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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.
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PAPER FORMAT
There will be one paper in this subject.
Time period : 2:30 p.m.
Maximum Marks : 80
Units and their weightage
S.No | Topic | Marks |
1 | Real Numbers | 1+1+2 = 4 Marks |
2 | Polynomials | 1+3 = 4 Marks |
3 | Linear Equation in two variables | 1+2+3 = 6 Marks |
4 | Quaratic Equation | 1+3+4 = 8 Marks |
5 | Arthmetic progression | 1+1+3 = 5 Marks |
6 | Trigonometry | 1+1+2+3 = 7 Marks |
7 | Application to Trigonometry | 1+4 = 5 Marks |
8 | Co-ordinate Geometry | 1+1+4 = 6 Marks |
9 | Triangles | 1+1+4 = 6 Marks |
10 | Circles | 1+1+3 = 5 Marks |
11 | Construction | 4 Marks |
12 | Area related to Os | 1+3 = 4 Marks |
13 | Surface Area & Volumes | 1+2+3 = 6 Marks |
14 | Probability | 1+1+2 = 4 Marks |
15 | Statistics | 2+4 = 6 Marks |
Total | 80 Marks |
Conditions of eligibility for admission to class X.
1. Candidates who have been studying in a School recognised by or affiliated to this Board or any other recognised Board of Secondary Education in India.
2. Candidates can not take admission directly in class X.
3. Candidates had completed a regular course of study for class IX and passed class IX examination from a school affilicated to this Board.
4. The candidates percentage for attendance should be 75% so that the Board to make him/her eligible for the Examinations.
5. Candidate can be admitted to a school only on the transfer of the parents(s) or shifting of their families from one place to another, after procuring from the student the marksheet and the Transfer Certificate duly countersigned by the Educational Authorities of the Board concerned.
6. There is no age limit for candidates taking the Examination
7. Candidate should have doucments in support of his having passed the qualifying or equivalent qualifying examination.
OFFCIAL SCHEDULE 2022
Date & Day | Subject | Time |
29-03-2022 (Tuesday) | Additional/ Optional Kashmiri/ Punjabi/ Urdu/ Hindi/ Persian/ Sanskrit/ Dogri/ Bhoti/ Arabic/ Computer Science | 11:00 A.M |
01-04-2022 (Friday) | English | 11:00 A.M |
05-04-2022 (Tuesday) | Social Science | 11:00 A.M |
07-04-2022 (Thursday) | Vocational Subjects Agriculture/ Apparels, Makeup and Home Functioning/ Automotive/ Beauty and Wellness/ Health Care/ IT & ITES/ Media & Entertainment/ Physical Education and Sports/ Plumber/ Retail/ Security/ Telecommunication/ Tourism and Hospitality/ Electronics and Hardware | 11:00 A.M |
11-04-2022 (Monday) | Mathematics/ Music/ Painting/ Art & Drawing | 11:00 A.M |
13-04-2022 (Wednesday) | Hindi/ Urdu | 11:00 A.M |
16-04-2022 (Saturday) | Science (Physics, Chemistry and Life Science)/ Home Science | 11:00 A.M |
Analysis of 2022 Question Paper
Code - B - 3 - X
1. There are total 40 questions in this part.
2. This question paper is divided into four sections: Section A, Section B, Section C and Section D.
3. All sections are compulsory. Solve all the parts of a question together.
4. Section A - Question number 1 to 20 comprises of twenty questions of 1 marks each.
5. Section B - Question number 21 to 26 comprises of six questions of 2 marks each.
6. Section C - Question number 27 to 34 comprises of eight questions of 3 marks each.
7. Section D - Question number 35 to 40 comprises of five questions of 4 marks each.
And
There is no overall choice. However, an internal choice has been provided In Question number 24 of section B, Question number 27, 30, 32 of section C and Question number 35, 37, 38 of section D.
Comment
1. The difficulty level of the Mathematics paper : Moderate to difficult
2. All the questions in the paper were asked from the latest syllabus and based on NCERT textbooks
4. The average range of expected marks was 60 (out of 80)
1. There are total 40 questions in this part.
2. This question paper is divided into four sections: Section A, Section B, Section C and Section D.
3. All sections are compulsory. Solve all the parts of a question together.
4. Section A - Question number 1 to 20 comprises of twenty questions of 1 marks each.
5. Section B - Question number 21 to 26 comprises of six questions of 2 marks each.
6. Section C - Question number 27 to 34 comprises of eight questions of 3 marks each.
7. Section D - Question number 35 to 40 comprises of five questions of 4 marks each.
8. There is no overall choice. However, an internal choice has been provided In Question number 24 of section B, Question number 27, 30, 32 of section C and Question number 35, 37, 38 of section D.
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