**KVS TGT Mathematics Syllabus 2023: **KVS TGT Maths Syllabus 2023along with KVS Recruitment Notification 2023 is released by Kendriya Vidyalaya Sangthan (KVS) on its official website. This time the KVS TGT Mathematics Syllabus and exam pattern has changed. We are providing here new syllabus and exam pattern for those candidates who are going to appear KVS TGT Recruitment Exam 2023 or preparing upcoming exam for the post of Trained Graduate Teacher Mathematics in Kendriya Vidyalayas. This KVS TGT Maths Syllabus is prescribed by Kendriya Vidyalaya Sangthan-kvsangthan.

**KVS Trained Graduate Teacher Mathematics Syllabus**

The KVS TGT Maths Computer Based Test is scheduled on 14 February 2023. So in this time the Syllabus of KVS TGT Mathematics is very helpful for preparation of exam. A detailed KVS TGT Syllabus of Mathematics will help the aspirants score better in the KVS and present better clarity of the topics to be covered.

**KVS TGT Mathematics Recruitment CBT 2023 – Overview**

Name of the Organization | Kendriya Vidyalaya Sangathan -KVS |

Exam Name | KVS TGT Mathematics Recruitment CBT 2022 |

Date of Exam | 14 February 2023 |

Conducting Board | KVS |

Name of Subject | Mathematics |

Name of the Posts | TGT (Trained Graduate Teacher) |

Total No. of Vacancies | …….. Posts |

Apply Mode | Online |

Job Location | All Over India |

Registration Date | 05th December 2022 to 2nd January 2023 |

Exam Mode | Online (Computer Based Test) |

Official Website | kvsangathan.nic.in |

**KVS TGT Mathematics Syllabus and Main Topic**

The syllabus for KVS TGT (Trained Graduate Teacher) Mathematics Mainly covers the following topics:

**KVS TGT Syllabus 2023: Check Kendriya Vidyalaya Trained Graduate Teacher CBT Exam Pattern Here**

**KVS TGT Mathematics Syllabus** **2023:** **Real Numbers**

- Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
- Fundamental Theorem of Arithmetic statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √2, √3, √5.
- Definition of nth root of a real number
- 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. 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.
- Rationalization of real numbers of the type and their combinations where x and y are natural number and a and b are integers.
- Laws of exponents with integral powers. Rational exponents with positive real bases

**KVS TGT Mathematics Syllabus** **2023:** **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.

**KVS TGT Mathematics Syllabus** **2023:** **Pair of Linear Equations in 2 Variables**

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

**KVS TGT Mathematics Syllabus** **2023: Polynomials**

- Definition of a polynomial in one variable, with examples and counter examples.
- Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples.
- Remainder Theorem with examples, Factor Theorem.
- Coefficients of a polynomial, terms of a polynomial and zero polynomial.
- Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
- Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem.
- The algebraic expressions and identities. Verification of identities:

**KVS TGT Mathematics Syllabus** **2023:** **Quadratic Equations**

- Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0).
- Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula.
- Relationship between discriminate and nature of roots.
- Arithmetic Progression, nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

**KVS TGT Mathematics Syllabus** **2023:** **Lines and Angles**

- 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 which are parallel to a given line are parallel.

**KVS TGT Mathematics Syllabus** **2023:** **Coordinate Geometry**

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

**KVS TGT Mathematics Syllabus** **2023:** **Introduction to Euclid’s Geometry**

- 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.

**KVS TGT Syllabus 2023: Check Kendriya Vidyalaya Trained Graduate Teacher CBT Exam Pattern Here**

**KVS TGT Mathematics Syllabus** **2023: Triangles**

- 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 the three sides of one triangle are equal to 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.
- 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).
- 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.
- The sides opposite to equal angles of a triangle are equal.
- If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
- If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
- If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

**KVS TGT Mathematics Syllabus** **2023:** **Circles**

- 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 subtend equal angles at the center and (motivate) its converse.
- 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.
- Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
- Angles in the same segment of a circle are equal.
- 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.
- 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.
- The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.
- Tangent to a circle at, point of contact

**KVS TGT Mathematics Syllabus** **2023:** **Areas**

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

**KVS TGT Mathematics Syllabus 2023: Probability**

- Classical definition of probability.
- Simple problems on finding the probability of an event.

**KVS TGT Mathematics Syllabus 2023: Quadrilaterals**

- The diagonal divides a parallelogram into two congruent triangles.
- A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
- In a parallelogram opposite angles are equal, and conversely.
- A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
- 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.
- In a parallelogram, the diagonals bisect each other and conversely.
- In a parallelogram opposite sides are equal, and conversely.

**KVS TGT Mathematics Syllabus 2023: Surface Areas and Volumes**

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

**KVS TGT Mathematics Syllabus 2023: Statistics**

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

**KVS TGT Mathematics Syllabus 2023: Heights and Distances:**

- 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°

**KVS TGT Mathematics Syllabus 2023: Trigonometry**

- Trigonometric ratios of an acute angle of a right-angled triangle.
- Proof of their existence (well defined); motivate the ratios whichever are defined at 00 and 900.
- Values of the trigonometric ratios of 300, 450 and 600.
- Relationships between the ratios.

**KVS TGT Mathematics Syllabus 2023: Trigonometric Identities**

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