OFFICIAL SYLLABUS
MATHEMATICS (THEORY)
UNIT I: NUMBER SYSTEMS
REAL NUMBERS
Review of representation of natural numbers, integers, rational numbers on the number line. Rational numbers as recurring/terminating decimals.
Examples of nonrecurring/nonterminating decimals
Definition of nth root of a real number.
Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing the learner to arrive at the general laws.)
Rationalization (with precise meaning) of real numbers of the type (& their combinations)
UNIT II: ALGEBRA
POLYNOMIALS
Definition of a polynomial in one variable, its coefficients, with examples and counterexamples, 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.
The analogy to integers, Factorization
Recall of algebraic expressions and identities.
LINEAR EQUATIONS IN TWO VARIABLES
Recall linear equations in one variable. Introduction to the equation in two variables. Prove that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life, and with algebraic and graphical solutions being done simultaneously.
UNIT III: COORDINATE GEOMETRY
COORDINATE GEOMETRY
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane, the graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y = mx + c and linking with the chapter on linear equations in two variables.
UNIT IV: GEOMETRY
LINES AND ANGLES
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 1800 and the converse.
2. (Prove) If two lines intersect, the vertically opposite angles are equal.
3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.
4. (Motivate) Lines, which are parallel to a given line, are parallel.
5. (Prove) The sum of the angles of a triangle is 180 0.
6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interiors' opposite angles.
TRIANGLES
1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence)
2. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
3. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle.
4. (Prove) The angles opposite to equal sides of a triangle are equal.
5. (Motivate) The sides opposite to equal angles of a triangle are equal.
QUADRILATERALS
1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides are parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and (motivate) its converse.
CIRCLES
Through examples, arrive at definitions of circle-related concepts, radius, circumference, diameter, chord, arc, subtended angle.
CONSTRUCTIONS
Construction of a triangle of given perimeter and base angles.
UNIT V: MENSURATION
SURFACE AREAS AND VOLUMES
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres), and right circular cylinders/ cones.
UNIT VI: STATISTICS AND PROBABILITY
STATISTICS
Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped / grouped, bar graphs, qualitative analysis of data to choose the correct form of presentation for the collected data.
PROBABILITY
History, Repeated experiments, and observed frequency approach to probability. The focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real-life situations, and from examples used in the chapter on statistics).
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