Mathematics Standard CBSE Class 10 Last 7 Years Boards Question Papers (Session 2021-22) Maths Previous Year Papers CBSE Grade X Board Examination 2021-2022

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TABLE OF CONTENTS

1. CBSE 10th Board Latest Syllabus For Year 2021-22 2. CBSE 10th Board Question Paper Design For Year 2021-22 3. CBSE Board Exam Paper 2021 – Sample Question Paper For Year 2020-21 ** 4. CBSE Board Exam Paper 2020 – Series JBB/1 Code 30/1/1 (Set 1) 5. CBSE Board Exam Paper 2020 – Series JBB/2 Code 30/2/1 (Set 1) 6. CBSE Board Exam Paper 2020 – Series JBB/3 Code 30/3/1 (Set 1) 7. CBSE Board Exam Paper 2020 – Series JBB/4 Code 30/4/1 (Set 1) 8. CBSE Board Exam Paper 2020 – Series JBB/5 Code 30/5/1 (Set 1) 9. CBSE Board Exam Paper 2020 – Series JBB/C Code 30/C/1 (Set 1) 10. CBSE Board Exam Paper 2020 – Series JBB Code 30(B) (Set 4) 11. CBSE Board Exam Paper 2020 – Series JBB/C Code 30(B)/C (Set 4) 12. CBSE Board Exam Paper 2019 – Series JMS/1 Code 30/1/1 (Set 1) 13. CBSE Board Exam Paper 2019 – Series JMS/2 Code 30/2/1 (Set 1) 14. CBSE Board Exam Paper 2019 – Series JMS/3 Code 30/3/1 (Set 1) 15. CBSE Board Exam Paper 2019 – Series JMS/4 Code 30/4/2 (Set 2) 16. CBSE Board Exam Paper 2019 – Series JMS/5 Code 30/5/1 (Set 1) 17. CBSE Board Exam Paper 2019 – Series JMS/C Code 30/1/1 (Set 1) 18. CBSE Board Exam Paper 2018 – Series TYM Code 30/1 (Set 1) 19. CBSE Board Exam Paper 2017 – Series HRK/1 Code 30/1/1 (Set 1) 20. CBSE Board Exam Paper 2016 – Series JSR/1 Code 30/1/1 (Set 1) 21. CBSE Board Exam Paper 2015 – Series RLH/1 Code 30/1/1 (Set 1)

** Due to Covid-19, the Mathematics Board Exam for Year 2021 was not held, therefore no board exam paper for the year 2021 is included. Instead, this book includes year 2021 Class 10 Sample Paper by the CBSE Board.

Latest Syllabus Exam 2021-22 MATHEMATICS (CODE NO. 041) CLASS X Session 2021-22 The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to meet the emerging needs of all categories of students. For motivating the teacher to relate the topics to real life problems and other subject areas, greater emphasis has been laid on applications of various concepts. The curriculum at Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject as a separate discipline. It is expected that students should acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve problems of height and distances. Carrying out experiments with numbers and forms of geometry, framing hypothesis and verifying these with further observations form inherent part of Mathematics learning at this stage. The proposed curriculum includes the study of number system, algebra, geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc. The teaching of Mathematics should be imparted through activities which may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments.

Objectives: The broad objectives of teaching of Mathematics at secondary stage are to help the learners to: 

consolidate the Mathematical knowledge and skills acquired at the upper primary stage;



acquire knowledge and understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles and symbols and underlying processes and skills;



develop mastery of basic algebraic skills;



develop drawing skills;



feel the flow of reason while proving a result or solving a problem;



apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method;



to develop ability to think, analyze and articulate logically;



to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases;



to develop necessary skills to work with modern technological devices and mathematical software.



to develop interest in mathematics as a problem-solving tool in various fields for its beautiful structures and patterns, etc.



to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics;



to develop interest in the subject by participating in related competitions;



to acquaint students with different aspects of Mathematics used in daily life;



to develop an interest in students to study Mathematics as a discipline.

COURSE STRUCTURE CLASS – X CLASS X Session 2021-22 Units

Unit Name

Marks

I

NUMBER SYSTEMS

06

II

ALGEBRA

20

III

COORDINATE GEOMETRY

06

IV

GEOMETRY

15

V

TRIGONOMETRY

12

VI

MENSURATION

10

VII

STATISTICS & PROBABILITY

11

Total

80

UNIT I: NUMBER SYSTEMS 1. REAL NUMBER

(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 irrationality of √ 2 , √ 3 , √ 5 Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals. UNIT II: ALGEBRA 1. POLYNOMIALS

(7 Periods)

Zeros of a polynomial. Relationship between zeros and coefficients of 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 and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations. 3. QUADRATIC EQUATIONS

(15 Periods)

Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated. 4. ARITHMETIC PROGRESSIONS

(8 Periods)

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems. UNIT III: COORDINATE GEOMETRY 1. LINES (In two-dimensions)

(14 Periods)

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle. UNIT IV: 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. 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 of 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 angle. 2. CIRCLES

(8 Periods)

Tangent to a circle at, point of contact 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. (Motivate) Alternative Segment theorem: If a chord is drawn through the point of contact of a tangent to a

circle, then the angles made by the chord with the tangent are respectively equal to the angles subtended by the chord in the alternate segments. 3. CONSTRUCTIONS

(8 Periods)

1. Division of a line segment in a given ratio (internally). 2. Tangents to a circle from a point outside it. 3. Construction of a triangle similar to a given triangle. UNIT V: TRIGONOMETRY 1. INTRODUCTION TO TRIGONOMETRY

(10 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 0° and 90°. Values of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios. 2. TRIGONOMETRIC IDENTITIES

(15 Periods)

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles. 3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression.

(8 Periods)

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°. 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 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.) 2. SURFACE AREAS AND VOLUMES

(12 Periods)

1. 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

(18 Periods)

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph. 2. PROBABILITY Classical definition of probability. Simple problems on finding the probability of an event.

(10 Periods)

MATHEMATICS – Standard QUESTION PAPER DESIGN CLASS X Session 2021-22 Time: 3 Hours S. No. Typology of Questions

1

Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.

Max. Marks: 80 Total Marks

% Weightage (approx.)

43

54

Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas. 2

Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.

19

24

3

Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations.

18

22

80

100

Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions. Total

INTERNAL ASSESSMENT

20 MARKS

Pen Paper Test and Multiple Assessment (5+5)

10 Marks

Portfolio

05 Marks

Lab Practical (Lab activities to be done from the prescribed books)

05 Marks

PRESCRIBED BOOKS: 1. Mathematics - Textbook for class X - NCERT Publication 2. Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication 3. Laboratory Manual - Mathematics, secondary stage - NCERT Publication 4. Mathematics exemplar problems for class X, NCERT publication.

Year 2021 MATHEMATICS (STANDARD) BOARD SAMPLE QUESTION PAPER Time allowed: 3 hours

Maximum Marks: 80 Instructions

General Instructions: 1. This question paper contains two parts A and B. 2. Both Part A and Part B have internal choices. Part – A: 1. It consists two sections - I and II. 2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 3. Section II has 4 questions on case study. Each case study has 5 case-based sub-parts. An examinee is to attempt any 4 out of 5 sub-parts. Part – B: 1. Question No 21 to 26 are Very short answer Type questions of 2 mark each. 2. Question No 27 to 33 are Short Answer Type questions of 3 marks each. 3. Question No 34 to 36 are Long Answer Type questions of 5 marks each. 4. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks.

PART A Section-I Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 1. If xy = 180 and HCF (x,y) = 3, then find the LCM (x,y). OR The decimal representation of

14587 will terminate after how many decimal places? 21 ×5 4

2. If the sum of the zeroes of the quadratic polynomial 3x2 - kx + 6 is 3, then find the value of k. 3. For what value of k, the pair of linear equations 3x + y = 3 and 6x + ky = 8 does not have a solution.

4. If 3 chairs and 1 table costs Rs. 1500 and 6 chairs and 1 table costs Rs.2400. Form linear equations to represent this situation. 5. Which term of the A.P. 27, 24, 21,…..is zero? OR In an Arithmetic Progression, if d = - 4, n = 7, an = 4, then find a. 6. For what values of k, the equation 9x2 + 6kx + 4 = 0 has equal roots? 7. Find the roots of the equation x2 + 7x + 10 = 0 OR For what value(s) of ‘a’ quadratic equation 30 ax2 - 6x + 1 = 0 has no real roots? 8. If PQ = 28cm, then find the perimeter of ∆ PLM

9. If two tangents are inclined at 60° are drawn to a circle of radius 3cm then find length of each tangent. OR PQ is a tangent to a circle with centre O at point P. If ∆ OPQ is an isosceles triangle, then find ∠ OQP. 10. In the ∆ ABC, D and E are points on side AB and AC respectively such that DE II BC. If AE = 2cm, AD = 3cm and BD = 4.5cm, then find CE. 11. In the figure, if B1, B2, B3,…... and A1,A2, A3,….. have been marked at equal distances. In what ratio C divides AB?

12. sin A + cos B = 1, A = 30° and B is an acute angle, then find the value of B. 13. If x = 2sin2θ and y = 2cos2θ + 1, then find x + y. 14. In a circle of diameter 42cm, if an arc subtends an angle of 60° at the centre where π =

22 , then what 7

will be the length of arc. 15. 12 solid spheres of the same radii are made by melting a solid metallic cylinder of base diameter 2cm and height 16cm. Find the diameter of the each sphere. 16. Find the probability of getting a doublet in a throw of a pair of dice. OR Find the probability of getting a black queen when a card is drawn at random from a well-shuffled pack of 52 cards.

Section-II Case study based questions are compulsory. Attempt any four sub parts of each question. Each subpart carries 1 mark 17. Case Study based-1 SUN ROOM The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using

• Four clear glass panels, trapezium in shape, all the same size • One tinted glass panel, half a regular octagon in shape

(a) Refer to Top View Find the mid-point of the segment joining the points J (6, 17) and I (9, 16). (i) (33/2,15/2) (ii) (3/2,1/2) (iii) (15/2,33/2)

(iv) (1/2,3/2)

(b) Refer to Top View The distance of the point P from the y-axis is (i) 4 (ii) 15

(iii) 19

(iv) 25

(c) Refer to Front View The distance between the points A and S is (i) 4 (ii) 8

(iii) 16

(iv) 20

(d) Refer to Front View Find the co-ordinates of the point which divides the line segment joining the points A and B in the ratio 1:3 internally. (i) (8.5,2.0) (ii) (2.0,9.5) (iii) (3.0,7.5) (iv) (2.0,8.5)

(e) Refer to Front View If a point (x,y) is equidistant from the Q(9,8) and S(17,8),then (i) x+y=13 (ii) x-13=0 (iii) y-13=0

(iv) x-y=13

18. Case Study Based- 2 SCALE FACTOR AND SIMILARITY SCALE FACTOR A scale drawing of an object is the same shape as the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. SIMILAR FIGURES The ratio of two corresponding sides in similar figures is called the scale factor.

Scale factor =

length in image corresponding length in object

If one shape can become another using Resizing then the shapes are Similar

Rotation or Turn

Reflection or Flip