CBSE Class IX Maths Syllabus and Sample Papers
Study Material for Class VIII (8th)
CBSE syllabus, sample papers, unit tests and solutions of sample papers, CBSE syllabus for class IX and VIII for all subjects, chapter-wise basic concepts of mathematics for class IX, chapter-wise planning in mathematics for class IX, Study material for class VIII.
RESOURCE CENTRE MATHEMATICS
CHAPTER WISE EXPLANATION |
CHAPTER 1: Number System (Algebra)Syllabus: REAL NUMBERS (18) Periods
1. Review of representation of natural numbers, integers,
and rational numbers on the number line. Rational numbers as recurring/
terminating decimals. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. Existence
of non-rational numbers (irrational numbers) such as , 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. Rationalization (with precise meaning) of real numbers of
the type  ,  and (and their combinations) where x and y are natural number and a
and b are integers.
5. Recall of laws of exponents with integral powers.
Rational exponents with positive real bases (to be done by particular cases,
allowing learner to arrive at the general laws.) Basics & Formulas
Assignment
Solved Explanation of the questions
Multiple Choice Questions Ch-1 Class IX
Lesson Plan Mathematics |
CHAPTER 2: PolynomialsSyllabus: Definition of a polynomial in one variable, with examples
and counter examples. Coefficients of a polynomial, terms of a polynomial and
zero polynomial. 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:
and their use in factorization of polynomials.
Basics & Formulas
Algebraic Identities
Assignment
Multiple Choice Questions Ch-2 Class IX
Lesson Plan Mathematics |
CHAPTER 3: Coordinate GeometrySyllabus: The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations. Basics & Formulas
Assignment
Lesson Plan Mathematics |
CHAPTER 4: Linear Equations in two variablesSyllabus: 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.Explain 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. Multiple Choice Questions Ch-4 Class IX
Lesson Plan Mathematics
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CHAPTER 5: Euclid's GeometrySyllabus: 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. 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. Lesson Plan Mathematics
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CHAPTER 6: Lines and angles (Geometry)Syllabus: 1. (Motivate) If a ray stands on a line, then the sum of the
two adjacent angles so formed is 180O and the converse. 2. (Prove) If two lines intersect, vertically opposite
angles are equal.
3. (Motivate) Lines which are parallel to a given line are
parallel. Basics & Formulas
Lesson Plan Mathematics
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CHAPTER 7: Triangles (Geometry) 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. Congruence of Triangles
Properties of Triangle
Lesson Plan Mathematics
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CHAPTER 8: Quadrilaterals (Geometry)Syllabus: 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. Basics & Formulas
Theorems on chapter 8
Lesson Plan Mathematics
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CHAPTER 9: Area Related to QuadrilateralsDeleted for the session 2022-23
Basics & Formulas
Planning |
CHAPTER 10: Circles (Geometry)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) Equal chords of a circle (or of congruent
circles) are equidistant from the center (or their respective centers) and
conversely. 4.(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. 5.(Motivate) Angles in the same segment of a circle are
equal. 6.(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.
7.(Motivate) The sum of either of the pair of the opposite
angles of a cyclic quadrilateral is 180° and its converse. Basics & Formulas
Planning |
CHAPTER 11: Constructions (Geometry)
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CHAPTER 12 Heron's Formula (Area of Triangles)Syllabus: Area of a triangle using Heron's formula (without proof)
Planning |
CHAPTER 13: Surface area and Volumes (Solid Geometry)Syllabus: Surface areas and volumes of spheres (including hemispheres) and right circular cones. Basics & Formulas
Planning |
CHAPTER 14: Statistics (Mean, Mode, Median)Basics & Formulas
Planning |
CHAPTER 15: Probability (Tossing of Coins & Dice)Deleted for session 2022-23 Basics & Formulas
Assignments |
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Maths STUDY – MATERIAL (For 9th Standard) Exemplar Solution
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Sample Papers (Maths): Click Here Objective Type Questions (Maths): Click Here
Question Bank (Maths): Click Here
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