Syllabus school Lecturer - MATHEMATICS

RAJASTHAN PUBLIC SERVICE COMMISSION, AJMER
SYLLABUS FOR EXAMINATION FOR THE POST OF
LECTURER - MATHEMATICS,
(SCHOOL EDUCATION)
PAPER - I
General Awareness and General Studies
1. 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.
‐ 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.
‐ 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.
‐ 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.
‐ Maharana Pratap, struggle with the Mugals.
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.
Mensuration :
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
lkekU; fgUnh
• Lkaf/k vkSj laf/k foPNsn A
• milxZ A
• izR;; A
• foijhrkFkZd ¼foykse½ 'kCn A
• vusdkFkZd 'kCn A
• 'kCn & ;qXe A
• 'kCn & 'kqfn~/k % v’kqn~/k 'kCnksa dk 'kqn~/khdj.k vkSj 'kCnxr v’kqfn~/k dk dkj.k A
• okD; & 'kqfn~/k % v’kqn~/k okD;ksa dk 'kqn~/khdj.k vkSj okD;xr v’kqfn~/k dk dkj.k A
• fØ;k % ldeZd vkSj vdeZd fØ;k,¡ A
• v¡xjsth ds ikfjHkkf"kd ¼rduhdh½ 'kCnksa ds lekukFkZd fgUnh 'kCn A
GENERAL ENGLISH :
• 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).
• Antonyms.
• Forming new words by using prefixes and suffixes.
• Confusable words.
3. Current Affairs
Economic Planning in India, 11th 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.
Indian Polity:
- Salient 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.
- Cabinet, Prime Minister and his powers.
- Parliament, speaker and his functions.
- Beurocratic set up of India.
- Political parties and their role – Theory and practice.
- Supreme court – Organization and powers, Commissions and Boards at -national level.
Geography of Rajasthan
Location, extent, shape, size, physical features climate, demographic characterstics, agriculture, mineral resources, energy resources. Tourism and transport. Industries and trade.
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 , Functions of RIE, SIERT, BSER, IASE, CTE, DIET, 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
* * * * *
Scheme of Examination
S. No.
Subject
No. of Questions
Total Marks
1
History of Rajasthan and Indian History with special emphasis on Indian National Movement
15
30
2
Mental Ability Test, Statistics (Secondary Level), Mathematics (Secondary Level), Language Ability Test : Hindi, English
20
40
3
Current affairs
10
20
4
General Science, Indian Polity, Geography of Rajasthan
15
30
5
Educational Management, Educational Scenario in Rajasthan, Right to Education Act, 2009
15
30
Total
75
150
Note : 1 All the question in the Paper shall be Multiple Choice Type Question.
2 Negative marking shall be applicable in the evaluation of answers. For every wrong answer one-third of the marks
prescribed for that particular question shall be deducted.
Explanation : Wrong answer shall mean an incorrect answer or multiple answer.
3 Duration of the paper shall be 1 Hour 30 Minutes.
Paper - II
Part – I (Senior Secondary Standard)
1 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.
Part – II (Graduation Standard)
1 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, projectiles.
Part – III (Post Graduation Standard)
1 Linear Algebra and Metric Space : Vector spaces, linear dependence and independence, bases, dimensions, linear transformations, matrix representation, algebra of matrices, characteristic roots and vectors, determinants, 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, Curvature, 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, Geodesics.
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 :
* Learner, * Teacher, * 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.
* * * * *
Scheme of Examination
Subject Concerned
S. No.
Subject
No. of Questions
Total Marks
1
Knowledge of Subject Concerned : Senior Secondary Level
55
110
2
Knowledge of Subject Concerned : Graduation Level
55
110
3
Knowledge of Subject Concerned : Post Graduation Level
10
20
4
Educational Psychology, Pedagogy, Teaching Learning Material, Use of Computers and Information Technology in Teaching Learning
30
60
Total
150
300
Note : 1 All the question in the Paper shall be Multiple Choice Type Question.
2 Negative marking shall be applicable in the evaluation of answers. For every wrong answer one-third of the marks
prescribed for that particular question shall be deducted.
Explanation : Wrong answer shall mean an incorrect answer or multiple answer.
3 Duration of the paper shall be 3 Hours.
* * * * *

Note: Please see the RPSC website for final and confirm Syllabus