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Unit I: Number Systems

Real Numbers (Periods 15)

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 2 , 3, 5 , decimal expansions of rational numbers in terms of terminating/non-terminating

recurring decimals.

Unit II: Algebra

1. Polynomials (Periods 6)

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 (Periods 15)

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 (Periods 15)

Standard form of a quadratic equation ax2

+ bx + c = 0, (a ≠ 0). Solution of 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 (AP) (Periods 8)

Motivation for studying AP. Derivation of standard results of finding the n

th term and sum of

first n terms.

Unit III: Trigonometry

1. Introduction to Trigonometry (Periods 18)

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well

defined); motivate the ratios, whichever are defined at 0° and 90°. Values (with proofs) of the

trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

Trigonometric Identities: Proof and applications of the identity sin2

A + cos2

A = 1. Only simple

identities to be given. Trigonometric ratios of complementary angles.

2. Heights and Distances (Periods 8)

Simple and believable problems on heights and distances. Problems should not involve more

than two right triangles. Angles of elevation/depression should be only 300

, 450

, 600

.

Unit IV: Coordinate Geometry

Lines (In two-dimensions) (Periods 15)

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 (Periods 15)

Definitions, examples, counterexamples 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.

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 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 triangle.

2. Circles (Periods 8)

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 a circle are equal.

3. Constructions (Periods 8)

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 (Periods 12)

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 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and

circle should be taken.)

2. Surface Areas and Volumes (Periods 12)

1. 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.

2. 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 (Periods 15)

Mean, median and mode of grouped data (bimodal situation to be avoided).

Cumulative frequency graph.

2. Probability (Periods 10)

Classical definition of probability. Connection with probability as given in Class IX.

Simple problems on single events, not using set notation

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