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APPSC TGT Mathematics Free Mock Test
Crack the APPSC TGT Mathematics Mock Test 2026 with the help of an online Test series or a free mock test. Every sample paper in the APPSC TGT Mathematics Exam has a designated weight, so do not miss out on any paper. Prepare for the APPSC TGT Mathematics mock test and check your test scores.
APPSC TGT (Mathematics) Syllabus 2026, Exam Pattern
APPSC TGT Mathematics Syllabus 2026, Exam Pattern, Exam Date 2026
Detail Information about APPSC has published notification 2026 for the recruitment of TGT Mathematics vacancies. Those Candidates who are Interested to the following vacancy and completed all Eligibility Criteria can read the Notification & Apply Online. In this page we provide the Complete Syllabus of this Recruitment with Latest Update Exam Pattern and the Exam Date also.
APPSC TGT Mathematics Syllabus 2026 - Overview
| Organization Name | Arunachal Pradesh Staff Selection Commission (APSSC) |
| Post Name | Trained Graduate Teacher (Mathematics) Examination - 2026 (Secondary Level) |
| No of Posts | 35 Posts |
| Application Mode | Online |
| Category | Syllabus and Exam Pattern |
| Job Location | Arunachal Pradesh |
| Official website | appsc.gov.in |
APPSC TGT Mathematics Syllabus 2026
General English: Questions in this section will be designed to test fundamental language skills, Grammar rules, vocabulary skills, reading and comprehension.
General Studies: Questions in this section will aim at testing the candidate's general awareness of the surrounding environment and its implication to the society as expected from an educated person without any specialized study. It will include current afflairs, recent developments, day to day pragmatic observations and matters of importance. This section will also include questions pertaining to general awareness related to International, National and North-East India.
Aptitude:
1. Teaching, Maxims of teaching
2. Learning, Learning objectives and outcomes
3. Teaching & Instruction, Events of instruction
4. Factors Affecting Teaching
5. Teaching techniques, teaching style, classroom management
6. Ethics in teaching
Pedagogy:
1. Understanding the Learner - growth, maturation and development, Domains of
Development: Physical, Cognitive, Socio-emotional, Moral etc., deviations in
development and its implications, Understanding Adolescent behaviour.
2. Understanding Teaching Leaming - Principles of Leaming, Theories - Behaviourism,
Cognitivism and Constructivism, Role of teacher, role of learner. Nature of teacherstudent relationship, Factors affective learning.
3. Teaching strategies & methods, Active learning, Classroom environment, Classroom
Communication, Skill components in Teaching.
4. Planning instruction - session plan, lesson plan.
5. Curriculum & Syllabus, Outcome based curriculum
6. NEP 2020 - implications for school.
7. ICT in teaching-learning, Instructional resource.
8. Assessment 8. Evaluation Formative, Summative, Self-assessment, Peer
assessment, Providing & receiving feedback, NRT, CRT, Difect & Indirect assessment,
Assessment tools, Constructive alignment.
9. Teacher as a mentor, academic leader, counsellor, promoting holistic development of learners.
10. National curriculum framework and syllabus design.
11. Learning outcomes, Foundational Literacy and Numeracy (FLN) and level wise
competencies.
12. Educational lndicators with emphasis to those which are directly related to teachers
Concerned Subject (Mathematics) :
PAPER-I
Unit I:
1. Linear equation in two variables:
Pairs of linear equation in two variables, condition for consistency and inconsistency, solution of pair of linear equations in two variables, algebraic method of solving a pair of linear equation, substitution method, elimination method, cross multiplication method.
2. Principle of Mathematical Induction: Process of proof by induction, the principle of mathematical induction and its simple application.
3. Complex number and quadratic equation:
Need for complex number especially to motivate by inability to solve quadratic equation x² + 10. Brief description of Properties of complex numbers. Argand plane and polar representation of a complex number, solution of quadratic equation in the complex number system.
4. Linear In equation:
Linear inequation, solution of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of a system of linear inequalities in two variables.
5. Permutations and Combinations: Fundamental Principle of counting, factorial n (nl). Permutations and combinations and their simple applications.
6. Binomial Theorem: Statements and proof of the binomial theorem for positive integral indices. General and Middle terms in binomial expansion, simple application.
7. Sequence and Series:
Sequence and series, Arithmetic progression (A.P), Arithmetic Mean (A.M). Geometric Progression (G.P), Geometric Mean (G.M), sum of n terms of A.P and G.P, General terms of A.P & G.P, relation between A.M to G.M, sum of 'n terms of the special series En (sum of first n natural numbers), En² (sum of square of first n natural numbers) and En³ (sum of cubes of first n natural numbers).
8. Real numbers: Laws of exponent with integral powers, rational exponents with positive real bases, fundamental theorem arithmetic, LCM and HCF.
9. Polynomials:
Definition of polynomial in one variable, coefficient of polynomial, zero of a polynomial, degree of polynomial. Constant, linear, quadratic and cubic polynomials, relation between zeros and coefficient of quadratic polynomials, factor theorem, remainder theorem. The algebraic expressions and identities.
UNIT-II: Geometry
1. Triangles :
Triangle and its various kinds of centres, congruency of triangles, theorems related to congruent triangles, Similar triangles, properties of similar triangles, theorems related to similar triangles.
2. Quadrilaterals : Quadrilateral, parallelogram and its properties, rhombus and its properties, trapezium, square and rectangle.
3. Circle :
Definition of circle, chord of circle and related theorems, angles subtended by chords of a circle, sector and segment of a circle, area of circle, tangent to a circle and related theorems, common tangents to two or more circles, point of contact.
UNIT-III: AREAS AND VOLUME : Area of a triangle using Heron's formula and its application in finding the area of a quadrilateral, surface area and volume of cubes, cuboids, cone, cylinder, spheres and hemisphere
UNIT-IV: STATISTICS :
Introduction of statistics, collection of data, presentation of data in tabular form, Mean, median, mode of ungrouped and grouped data, mean deviation and standard deviation of ungrouped and grouped data, variance.
PAPER-II :-
Unit I:
Matrices and Determinants: - Concept, notion order, equality, types of matrices, transpose of a matrix, symmetric and skews-symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication, Concept of elementary row and column transformation, Invertible matrices. Determinant of a square matrix (up to 3x3 order), properties of determinant, Minors and co-factors and application of determinants in finding the area of a triangle, Adjoint and inverse of a matrix, solving a system of linear equations in two or three variable (having unique solution) using inverse of a matrix.
UNIT-II: PROBABILITY :
Multiplication theorem on probability, conditional probability independent events, total probability, Baye's theorem, Random variables and probability distribution, mean and variance of random variable, Bernoulli's trails and Binomial distribution.
UNIT-III: VECTOR :
Vector and scalars, Direction cosines and direction ratios of a vector, types of vectors, addition of vectors, multiplication of a vector by a scalar, section formula, scalar(dot) product and-vector (cross) Product of two vectors, projection of a vector on another vector, scalar and vector product of three vectors,
UNIT IV: CALCULUS :
1. DIFFERENTIAL CALCULUS
Continuity and differentiability, derivative of composite function, chain rule, derivative of inverse trigonometric function, derivative of implicit function, Concept of exponential and logarithmic function and their derivatives, Logarithmic differentiation, derivative of function expressed in parametric forms. Second order derivative. Application of derivatives rate of change of quantities, increasing and decreasing functions, tangent and normal, maxima and minima, approximation.
2. INTEGRAL CALCULUS
Integration as inverse process of differentiation, integration of functions by substation, by partial fraction and by parts. Definite integrals, properties of definite integral, Application of integrals in finding the area under simple curves, especially lines/circles/parabolas /ellipses (in standard form only) and area between the two above said curves,
3. DIFFERENTIAL EQUATION
Definition, order and degree of differential equation, general and particular solution of a differential equation, Formation of differential equation, differential equation of first order and first degree, solution of differential equation by the method of separation of variables, homogenous differential equation, Solution of linear differential equations of first order and first degree.
UNIT-V: ANALYTICAL GEOMETRY
Co-ordinate Geometry, the Cartesian plane, coordinates of a point in Cartesian plane, distance between two points, sections formula, area of a triangle, straight line, slope of a line, various forms of equation of a line, general equation of line distance of a point form a line, Conic section, eclipse, parabola, hyperbola, circle, pair of straight lines. Homogenous equation of 2nd degree, angle between a pair of straight lines, Condition for general equation of 2nd degree to represent a pair of straight lines, vector and Cartesian form of equation of straight lines in space. Shortest distance between two lines in space and equation of shortest distance, Vector and Cartesian equation of a plane, General equation of a sphere, intersection of plåne and sphere, equation of a tangent plane.
UNIT-VI: TRIGONOMETRY
Trigonometric ratios of an acute angle of a right-angled triangle, relationship between the trigonometric ratios, trigonometric identities, trigonometric ratios of complementary angles, height and distances.
Positive and negative angles, measuring angles in radian and degree and their conversion from one measure to another measure. Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x, and tan 3x. General solution of trigonometrie equations. Simple application of sine and cosine formula, Inverse trigonometric function: definition, domain, range and principle value branch. Elementary properties of inverse trigonometric function, De-moivre's theorem for rational indices, expansion of sin nx and cos nx in power of x, exponential expression for circular function and its arguments, Gregory's Series, hyperbolic function.
General Studies: Questions in this section will aim at testing the candidate's general awareness of the surrounding environment and its implication to the society as expected from an educated person without any specialized study. It will include current afflairs, recent developments, day to day pragmatic observations and matters of importance. This section will also include questions pertaining to general awareness related to International, National and North-East India.
Aptitude:
1. Teaching, Maxims of teaching
2. Learning, Learning objectives and outcomes
3. Teaching & Instruction, Events of instruction
4. Factors Affecting Teaching
5. Teaching techniques, teaching style, classroom management
6. Ethics in teaching
Pedagogy:
1. Understanding the Learner - growth, maturation and development, Domains of
Development: Physical, Cognitive, Socio-emotional, Moral etc., deviations in
development and its implications, Understanding Adolescent behaviour.
2. Understanding Teaching Leaming - Principles of Leaming, Theories - Behaviourism,
Cognitivism and Constructivism, Role of teacher, role of learner. Nature of teacherstudent relationship, Factors affective learning.
3. Teaching strategies & methods, Active learning, Classroom environment, Classroom
Communication, Skill components in Teaching.
4. Planning instruction - session plan, lesson plan.
5. Curriculum & Syllabus, Outcome based curriculum
6. NEP 2020 - implications for school.
7. ICT in teaching-learning, Instructional resource.
8. Assessment 8. Evaluation Formative, Summative, Self-assessment, Peer
assessment, Providing & receiving feedback, NRT, CRT, Difect & Indirect assessment,
Assessment tools, Constructive alignment.
9. Teacher as a mentor, academic leader, counsellor, promoting holistic development of learners.
10. National curriculum framework and syllabus design.
11. Learning outcomes, Foundational Literacy and Numeracy (FLN) and level wise
competencies.
12. Educational lndicators with emphasis to those which are directly related to teachers
Concerned Subject (Mathematics) :
PAPER-I
Unit I:
1. Linear equation in two variables:
Pairs of linear equation in two variables, condition for consistency and inconsistency, solution of pair of linear equations in two variables, algebraic method of solving a pair of linear equation, substitution method, elimination method, cross multiplication method.
2. Principle of Mathematical Induction: Process of proof by induction, the principle of mathematical induction and its simple application.
3. Complex number and quadratic equation:
Need for complex number especially to motivate by inability to solve quadratic equation x² + 10. Brief description of Properties of complex numbers. Argand plane and polar representation of a complex number, solution of quadratic equation in the complex number system.
4. Linear In equation:
Linear inequation, solution of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of a system of linear inequalities in two variables.
5. Permutations and Combinations: Fundamental Principle of counting, factorial n (nl). Permutations and combinations and their simple applications.
6. Binomial Theorem: Statements and proof of the binomial theorem for positive integral indices. General and Middle terms in binomial expansion, simple application.
7. Sequence and Series:
Sequence and series, Arithmetic progression (A.P), Arithmetic Mean (A.M). Geometric Progression (G.P), Geometric Mean (G.M), sum of n terms of A.P and G.P, General terms of A.P & G.P, relation between A.M to G.M, sum of 'n terms of the special series En (sum of first n natural numbers), En² (sum of square of first n natural numbers) and En³ (sum of cubes of first n natural numbers).
8. Real numbers: Laws of exponent with integral powers, rational exponents with positive real bases, fundamental theorem arithmetic, LCM and HCF.
9. Polynomials:
Definition of polynomial in one variable, coefficient of polynomial, zero of a polynomial, degree of polynomial. Constant, linear, quadratic and cubic polynomials, relation between zeros and coefficient of quadratic polynomials, factor theorem, remainder theorem. The algebraic expressions and identities.
UNIT-II: Geometry
1. Triangles :
Triangle and its various kinds of centres, congruency of triangles, theorems related to congruent triangles, Similar triangles, properties of similar triangles, theorems related to similar triangles.
2. Quadrilaterals : Quadrilateral, parallelogram and its properties, rhombus and its properties, trapezium, square and rectangle.
3. Circle :
Definition of circle, chord of circle and related theorems, angles subtended by chords of a circle, sector and segment of a circle, area of circle, tangent to a circle and related theorems, common tangents to two or more circles, point of contact.
UNIT-III: AREAS AND VOLUME : Area of a triangle using Heron's formula and its application in finding the area of a quadrilateral, surface area and volume of cubes, cuboids, cone, cylinder, spheres and hemisphere
UNIT-IV: STATISTICS :
Introduction of statistics, collection of data, presentation of data in tabular form, Mean, median, mode of ungrouped and grouped data, mean deviation and standard deviation of ungrouped and grouped data, variance.
PAPER-II :-
Unit I:
Matrices and Determinants: - Concept, notion order, equality, types of matrices, transpose of a matrix, symmetric and skews-symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication, Concept of elementary row and column transformation, Invertible matrices. Determinant of a square matrix (up to 3x3 order), properties of determinant, Minors and co-factors and application of determinants in finding the area of a triangle, Adjoint and inverse of a matrix, solving a system of linear equations in two or three variable (having unique solution) using inverse of a matrix.
UNIT-II: PROBABILITY :
Multiplication theorem on probability, conditional probability independent events, total probability, Baye's theorem, Random variables and probability distribution, mean and variance of random variable, Bernoulli's trails and Binomial distribution.
UNIT-III: VECTOR :
Vector and scalars, Direction cosines and direction ratios of a vector, types of vectors, addition of vectors, multiplication of a vector by a scalar, section formula, scalar(dot) product and-vector (cross) Product of two vectors, projection of a vector on another vector, scalar and vector product of three vectors,
UNIT IV: CALCULUS :
1. DIFFERENTIAL CALCULUS
Continuity and differentiability, derivative of composite function, chain rule, derivative of inverse trigonometric function, derivative of implicit function, Concept of exponential and logarithmic function and their derivatives, Logarithmic differentiation, derivative of function expressed in parametric forms. Second order derivative. Application of derivatives rate of change of quantities, increasing and decreasing functions, tangent and normal, maxima and minima, approximation.
2. INTEGRAL CALCULUS
Integration as inverse process of differentiation, integration of functions by substation, by partial fraction and by parts. Definite integrals, properties of definite integral, Application of integrals in finding the area under simple curves, especially lines/circles/parabolas /ellipses (in standard form only) and area between the two above said curves,
3. DIFFERENTIAL EQUATION
Definition, order and degree of differential equation, general and particular solution of a differential equation, Formation of differential equation, differential equation of first order and first degree, solution of differential equation by the method of separation of variables, homogenous differential equation, Solution of linear differential equations of first order and first degree.
UNIT-V: ANALYTICAL GEOMETRY
Co-ordinate Geometry, the Cartesian plane, coordinates of a point in Cartesian plane, distance between two points, sections formula, area of a triangle, straight line, slope of a line, various forms of equation of a line, general equation of line distance of a point form a line, Conic section, eclipse, parabola, hyperbola, circle, pair of straight lines. Homogenous equation of 2nd degree, angle between a pair of straight lines, Condition for general equation of 2nd degree to represent a pair of straight lines, vector and Cartesian form of equation of straight lines in space. Shortest distance between two lines in space and equation of shortest distance, Vector and Cartesian equation of a plane, General equation of a sphere, intersection of plåne and sphere, equation of a tangent plane.
UNIT-VI: TRIGONOMETRY
Trigonometric ratios of an acute angle of a right-angled triangle, relationship between the trigonometric ratios, trigonometric identities, trigonometric ratios of complementary angles, height and distances.
Positive and negative angles, measuring angles in radian and degree and their conversion from one measure to another measure. Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x, and tan 3x. General solution of trigonometrie equations. Simple application of sine and cosine formula, Inverse trigonometric function: definition, domain, range and principle value branch. Elementary properties of inverse trigonometric function, De-moivre's theorem for rational indices, expansion of sin nx and cos nx in power of x, exponential expression for circular function and its arguments, Gregory's Series, hyperbolic function.
APPSC TGT Mathematics Exam Pattern 2026 (Expected)
Negative Marking : 0.66
Exam Date 2026 : 12th July 2026
Starting Date of Application Form : 26th March 2026
Last Date of Application Form : 27th April 2026
Total Post : 35
| Paper | Subject | No.of Question | Marks | Duration |
| Paper 1 | General English, General Studies, Aptitude and Pedagogy (Objective) |
150 | 150 | 2 Hour |
| Paper 2 | Concerned Subject (Mathematics) | 150 | 300 | 2 Hour |
| Total | 300 | 450 |
Exam Date 2026 : 12th July 2026
Starting Date of Application Form : 26th March 2026
Last Date of Application Form : 27th April 2026
Total Post : 35
APPSC TGT Mathematics Exam Free Online Test Series
Crack APPSC TGT Mathematics Mock Test 2026 with the help of Online Test Series or Free Mock Test. Every Sample Paper in Arunachal Pradesh TGT Exam has a designated weightage so do not miss out any Paper. Preprare for APPSC TGT Mock Test and check your test scores.
APPSC TGT Mathematics Exam Free Online Question Bank
APPSC TGT Mathematics question answer with solutions are available in Hindi & English. Join MCQ, Important Questions, Question Bank, questions and answers for Free APPSC TGT Mathematics exam preparation.
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Appsc TGT Mathematics 2026 Free Mock Test Frequently Asked Questions (FAQ's)
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