**NVS TGTs Mathematics Syllabus 2022**

Mathematics is an important subject in NVS TGT Exam. The weightage of Subject Knowledge (Mathematics)is 80 marks. Candidates can read the detailed syllabus of the NVS TGT Mathematics syllabus mentioned below.

**Real Number:**

- Representation of natural numbers, integers, and 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. Examples of nonrecurring /non-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 the number line and conversely, every point on the number line represents a unique real number. - Laws of exponents with integral powers. Rational exponents with positive real bases. Rationalization of real numbers. Euclid’s division lemma, Fundamental

The theorem of Arithmetic. Expansions of rational numbers in terms of terminating / non-terminating recurring decimals.

**Elementary Number Theory:**

- Peano’s Axioms, Principle of Induction; First Principal, Second Principle, Third Principle, Basis Representation Theorem, Greatest Integer Function, Test of

Divisibility, Euclid’s algorithm, The Unique Factorisation Theorem, Congruence, Chinese Remainder Theorem, Sum of divisors of a number. Euler’s totient function, Theorems of Fermat and Wilson.

**Matrices:**

- R, R2, R3 as vector spaces over R and concept of Rn. The standard basis for each of them. Linear Independence and examples of different bases. Subspaces of R2,

R3. Translation, Dilation, Rotation, and Reflection in a point, line and plane. Matrix form of basic geometric transformations. Interpretation of eigenvalues and

eigenvectors for such transformations and eigenspaces as invariant subspaces. Matrices in diagonal form. Reduction to diagonal form up to matrices of order 3.

Computation of matrix inverses using elementary row operations. The rank of a matrix, Solutions of a system of linear equations using matrices.

**Polynomials:**

- Definition of a polynomial 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 multiples. Zeros/roots of a polynomial/equation. Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization of quadratic and cubic polynomials using the Factor Theorem. Algebraic expressions and identities and their use in the factorization of polynomials. Simple expressions are reducible to these polynomials.

**Linear Equations in two variables:**

- Introduction to the equation in two variables. Proof that a linear equation in two variables has infinitely many solutions and justifies their being written as

ordered pairs of real numbers, Algebraic and graphical solutions.

**Pair of Linear Equations in two variables:**

- Pair linear equations in two variables. Geometric representation of different possibilities of solutions/inconsistency. Algebraic conditions for the number of

solutions. Solution of pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication.

**Quadratic Equations:**

- The standard form of a quadratic equation. Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e. by using

the quadratic formula. Relationship between discriminant and nature of roots. Relation between roots and coefficients, Symmetric functions of the roots of an

equation. Common roots.

**Arithmetic Progressions:**

- Derivation of standard results of finding the nth term and sum of the first n terms.

**Inequalities:**

- Elementary Inequalities, Absolute value, Inequality of means, Cauchy – Schwarz Inequality, Tchebychef’s Inequality.

**Combinatorics:**

- Principle of Inclusion and Exclusion, Pigeon Hole Principle, Recurrence Relations, Binomial Coefficients.

**Calculus:**

- Sets. Functions and their graphs: polynomial, sine, cosine, exponential and logarithmic functions. Step function, Limits and continuity. Differentiation,

Methods of differentiation like the Chain rule, Product rule and Quotient rule. Second order derivatives of the above functions. Integration is a reverse process of

differentiation. Integrals of the functions introduced above.

**Euclidean Geometry:**

- Axioms/postulates and theorems. The five postulates and Euclid. Equivalent versions of the fifth postulate. Relationship between axiom and theorem. Theorems and lines and angles, triangles and quadrilaterals, Theorems on areas of parallelograms and triangles, Circles, theorems on circles, Similar triangles, and Theorem on similar triangles. Constructions.

Ceva’s Theorem, Menalus Theorem, Nine Point Circle, Simson’s Line, Centres of the similitude of Two Circles, Lehmus Steiner Theorem, Ptolemy’s Theorem.

**Coordinate Geometry:**

- The Cartesian plane, coordinates of a point, Distance between two points and section formula, Area of a triangle.

**Areas and Volumes:**

- Area of a triangle using Hero’s formula and its application in finding the area of a quadrilateral. Surface areas and volumes of cubes, cuboids, spheres

(including hemispheres) and right circular cylinders/cones. Frustum of a cone. - Area of a circle: area of sectors and segments of a circle.

**Trigonometry:**

- Trigonometric ratios of an acute angle of a right-angled triangle. Relationships between the rations. Trigonometric identities. Trigonometric ratios of complementary angles. Heights and distances.

**Statistics:**

- Introduction to Statistics: Collection of data, presentation of data, tabular form, ungrouped / grouped, bar graphs, histograms, frequency polygons,

qualitative analysis of data to choose the correct form of presentation for the collected data. - Mean, median, and mode of ungrouped data. Mean, median and mode of grouped data. Cumulative frequency graph.

**Probability:**

- Elementary Probability and basic laws. Discrete and Continuous Random variable, Mathematical Expectation, Mean and Variance of Binomial, Poisson

and Normal distribution. The sample mean and Sampling Variance. Hypothesis testing using standard normal variate. Curve Fitting. Correlation and

Regression. Elementary Probability and basic laws. Discrete and Continuous Random variable, Mathematical Expectation, Mean and Variance of Binomial, Poisson

and Normal distribution. The sample mean and Sampling Variance. Hypothesis testing using standard normal variate. Curve Fitting. Correlation and Regression.

## NVS TGTs Mathematics Exam Pattern 2022

NVS TGT Exam Pattern gives an overall idea about the question format, marking scheme, and weightage of each topic covered. NVS TGT Mathematics tests will be conducted in English and Hindi except for the English Language. There will be a deduction of 0.25 marks for each wrong answer in the Objective test. Candidates can check the exam pattern of TGT Mathematics from the table mentioned below. NVS TGT Mathematics exam will be conducted for 150 marks.

Test | Subject | Number of questions | Total marks | Duration of the test |

Part-I | Reasoning Ability | 10 | 10 | 3 Hours |

Part-II | General Awareness | 10 | 10 | |

Part-III | Teaching Aptitude | 10 | 10 | |

Part-IV | Knowledge of ICT | 10 | 10 | |

Part-V | Subject Knowledge (difficulty level Graduation) | 80 | 80 | |

Total | 120 | 120 | ||

Part-VI | Language Competency General Hindi, General English and Regional Language*-10 marks each subject). | 30 | 30 |

## NVS TGT Mathematics Study Material

NVS TGT Mathematics study material 2022 is extremely necessary for a candidate’s preparation. NVS TGT Mathematics study material acts as a torchbearer for candidates. For fresher candidates, NVS TGT study material 2022 will help them lay the groundwork for their exam preparation. Through this, you will get good speed and will be able to solve problems in lesser time. Candidates can read the study notes important for the NVS TGT Mathematics exam from the table mentioned below

Serial No. | Topic | Link |

1. | Concept & Tricks on Number System | Read Here |

2. | Basic Formulas & Short Tricks on Algebra | Read Here |

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