OFFICIAL SYLLABUS
Ist Term Course
Marks:100
Time: 3 hours
Unit I: Number System
Marks : 17
Real Numbers: Review of representation of natural number, integers, rational numbers on the numbers line. Representation of terminating/ non terminating recurring decimals on the number line through successive magnification. Rational number as recurring numbers as recurring/ terminating decimals.
Existence of non- rational numbers (irrational numbers) and their representation on the number line.
Explaining that every real number is represented by a unique point on number line and conversely, every point on number line represents a unique real number. Definition of nth root of a real number. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learners to arrive at the general laws).
Rationalization (with precise meaning) of real numbers of the type (and their combinations)
Unit II: Polynomials
Marks: 18
Definition of a polynomials in one variable. Its coefficients, with examples and counter examples, its terms, Zero polynomial. Degree of a polynomial, constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiplies. Zeros/roots of a polynomial/ equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statements and proof of the Factor Theorem.
Factorization
Recall of algebraic expressions and identities
Unit III: Lines and Angles
Marks: 10
Introduction to Euclids Geometry, the five postulates of Euclid, version of the fifth postulate, Relationship between Axiom and theorem.
1. Given two distinct point, there exists one and only one line through them.
2. (Prove) T wo distinct line can not have more than one point in common. 3. (Motivate) If a ray stands on a line, then the sum of two adjacent angles so formed is 1800 degree and the converse. 4. (Prove) If two line interest, the vertically opposite angles are equal. 5. (Motivate) Results on corresponding angles, alternative angles, interior angles when a transversal interest two parallel lines. 6. Lines which are parallel to a given line are parallel. 7. (Prove) The sum of the angles of a triangle is 1800 . 8. (Motivatei) If one side of a triangle is produced, the exterior angles so formed is equal to the sum of the two interior opposite angles.
Unit IV Triangles
Marks: 20
(i) (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).
(ii) (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).
(iii) (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
(iv) (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)
(v) . (Prove) The angles opposite to equal sides of a triangle are equal.
(vi) (Motivate) The sides opposite to equal angles of a triangle are equal.
Unit V Quadrilaterals
Marks: 15
(i) (Prove) The diagonal divides a parallelogram into two congruent triangles.
(ii) (Motivate) In a parallelogram opposite sides are equal, and conversely.
(iii) (Motivate) In a parallelogram opposite angles are equal, and conversely.
(iv) (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
(v) (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
(vi) (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.
Unit VI Areas of Parallelograms and Triangles
Marks : 10
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 base and between the same parallels are equal in area and its converse.
Unit VII Constructions
Marks: 10
(i) Construction of bisectors of line segments and angles of measure 60etc., equilateral triangles.60o, 90o, 45o
(ii) Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
(iii) Construction of a triangle of given perimeter and base angles.
II Term Course
Unit VIII Linear Equation in Two Variables
Marks: 10
Recall of linear equations in one variable. Introduction to the equation in two variables. Prove that a linear equation in two variable has infinitely many solution and justify their being written as ordered pairs of real numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solution being done
simultaneously.
Unit IX Coordinate Geometry
Marks 10
The Cartesian plane. Coordinates of a point, names and terms associated with co-ordinate plane notations plotting points in the plane, graph of a linear equations as examples: focus on linear equations o
...
OFFICIAL SYLLABUS
Ist Term Course
Marks:100
Time: 3 hours
Unit I: Number System
Marks : 17
Real Numbers: Review of representation of natural number, integers, rational numbers on the numbers line. Representation of terminating/ non terminating recurring decimals on the number line through successive magnification. Rational number as recurring numbers as recurring/ terminating decimals.
Existence of non- rational numbers (irrational numbers) and their representation on the number line.
Explaining that every real number is represented by a unique point on number line and conversely, every point on number line represents a unique real number. Definition of nth root of a real number. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learners to arrive at the general laws).
Rationalization (with precise meaning) of real numbers of the type (and their combinations)
Unit II: Polynomials
Marks: 18
Definition of a polynomials in one variable. Its coefficients, with examples and counter examples, its terms, Zero polynomial. Degree of a polynomial, constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiplies. Zeros/roots of a polynomial/ equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statements and proof of the Factor Theorem.
Factorization
Recall of algebraic expressions and identities
Unit III: Lines and Angles
Marks: 10
Introduction to Euclids Geometry, the five postulates of Euclid, version of the fifth postulate, Relationship between Axiom and theorem.
1. Given two distinct point, there exists one and only one line through them.
2. (Prove) T wo distinct line can not have more than one point in common. 3. (Motivate) If a ray stands on a line, then the sum of two adjacent angles so formed is 1800 degree and the converse. 4. (Prove) If two line interest, the vertically opposite angles are equal. 5. (Motivate) Results on corresponding angles, alternative angles, interior angles when a transversal interest two parallel lines. 6. Lines which are parallel to a given line are parallel. 7. (Prove) The sum of the angles of a triangle is 1800 . 8. (Motivatei) If one side of a triangle is produced, the exterior angles so formed is equal to the sum of the two interior opposite angles.
Unit IV Triangles
Marks: 20
(i) (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).
(ii) (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).
(iii) (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
(iv) (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)
(v) . (Prove) The angles opposite to equal sides of a triangle are equal.
(vi) (Motivate) The sides opposite to equal angles of a triangle are equal.
Unit V Quadrilaterals
Marks: 15
(i) (Prove) The diagonal divides a parallelogram into two congruent triangles.
(ii) (Motivate) In a parallelogram opposite sides are equal, and conversely.
(iii) (Motivate) In a parallelogram opposite angles are equal, and conversely.
(iv) (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
(v) (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
(vi) (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.
Unit VI Areas of Parallelograms and Triangles
Marks : 10
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 base and between the same parallels are equal in area and its converse.
Unit VII Constructions
Marks: 10
(i) Construction of bisectors of line segments and angles of measure 60etc., equilateral triangles.60o, 90o, 45o
(ii) Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
(iii) Construction of a triangle of given perimeter and base angles.
II Term Course
Unit VIII Linear Equation in Two Variables
Marks: 10
Recall of linear equations in one variable. Introduction to the equation in two variables. Prove that a linear equation in two variable has infinitely many solution and justify their being written as ordered pairs of real numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solution being done
simultaneously.
Unit IX Coordinate Geometry
Marks 10
The Cartesian plane. Coordinates of a point, names and terms associated with co-ordinate plane notations plotting points in the plane, graph of a linear equations as examples: focus on linear equations of the type ax + by + c = 0 by writing it as y = mx + c and linking it with chapter on linear equations in two variables.
Unit X Circles
Marks :25
Definition of circles, related concepts, radius, circumference, diameter, chord, arc, subtended angle.
1. (Prove) Equal chords of a circle subtend equal angles at the centre and its converse.
2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord and conversely, the line drawn through the centre of a circle to bisects 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 centre (s) and
conversely.
Unit XI Heron’s Formula
Marks: 10
Area of triangle using Heron’s formula (without proof) and its application in finding the area of a Quadrilateral.
Unit XII Surface Area and Volumes
Marks: 20
Surface areas and volumes of cubes, cuboids, Sphere (Including hemispheres) and right circular cylinders/ cones.
Unit XIII Statistics
Marks: 15
Introduction to Statistics, Collection of data, Presentation of data-tabular form, ungrouped grouped, bar graphs, histogram (with varying base lengths) frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean (arithmetic mean), Median, Mode of ungrouped data.
Unit XIV Probability
Marks: 10
History, Repeated experiments and observed frequency approach to Probability. Focus is on empiricalProbability
Book Prescribed:Mathematics: A Text Book for Class IX published by Jammu and KashmirState Board of School Education.
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