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Teachers Service Commission has recently changed the curriculum of all level teachers for the recruitment by open competition. The examination system is divided into two categories; General Examination and Subjective examination.General examination is of 100 full marks and objective/multiple choice questions will be asked. The pass marks is 50. This examination is for all the subjects. Here you will get both types TSC Secondary level Mathematics Curriculum. The curriculum of General Examinations can be obtained from the given link below.

Curriculum of General Examination

Second paper is of subject wise. Each subject teachers should attend and pass this examination. It will be subjective type and full marks is 100 . Time is 3 hours Here you will get the curriculum of Mathematics for the Secondary level.

**Section A**

Unit:1 Teaching Arithmetic

- Set theory: Set and notations, Relation between sets, Operations on sets, Algebra of sets, Venn-Diagrams and related problems
- Percentage and Application: Money Exchange, Discount and VAT, Profit and loss, Home arithmetic
- Sequence and Series: Arithmetic, Geometric and Harmonic sequence and series, nth term and sum, A.M, G.M, H.M and their relations
- Investment and Growth: Compound interest, Compound depreciation, Population growth
- Mensuration: Area of triangle, Area and volume of prism, Area and volume of cylinder and sphere, Area and volume of pyramid and cone, Cost and estimation

Unit 2: Teaching Algebra and Geometry

- School Algebra: Algebraic Expressions, Radical and surds, Polynomials and rationales, Indices, Linear and quadratic equation
- Geometry: Triangle, Quadrilateral, Circle, Tangent to Circle, Construction
- Analytic Geometry: Straight line, Homogeneous equation, Pair of lines, Angle between two lines
- Transformation Geometry: Reflection, Rotation, Translation and Enlargement
- Vector and Scalar: Definitions, Scalar product, Vector product, Application vector in geometry

Unit 3: Teaching Pre-Calculus

- Matrices and Determinants: Definition of matrix, Transpose and inverse, Determinants of 2×2 and 3×3 matrix, Properties of determinants and problems, Solution of system of linear equation (Cramer’s rule)
- Linear Programming, Function and Graph: Graphical, Simplex Method, Odd and even functions, Symmetry (about origin, X-axis and Y-axis), Sketching graphs of quadratic function
- Trigonometry: Unit circle, algebric, Trigonometric, exponential and their graph, composite and inverse function.Trigonometric identities, general values, solution of triangles and inverse functions
- Complex Number: Definition, Absolute value, Conjugate, Algebra of complex number, De- Moivre’s theorem
- Conic Section: Definition, Ellipse, Parabola and Hyperbola (standard equation and example)

Unit 4: Teaching Statistics

- Counting Principles and Induction: Counting principle, permutation, combination, mathematical induction
- Probability: Mathematical expectation, conditional probability, Bayes’ theorem
- Measures of Central Tendency: Mean, Median, Mode, Relations among them
- Measure of Dispersion: Range and Quartile deviation, Mean deviation, Standard deviation, Coefficient of variation.
- Correlation and Regression: Correlation coefficient and its properties, Pearson’s correlation, Spearman’s correlation, Regression equations of two variables

Unit 5: Overview of Mathematics Curriculum of Secondary Level

- Curriculum and Textbook: Comparative study of mathematics curriculum, Textbooks and Teachers guide of grade 9 -12
- Teaching Materials: Development and use of of teaching and supplementary materials in mathematics teaching
- Evaluation and Testing: Testing and and evaluation in mathematics teaching, specification grid
- Assessment: Continuous assessment system, grading system in student assessment
- Error analysis: Correction of error and error analysis

**Section B **

Unit 6: Calculus and Mechanics

- Limit and Continuity: Meaning of x→a, Limit of a function, Left hand and right-hand limit, Continuities and discontinuities of a function.
- Derivative: Derivative and its geometrical meaning (slope of tangent), Techniques of differentiation, Application of derivative (Maxima/Minima, increasing/decreasing, concavity), Rolle’s and Mean value theorem
- Integration: Definition, Techniques of integrations (substitutions, by parts), Fundamental theorem of calculus, Application of integration (area, volume)
- Numerical Interpolation: Interpolation, numerical differentiation numerical integration
- Dynamics and Statics: Introduction, Mechanics, Law of forces, Resultant forces and equilibrium forces

Unit 7: Geometry and Differential Equation

- Euclidean Geometry and its Elements: Introduction to Euclidian Geometry, Fifth postulates, Foundations, Congruence, Similarity
- Non-Euclidean Geometry: Shortcomings of Euclidean Geometry, Discovery of Non Euclidean Geometry, Elliptic Geometry, Hyperbolic Geometry, Comparison among three geometries
- Three-Dimensional Geometry: Coordinate System, Direction cosines/ratios, Equation of straight line
- Surface Topology: Polyhedron, Euler’s Formula, Euler’s characteristics for surface, Orient ability of surface and four color problems
- Differential Equation: Order and degree, First order first degree equation, Method of variable separable, Homogeneous equation

Unit 8: History of Mathematics and Geometric Transformation

- Numeration System: Egyptian, Babylonian, Roman, Hindu-Arabic and Devanagari, Characteristics of the numeration system
- History of Mathematics: The problems of Antiquity, Medieval mathematics, Modern mathematics
- Isometric Transformation: Reflection, rotation, half turn and glide reflection and derivation
- Non-Isometric Transformation: Enlargement and reduction and derivation

Unit 9: Probability

- Joint Probability Distribution: Marginal and conditional distribution, moment and moment generating function.
- Discrete Probability Distribution: Binomial, poison, hyper geometric distribution (Derivation of mean, variance, moment generating function)
- Continuous Probability Distribution: Normal distribution, beta and gamma distribution.
- Hypothesis Testing: Introduction, types of error, critical value and significance level. T-test and Z-test.
- Non-Parametric Test: Introduction and application, sign test, rank test, H- test and test of randomness.

Unit 10: Recent Trends in Mathematics Education

- Philosophy of Mathematics Education: Introduction and its components, Foundations of mathematics education, components and shift in philosophy.
- Learning Theories of Mathematics Education: Three major schools of thoughts (Behaviorist, Cognitivist & Constructivist), Major contributions of major theorists (Piaget and Bruner )
- Trends in Mathematics Education: Objectives and contents, Methods and materials, Students’ and Teachers’ role, Assessments, Research in mathematics
- Issues of Mathematics Education: Introduction, Teaching and learning, Assessment of mathematics, Culture of mathematics teaching
- ICT in Mathematics Education: Introduction, Use of ICT tools to explore mathematical knowledge, Models on Teaching mathematics using ICTs

The specification grid is given below.

February 23, 2020