,CBSE XCBSE IXCBSE VIIICBSE VIICBSE VI
Free sample CBSE/NCERT Class 9 Mathematics animated/multimedia lesson videos and tests
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Number of Animated lessons
Linear equation in two variables
Introduction to Euclid’s Geometry
Lines and angles
Areas of parallelograms and triangles
Surface areas and volumes
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,Mathematics Course Structure Class IX
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
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.
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
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
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.)
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.
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
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.
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).