KVS TGT Maths Syllabus 2023 – Download KVS TGT Metathetic Syllabus PDF

Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers

Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2 & √3, and their representation on the number line. Explain that every real number is represented by a unique point on the number line; conversely, viz., every point on the number line represents a unique real number.

Definition of nth root of a real number.

Rationalization of real numbers.

Laws of exponents with integral powers. Rational exponents with positive real bases.

Fundamental Theorem of Arithmetic statements after reviewing work done earlier and illustrating and motivating through examples, Proofs of the irrationality of √2, √3 & √5.

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. A constant, linear, quadratic and cubic polynomial Monomials, binomials, trinomials. Factors and multiples.

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

Remainder Theorem with examples, 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.

Linear Equations in Two Variables, 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.

Pair of Linear Equations in Two Variables, Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for several solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems.

A standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization and using the quadratic formula. Relationship between discriminant and nature of roots.

Arithmetic Progression, nth term and a sum of the first n terms of A.P. and their application in solving daily life problems.

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, and notations. Graphs of linear equations. Distance formula. Section formula (internal division)

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomena 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.

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180 degrees and the converse.

If two lines intersect, vertically opposite angles are equal.

Lines that are parallel to a given line are parallel.

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).

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).

Two triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle (SSS Congruence).

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).

The angles opposite to equal sides of a triangle are equal.

The sides opposite to equal angles of a triangle are equal.

If a line is drawn parallel to one side of a triangle to intersect the other in distinct points, the other two sides are divided in the same ratio.

If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

If the corresponding angles are equal in two triangles, their corresponding sides are proportional, and the triangles are similar.

If the corresponding sides of two triangles are proportional, their corresponding angles are equal, and the two triangles are similar.

If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.

Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

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.

Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.

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.

Angles in the same segment of a circle are equal.

If a line segment joining two points subtends an equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

The sum of either pair of opposite angles of a cyclic quadrilateral is 180° and its converse.

Tangent to a circle at the point of contact

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

The lengths of tangents drawn from an external point to a circle are equal.

Using Heron’s formula, the Area of sectors and segments of a circle is, Area of a triangle. Problems based on areas and perimeter/circumference of the above-said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to a central angle of 60°, 90° and 120°.

Surface areas and volumes of spheres (including hemispheres) and right circular cones. Surface areas and volumes of combinations of any of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

Bar graphs, histograms (with varying base lengths), and frequency polygons. Mean, median and mode of grouped data.

The classical definition of probability.Simple problems in finding the probability of an event

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0 degrees and 90 degrees. Values of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios.

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities are to be given.

The angle of elevation, Angle of Depression. Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, and 60°