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Course Structure
CLASS X
One Paper Time : 3 Hours Marks : 80
UNITS MARKS
I. NUMBER SYSTEMS 04
II. ALGEBRA 20
III. TRIGONOMETRY 12
IV. COORDINATE GEOMETRY 08
V. GEOMETRY 16
VI. MENSURATION 10
VII. STATISTICS AND PROBABILITY 10
TOTAL 80
UNIT I : NUMBER SYSTEMS
1. REAL NUMBERS (15) Periods
Euclid's division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier
and after illustrating and motivating through examples, Proofs of results - irrationality of  decimal
expansions of rational numbers in terms of terminating/non-terminating recurring decimals.
UNIT II : ALGEBRA
1. POLYNOMIALS (6) Periods
Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference
to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real
coefficients.
2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods
Pair of linear equations in two variables. Geometric representation of different possibilities of solutions/
inconsistency.
Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically
- by substitution, by elimination and by cross multiplication. Simple situational problems must be included.
Simple problems on equations reducible to linear equations may be included.
3. QUADRATIC EQUATIONS (15) Periods
Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solution of the quadratic equations
(only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship
between discriminant and nature of roots.
Problems related to day to day activities to be incorporated.
4. ARITHMETIC PROGRESSIONS (8) Periods
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.
UNIT III : TRIGONOMETRY
1. INTRODUCTION TO TRIGONOMETRY (12) Periods
Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined);
motivate the ratios, whichever are defined at 0o & 90o. Values (with proofs) of the trigonometric ratios of
30o, 45o & 60o. Relationships between the ratios.
2. TRIGONOMETRIC IDENTITIES (16) Periods
Proof and applications of the identity sin2 A + cos2 A = 1. Only simple identities to be given. Trigonometric
ratios of complementary angles.
3. HEIGHTS AND DISTANCES (8) Periods
Simple and believable problems on heights and distances. Problems should not involve more than two right
triangles. Angles of elevation / depression should be only 30o, 45o, 60o.
UNIT IV : COORDINATE GEOMETRY
1. LINES (In two-dimensions) (15) Periods
Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of
geometrical representation of quadratic polynomials. Distance between two points and section formula
(internal). Area of a triangle.
UNIT V : GEOMETRY
1. TRIANGLES (15) Periods
Definitions, examples, counter examples of similar triangles.
1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct
points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
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3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are
proportional and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are
equal and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including
these angles are proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the
hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each
other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their
corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other
two sides.
9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the
angles opposite to the first side is a right traingle.
2. CIRCLES (8) Periods
Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to circle are equal.
3. CONSTRUCTIONS (8) Periods
1. Division of a line segment in a given ratio (internally)
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.
UNIT VI : MENSURATION
1. AREAS RELATED TO CIRCLES (12) Periods
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and
perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems
should be restricted to central angle of 60o, 90o & 120o only. Plane figures involving triangles, simple
quadrilaterals and circle should be taken.)
2. SURFACE AREAS AND VOLUMES (12) Periods
(i) Problems on finding surface areas and volumes of combinations of any two of the following: cubes,
cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into another and other mixed problems. (Problems
with combination of not more than two different solids be taken.)
UNIT VII : STATISTICS AND PROBABILITY
1. STATISTICS (15) Periods
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
2. PROBABILITY (10) Periods
Classical definition of probability. Connection with probability as given in Class IX. Simple problems on
single events, not using set notation.
INTERNAL ASSESSMENT 20 Marks
Evaluation of activities 10 Marks
Project Work 05 Marks
Continuous Evaluation 05 Marks
RECOMMENDED BOOKS
1. Mathematics - Textbook for class IX - NCERT Publication
2. Mathematics - Textbook for class X - NCERT Publication
3. Guidelines for Mathematics Laboratory in Schools, class IX- CBSE Publication
4. Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication
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