The syllabus consist of two papers as follows : RPSC Mathematics grade 1 Lecturer Exam Paper is Objective type. Paper I and Paper I will be of 3 hours duration respectively. In Exam there will be 150 questions each of biology Paper II. All Questions carry equal marks. There will be negative marking For every wrong answer one-third of the marks.

RPSC MATHEMATICS GRADE 1 School Teacher Syllabus



PAPER I : Part I (History of Rajasthan and Indian History with special emphasis on Indian National Movement)

Development of Art, Science and Literature during Mouryan and Gupta Periods.

Ancient Indian education system and educational institutions of learning, Indian cultural expansion abroad.

Mahatma Gandhi and National movement.

Freedom Struggle of 1857 and Rajasthan. Peasant and labour movement. Vijay Singh Pathik, Arjun Lal Sethi, Kesari Singh and Joravar Singh Bareth.

Maharana Pratap, struggle with the Mugals.

Growth of education during British period, Freedom Struggle of 1857. Rise of Nationalist movement, Prominent leaders of national movement, V.D. Savarkar, Bankim Chandra, Lal, Bal, Pal, Chandra Shekhar Azad, Bhagat Singh, Sukhdev, Ras Behari Bose, Subhash Chandra Bose., social and religious renaissance- Raja Ram Mohan Roy, Dayanand Saraswati and Vivekanand.

Shivaji and the Maratha Swaraj, Rajput polity, society and culture during 7 th to 12 th centuries.

Bhakti movement and cultural synthesis, development of education, language, literature, Art and Architecture during Mugal Period.

2. Mental Ability Test

Analogy, series completion, coding-decoding, blood relations, logical venn diagrams, alphabetical test, number ranking and time sequence test, mathematical operations, arithmetical reasoning, data interpretation, data sufficiency, cubes and dice, construction of sequences and triangles.

Statistics (Secondary Level)

Collection of data, presentation of data, graphical representation of data, measures of central tendency, mean, mode, median of ungrouped and grouped data.

Mathematics (Secondary Level)

Natural, rational and irrational numbers, real numbers and their decimal expansions, operations on real numbers, laws of exponents for real numbers, rational numbers and their decimal expansions. Zeroes of a polynomial. Relationship between zeroes and coefficients of a polynomial. Division algorithm for polynomials. Algebraic methods of solution of pair of linear equations in two variables.


Surface area of a cuboid and a cube, right circular cylinder, right circular cone, sphere. Volume of a cuboid, cylinder, right circular cone and sphere, Surface area and volume of a combination of solids conversion of solid from shape to another.

Language ability test : Hindi, English

सामान्य हिंदी

संधी और संधि विच्छेद |

उपसर्ग |

प्रत्याय |

विपरीतार्थक (विलोम) शब्द |

अनेकार्थक शब्द |

शब्द युग्म |

शब्द शुद्धी : अशुद्ध का शुद्धीकरण और शब्दगत अशुद्धी का कारण |

वाक्य शुद्धी अशुद्ध वाक्य शुद्धीकरण और वाक्य अशुद्धी का कारण |

क्रिया सकर्मक और अकर्मक क्रियाए |

अंगरेजी की परिभाशिक (तकनीकी) शब्दो के समानार्थिक हिंदी शब्द |


Tenses/Sequence of Tenses.

Voice : Active and Passive.

Narration : Direct and Indirect.

Use of Articles and Determiners.

Use of Prepositions.

Correction of sentences including subject, Verb, Agreement, Degrees of Adjectives, Connectives and words wrongly used.

Glossary of official, Technical Terms (with their Hindi Versions).


Forming new words by using prefixes and suffixes.

Confusable words.

3. Current Affairs

Economic Planning in India

12th five year plan, Census of India 2011

Various development programme of India and Rajasthan

Poverty eradication programme,

Youth employment programme

Health and Hygiene Schemes of Rajasthan, Space programmes of India, Atomic Energy programmes

India and the world events of importance

Persons and places of India in News

Contemporary events in Science and Technology in India

National and International Awards and Prizes

Latest Books and Authors of India

Sports and games.

4. General Science

Atoms and molecules

Chemical reactions and equations

Carbon and its compounds,

Force and laws of motion

Work and energy

Tissues, Control and coordination

Heredity and evolution

Management of natural resources

Protection of environment

Biodiversity and sustainable development.

Geography of Rajasthan Location, extent, shape, size, physical features climate, demographic characterstics, agriculture, mineral resources, energy resources. Tourism and transport. Industries and trade.

Indian Polity:
❶Salient feature of the constitution of India, Indian Executive, Legislature, and Judiciary - Organization, Theory and practice, Elections in India. The president of India, Election and emergency powers of the president.
❷Cabinet, Prime Minister and his powers.
❸Parliament, speaker and his functions.
❹Beurocratic set up of India.
❺Political parties and their role – Theory and practice.
❻Supreme court – Organization and powers, Commissions and Boards at -national level.

5. Educational Management, Educational scenario in Rajasthan, Right to Education Act 2009

Concept and functions of educational management

Educational management in Rajasthan

School as a unit of decentralized planning

Educational management information System(EMIS)

Institutional planning

School mapping

Block Resource Centre(BRC)

School Management Committee(SMC)

District Information System for Education(DISE)

Sarva Shiksha Abhiyan(SSA)

Rashtriya Madhyanik Shiksha Abhiyan(RMSA).

Organisation of educational set up at primary and secondary in Rajasthan


Rajasthan Educational Intiative

Balika Shiksha Foundation

Kasturba Gandhi Balika Vidalaya

Rajasthan text book board

Bharat Scouts and Guides

Rasthriya Military school

Sainik school

Public school

Model school

E-Mitra, E-Governance, Rajshiksha, Edusat, Gyandarshan, Gyanvani.

Provisions of Right of Children to Free and Compulsory Education Act, 2009

Paper - II : Part - I (Senior Secondary Standard)

Sets, Relations and Functions

Different kinds of sets and their basic properties

Relations, types of relations

Different types of real valued functions.

2 Limit, Continuity and Differentiability :

Limit, continuity and differentiability of algebraic functions,

trigonometric functions

exponential functions and logarithmic functions.

3 Complex and Vector Algebra :

Complex numbers and their algebraic properties

polar representation,

square root of a complex number

Vectors and scalars

types of vectors and their algebraic properties

scalar and vector product of two vectors

scalar triple product.

4 Differential calculus

Derivatives of sum, difference, product and quotient of functions

Derivatives of polynomial and trigonometric functions

Derivatives of implicit and explicit functions

Increasing and decreasing functions

Concept of second order derivative.

5 Integral calculus

Integration of functions by the method of substitution

partial fraction and by parts.

Basic properties of definite integrals and their uses to evaluate them.

6 Differential equations

Order and degree of a differential equation

solution of differential equations of first order and first degree.

7 Permutations and combinations

Derivation of formulae

their connections and simple applications.

Binomial theorem : Binomial theorem for positive integral indices

general and middle terms in binomial expansion.

8 Matrices

Various types of matrices

their basic operations and properties

Invertible matrices and their inverse.

Determinant : Determinant of a square matrix and their properties

Solution of system of linear equations in two or three variables using inverse of a matrix.

9 Two dimensional geometry

Straight line

standard equations and simple properties of circle, parabola, ellipse, hyperbola.

10 Applications of derivatives and integrals

Tangent and normals

maxima and minima of functions of one variable

Area under simple curves

area between the simple curves.

11 Statistics

Mean, Mode, Median for grouped data

measure of dispersion

Probability and their elementary laws

conditional probability.

Paper II (Graduation Standard)

Group Theory

Groups and their simple properties

order of an element

order of a group

permutation groups

cyclic groups and their properties

subgroups and their basic algebraic properties

cosets and their properties.

2 Normal subgroup and Rings

Normal subgroups and quotient groups

theorems on homomorphism and isomorphism.

Rings, ideals, integral domain and fields.

3 Theory of equations

Relation between the roots and coefficients of general polynomial equation in one variable

Transformation of equations

Descartes' rule of signs

solution of cubic equations by Cardon's method

Biquadratic equations by Ferari's method.

4 Calculus

Partial derivatives

curvature, asymptotes

envelopes and evolutes

maxima and minima of functions upto two variables

Beta and Gamma functions

double and triple integrals.

5 Advanced Calculus

Mean value theorems (Rolle's, Lagrange's, Taylor's theorems)

sequence and series with convergence properties.

6 Complex Analysis

Continuity and differentiability of complex functions

Analytic functions

Cauchy - Riemman equation

Harmonic functions

Conformal mappings.

7 Ordinary and Partial differential equations

Linear differential equations of first order and higher degree

Clairaut's form

Linear differential equations of constant coefficients

ordinary homogeneous differential equations

Linear differential equations of second order with variable coefficients

Partial differential equations of first order

solution by Lagrange's method.

8 Vector calculus

Gradient, divergence and curl, identities related to them

Line, surface and volume integrals

Applications of Gauss, Stoke's and Green's theorems.

9 Three dimensional geometry

Direction ratios and cosines

straight line, plane, sphere, cone and cylinder.

10 Statics

Equilibrium of co-planner forces, moments, friction, virtual work catenary.

11 Dynamics

Velocities and acceleration along radial and transverse directions and along tangential and normal directions

simple harmonic motion

Rectilinear motion under variable laws

Hook's law and problems


Part - III (Post Graduation Standard)

1 Linear Algebra and Metric Space

Vector spaces

linear dependence and independence



linear transformations

matrix representation

algebra of matrices

characteristic roots and vectors


Cayley – Hamilton theorem.

Metric Spaces : Bounded and unbounded metric spaces

Open and closed sets in a metric space

Cantor's ternary set, closure, bases, product spaces.

2 Integral transforms and special functions

Hyper-geometric functions

Legendre's polynomials,

Bessel's functions

Recurrence relations and orthogonal properties.

Laplace transform

inverse Laplace transform

Fourier sine and cosine transforms

Convolution theorem.

3 Differential Geometry and Tensors

Curves in spaces


Torsion, Skew curvature

Serret - Frenet formulae

Helices Osculating circle and sphere.

Types of tensors and their algebraic properties

Christoffel's symbols

covariant and contravariant differentiation


4 Numerical Analysis

Newton's formula for forward and backward interpolation for equal intervals,

Divided difference

Newton's Lagrange's, Starling's and Bessel's interpolation formulae.

5 Optimization Technique's

Convex set and its properties

Solution of a L.P.P. by using Simplex methods

Duality, Assignment

Transportation and Game theory.

Part IV (Educational Psychology, Pedagogy, Teaching Learning Material, Use of computers and Information Technology in Teaching Learning)

1. Importance of Psychology in Teaching-Learning :



Teaching-learning process,

School effectiveness.

2. Development of Learner :

Cognitive, Physical, Social, Emotional and Moral development patterns and characteristics among adolescent learner.

3. Teaching – Learning

Concept, Behavioural, Cognitive and constructivist principles of learning and its implication for senior secondary students.

Learning characteristics of adolescent and its implication for teaching.

4. Managing Adolescent Learner

Concept of mental health and adjustment problems.

Emotional Intelligence and its implication for mental health of adolescent.

Use of guidance techniques for nurturing mental health of adolescent.

5. Instructional Strategies for Adolescent Learner

Communication skills and its use.

Preparation and use of teaching-learning material during teaching.

Different teaching approaches: Teaching models- Advance organizer, Scientific enquiry, Information, processing, cooperative learning.

Constructivist principles based Teaching.

6. ICT Pedagogy Integration

Concept of ICT.

Concept of hardware and software.

System approach to instruction.

Computer assisted learning.

Computer aided instruction.

Factors facilitating ICT pedagogy integration.