degree of a polynomial. Constant,linear, quadratic and cubic polynomials; monomials, binomials, trinomials. Factorsand multiples. Zeros of a polynomial. State and motivate the Remainder Theorem withexamples. 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 theFactor Theorem) dt quadratic & cubic polynomial.Recall of algebraic expressions and identities. Further verification of identitiesof 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 ± xy + y²), x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx) and their use in factorization of polymonials. Simpleexpressions reducible to these polynomials.

UNIT III: GEOMETRY

1. INTRODUCTION TO EUCLID’S GEOMETRY

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizingobserved phenomenon into rigorous mathematics with definitions, common/obvious notions,axioms/postulates and theorems. The five postulates of Euclid. Equivalent versionsof the fifth postulate. Showing the relationship between axiom and theorem, forexample:• (Axiom) 1. Given two distinct points, there exists one and only one line throughthem. • (Theorem)2. (Prove) Two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent anglesso formed is 180° and the converse.2. (Prove) If two lines intersect, vertically opposite angles are equal.3. (Motivate) Results on corresponding angles, alternate angles, interior angleswhen 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 180°.6. (Motivate) If a side of a triangle is produced, the exterior angle so formedis equal to the sum of the two interior opposite angles.

3. TRIANGLES

1. (Motivate) Two triangles are congruent if any two sides and the included angleof 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 ofone 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 areequal to three sides of the other triangle (SSS Congruence).4. (Motivate) Two right triangles are congruent if the hypotenuse and a side ofone triangle are equal (respectively) to the hypotenuse and a side of the othertriangle.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

The Cartesian plane, coordinates of a point, names and terms associated with thecoordinate plane, notations, plotting points in the plane, graph of linear equationsas examples; focus on linear equations of the type Ax + By + C = 0 by writing itas y = mx + c.

UNIT V: MENSURATION

1. AREAS

Area of a triangle using Heron’s formula (without proof) and its application infinding the area of a quadrilateral. Area of cyclic quadrilateral (with proof) -Brahmagupta’s formula

,Units

Chapter name

Marks,1

Algebra (contd.)

23,2

Geometry (contd.)

30,3

Trigonometry (contd.)

29,4

Probability

7,

Total

90,,Second Term Syllabus

UNIT II: ALGEBRA (Contd.)

2. LINEAR EQUATIONS IN TWO VARIABLES

Recall of linear equations in one variable. Introduction to the equation in twovariables. Focus on linear equations of the type ax+by+c=0. Prove that a linearequation in two variables has infinitely many solutions and justify their beingwritten as ordered pairs of real numbers, plotting them and showing that they seemto lie on a line. Examples, problems from real life, including problems on Ratioand Proportion and with algebraic and graphical solutions being done simultaneously.

UNIT III: GEOMETRY (Contd.)

4. QUADRILATERALS

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.2. (Motivate) In a parallelogram opposite sides are equal, and conversely.3. (Motivate) In a parallelogram opposite angles are equal, and conversely.4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sidesis parallel and equal.5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.6. (Motivate) In a triangle, the line segment joining the mid points of any twosides is parallel to the third side and (motivate) its converse.

5. AREA

Review concept of area, recall area of a rectangle.1. (Prove) Parallelograms on the same base and between the same parallels have thesame area.2. (Motivate) Triangles on the same (or equal base) base and between the same parallelsare equal in area

6. CIRCLES

Through examples, arrive at definitions of circle related concepts, radius, circumference,diameter, chord, arc, secant, sector, segment subtended angle.1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate)its converse.2. (Motivate) The perpendicular from the center of a circle to a chord bisects thechord and conversely, the line drawn through the center of a circle to bisect achord is perpendicular to the chord.3. (Motivate) There is one and only one circle passing through three given non-collinearpoints.4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistantfrom the center (or their respective centers) and conversely.5. (Prove) The angle subtended by an arc at the center is double the angle subtendedby it at any point on the remaining part of the circle.6. (Motivate) Angles in the same segment of a circle are equal.7. (Motivate) If a line segment joining two points subtends equal angle at two otherpoints lying on the same side of the line containing the segment, the four pointslie on a circle.8. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateralis 180° and its converse.

7. CONSTRUCTIONS

1. Construction of bisectors of line segments and angles of measure 60°, 90°, 45°etc., equilateral triangles.2. Construction of a triangle given its base, sum/difference of the other two sidesand one base angle.3. Construction of a triangle of given perimeter and base angles.

UNIT V: MENSURATION (Contd.)

2. SURFACE AREAS AND VOLUMES

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) andright circular cylinders/cones.

UNIT VI: STATISTICS

Introduction to Statistics: Collection of data, presentation of data – tabular form,ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequencypolygons, qualitative analysis of data to choose the correct form of presentationfor the collected data. Mean, median, mode of ungrouped data.

UNIT VII: PROBABILITY

History, Repeated experiments and observed frequency approach to probability. Focusis on empirical probability. (A large amount of time to be devoted to group andto individual activities to motivate the concept; the experiments to be drawn fromreal – life situations, and from examples used in the chapter on statistics).