OFFICIAL SYLLABUS

Total Marks - 100 (External 80 Marks) & (Internal 20 Marks)

Time: 3 Hours

UNIT I - NUMBER SYSTEMS = 4 MARKS

Real Numbers - Euclid’s division lemma, Fundamental Theorem of Arithmetic –statements after reviewing work done earlier and after illustrating and motivating through examples. decimal expansions of rational numbers in terms of terminating / nonterminating recurring decimals.

UNIT II - ALGEBRA = 23 MARKS

Polynomials - 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.

Pair of Linear Equations in Two variables - Pair of Linear equations in two variables. Geometric representations of different possibilities of solutions/ inconsistency.

Algebraic conditions for a number of solutions. Solutions 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.

Quadratic Equations - Standard form of a quadratic equation. Solutions of quadratic equations ( only real roots ) by factorization and by completing the square i.e. by using the quadratic formula. Relationship between discriminant and nature of roots. Problems related to day-to-day activities to be incorporated.

Arithmetic Progressions (AP) - Motivation for studying AP. Derivation of standard results of finding the nth term and sum of the first n terms.

UNIT III - TRIGONOMETRY = 12 MARKS

Introduction to Trigonometry - 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 degrees and 90 degrees. Value ( with proofs ) of the trigonometric ratios of 30 degrees, 45 degrees, and 60 degrees. Relationships between the ratios.

Trigonometric Identities - Proof and applications of the identity sin ² A + cos² A = 1. Only simple identities are to be given. Trigonometric ratios of complementary angles.

Application to Trigonometry - 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 = 6 MARKS

Lines ( in two- dimensions) - Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representations of quadratic polynomials. Distance between two points and section formula ( internal ). Area of a triangle.

UNIT V - GEOMETRY = 15 MARKS

Triangles

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.

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 the sum of the squares on the other two sides, the angles opposite to the side is the right triangle.

Circles

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.

Constructions

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 = 10 MARKS

Areas Related to Circles

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 the area of segment of a circle, problems should be restricted to central angle of 60⁰ , 90⁰ and 120⁰ only. Plane figures involving triangles, simple quadrilaterals and circle should be taken)

Surface Areas and Volumes

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 cone.

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

Statistics

OFFICIAL SYLLABUS

Total Marks - 100 (External 80 Marks) & (Internal 20 Marks)

Time: 3 Hours

UNIT I - NUMBER SYSTEMS = 4 MARKS

Real Numbers - Euclid’s division lemma, Fundamental Theorem of Arithmetic –statements after reviewing work done earlier and after illustrating and motivating through examples. decimal expansions of rational numbers in terms of terminating / nonterminating recurring decimals.

UNIT II - ALGEBRA = 23 MARKS

Polynomials - 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.

Pair of Linear Equations in Two variables - Pair of Linear equations in two variables. Geometric representations of different possibilities of solutions/ inconsistency.

Algebraic conditions for a number of solutions. Solutions 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.

Quadratic Equations - Standard form of a quadratic equation. Solutions of quadratic equations ( only real roots ) by factorization and by completing the square i.e. by using the quadratic formula. Relationship between discriminant and nature of roots. Problems related to day-to-day activities to be incorporated.

Arithmetic Progressions (AP) - Motivation for studying AP. Derivation of standard results of finding the nth term and sum of the first n terms.

UNIT III - TRIGONOMETRY = 12 MARKS

Introduction to Trigonometry - 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 degrees and 90 degrees. Value ( with proofs ) of the trigonometric ratios of 30 degrees, 45 degrees, and 60 degrees. Relationships between the ratios.

Trigonometric Identities - Proof and applications of the identity sin ² A + cos² A = 1. Only simple identities are to be given. Trigonometric ratios of complementary angles.

Application to Trigonometry - 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 = 6 MARKS

Lines ( in two- dimensions) - Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representations of quadratic polynomials. Distance between two points and section formula ( internal ). Area of a triangle.

UNIT V - GEOMETRY = 15 MARKS

Triangles

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.

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 the sum of the squares on the other two sides, the angles opposite to the side is the right triangle.

Circles

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.

Constructions

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 = 10 MARKS

Areas Related to Circles

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 the area of segment of a circle, problems should be restricted to central angle of 60⁰ , 90⁰ and 120⁰ only. Plane figures involving triangles, simple quadrilaterals and circle should be taken)

Surface Areas and Volumes

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 cone.

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

Statistics

Mean, median, and mode of grouped data ( Bimodal situation to be avoided). Cumulative frequency graph.

Probability

The 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

1. Pen paper test

2. Project work like measurement of the school campus, the perimeter of boundary, etc.

3. Attendance and participation.

To Know More - Click Here