CBSE Syllabus For Class 9 Maths 2019: Every student Class 9 in CBSE affiliated schools must be aware of the CBSE Syllabus for Class 9 Maths in order to ace the Maths exam. This is a must because you need to finish the CBSE Class 9 Maths syllabus thoroughly. Otherwise, you will face a lot of difficulty in Class 10 as the Class 10 Maths syllabus is related to the CBSE syllabus for Class 9 Maths. So, all the students who are in Class 9 and will appear for the Class 10 board exams must have a clear knowledge of CBSE syllabus of Class 9 Maths and ensure they finish every concept and topic included in the syllabus.
Also, Maths plays an important role for students who want to take Science stream in Class 11-12 and appear for engineering entrance exams, like JEE, BITSAT, etc. So in this article, we will provide you with all the detailed information regarding CBSE Syllabus For Class 9 Maths 2019. Read on to find out.
CBSE Syllabus For Class 9 Maths 2019
Before getting into the detailed CBSE Syllabus For Class 9 Maths, let’s us look at the units included in CBSE Mathematics Syllabus along with the mark distribution:
|VI||Statistics & Probability||10|
Let us now see what all are included in each of these units.
CBSE Syllabus For Class 9 Maths: Number Systems
The CBSE Class 9 Syllabus for Number Systems is tabulated below:
|CBSE Syllabus For Class 9 Maths – Number Systems|
|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. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. The 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, viz. every point on the number line represents a unique real number.
3. Definition of nth root of a real number.
4. The existence of √x for a given positive real number x and its representation on the number line with geometric proof.
5. Rationalization (with precise meaning) of real numbers and their combinations where x and y are a natural number and a and b are integers.
6. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing the learner to arrive at the general laws.)
CBSE Syllabus For Class 9 Maths: Algebra
The CBSE Class 9 syllabus for Algebra is tabulated below:
|CBSE Syllabus For Class 9 Maths – Algebra|
|Polynomials (23 Periods)|| Definition of a polynomial in one variable, with examples and counterexamples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. A 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. Verification of identities:
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(x ± y)3 = x3 ± y3 ± 3xy (x ± y)
x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx) and their use in factorization of polynomials.
|Linear Equations in Two Variables (14 Periods)
|Recall of linear equations in one variable. Introduction to the equation in two variables.
Focus on linear equations of the type ax + by + c = 0. Prove that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Graph of linear equations in two variables. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.
CBSE Syllabus For Class 9 Maths: Coordinate Geometry
The CBSE Class 9 syllabus for Coordinate Geometry is tabulated below:
|CBSE Syllabus For Class 9 Maths – 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.|
CBSE Syllabus For Class 9 Maths: Geometry
The CBSE Class 9 syllabus for Geometry is tabulated below:
|CBSE Syllabus For Class 9 Maths – 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 180oand 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 Congruence).
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 (RHS Congruence).
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.
|4. Quadrilaterals (10 Periods)||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 sides is 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 two sides is parallel to the third side and in half of it and (motivate) its converse.
|5. Area (7 Periods)||Review concept of area, recall area of a rectangle.
1. (Prove) Parallelograms on the same base and between the same parallels have the same area.
2. (Motivate) Triangles on the same (or equal base) base and between the same parallels are equal in area.
|6. Circles (15 Periods)||Through examples, arrive at definition of circle and 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 the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three given non-collinear points.
4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
5. (Prove) The angle subtended by an arc at the center is double the angle subtended by 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 other points lying on the same side of the line containing the segment, the four points lie on a circle.
8. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180oand its converse.
|7. Constructions (10 Periods)||1. Construction of bisectors of line segments and angles of measure 60o, 90o, 45o etc., equilateral triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
3. Construction of a triangle of given perimeter and base angles.
CBSE Syllabus For Class 9 Maths: Mensuration
The CBSE Class 9 syllabus for Mensuration is tabulated below:
|CBSE Syllabus For Class 9 Maths – 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.|
|2. Surface Areas and Volumes (12 Periods)||Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.|
CBSE Syllabus For Class 9 Maths: Statistics & Probability
|CBSE Syllabus For Class 9 Maths – Statistics & Probability|
|1. Statistics (13 Periods)||Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequency polygons. Mean, median and mode of ungrouped data.|
|2. Probability (9 Periods)||History, repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real life situations, and from examples used in the chapter on statistics).|
Now you are provided with all the detailed information regarding CBSE Syllabus For Class 9 Maths. Make sure you understand the theory behind all these concepts before memorizing the formulas and practicing. Like any other subject, Maths too need an understanding of the theories.
Finish the NCERT Maths textbook first. Then take free CBSE Class 9 Maths mock tests and solve free CBSE Class 9 Maths practice questions on Embibe. These will help you in various competitive exams like Olympiads and NTSE as well.
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