Class 10th Mathematics Sample Papers CBSE Boards 2010



Mathematics, by the name only, everyone gets frightened. But, the subject is interesting to play with. Mathematics is the main scoring subject in which the skilled student can achieve maximum marks. Mathematics just only requires concentration and continuous practice of solving the problems to get desired results.

Following are the few samples for preparing you to present yourself in 10th class boards:

Mathematics Sample Paper 1
Mathematics Sample Paper 2
Mathematics Sample Paper 3
Mathematics Sample Paper 4
Mathematics Sample Paper 5

CBSE syllabus of class10th for March 2010 examinations is as follows:

UNIT I: Number Systems

1.Real numbers (15Periods)
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 algeberaically - 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 Progrssions(8Periods):
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.

UNIT III : Trignometry

1. Trignometric Ratios(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.Trignometric 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.
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 triangle.

2. Circles (8 Periods):
Tangents to a circle motivated by chords drawn from points coming closer and 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 (8Periods):
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 of plane figures (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 volume(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.


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22 Responses to “Class 10th Mathematics Sample Papers CBSE Boards 2010”  

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  1. 1 Divya Prakash Verma on Feb 8th, 2009 said:

    In Right angle triangle ABC. Right Angle At B. A circle with side AB as diameter is drawn to intersect the hypotenuse AC in P. Prove that tangent to the circle at P bisects the side BC.

  2. 2 shreya on Feb 10th, 2009 said:

    a contract on construction job specifies a penalty for delay of completion beyond a certain date as follows:rs200 for first day rs 250 for second day ,rs 300 for third day and so on. if the contracter pays rs 27,750 as penalty, find the number of days for which the contruction work is delayed.

  3. 3 ram on Feb 17th, 2009 said:

    hi iam ram now iam worry about board exams .. i cant study study anything because of tensions.. and full of emotions in mind … can u solve this problem? immediately plzz plz send to my mail id

  4. 4 krutika on Feb 19th, 2009 said:

    is there any change in CBSE pattern? If there is change please model question papers with answers of social, science, maths, hindi, english.

  5. 5 saif on Feb 19th, 2009 said:

    Points A(5,-1),B(-3,2) and C(-1,8) are the vertices of a triangleABC.Find the lengnth of median from A.Also find the coordinates of the point of division.

  6. 6 saif on Feb 19th, 2009 said:

    Hi this is Saif from Muscat(oman).Please help me out in this problem.

    The mean of n observation is x. If the first observation is increased by 1,second by 2,the third by 3 and so on,find the new mean (1)

    The rainwater from a roof 22m*20m drains into a cylinderical vessel having diameter of base 2m and height 3.5m.If vessel is not just full,find the rainfall in cm.(6)

  7. 7 singh on Mar 5th, 2009 said:

    hello sir,
    can u send me all the formulas and theroms.
    please send as soon as possible

  8. 8 k m basheer on Mar 7th, 2009 said:

    could i get all the above 2009 sample paper to my email?

  9. 9 AZFANA B on Mar 12th, 2009 said:

    The sum of 3 numbers wich are in A.P is 9 and sum of their squares is 35. Find the numbers.

  10. 10 Garvit on Mar 13th, 2009 said:

    How do I crack Language papers? Are they difficult?

  11. 11 mohit bansal on Mar 15th, 2009 said:

    cbse 10th math exam ka solution aa gaya kya

  12. 12 Gurkaran on Mar 16th, 2009 said:

    How much grace marks will be given to the students who attempted the 3 set of maths 2009 10class?

  13. 13 Priyanka on Mar 18th, 2009 said:

    marks will be given for those wrong question in set 3

  14. 14 LIJO on Mar 20th, 2009 said:

    How much grace marks will be given for the students who attempted 3rd set of mathematics?
    Please reply immediately………………

  15. 15 afroz basha on Apr 2nd, 2009 said:

    hello sir,
    iam afroz basha
    iam from kadapa iam request for u
    give me send 7th class model paper ,
    send me sir ,,,,,,

  16. 16 dharmendr kumar gautam on Apr 9th, 2009 said:

    sii i have 0ne problem because my maths paper in not properly right can u told me what can i do for my best n maths exam

  17. 17 Fathima Nuzra on Apr 28th, 2009 said:

    Sir,
    I am Fathima Nuzra. M from Riyadh. Grade 10th.
    Is the below given formulae important in the exam? If Yes ,Pls explain more easily how to derive it :-

    In, ax square +bx + c =0
    x = -b + root b square -4ac divided by 2a
    and (or)
    x = -b - root b square - 4ac divided by 2a

  18. 18 pradeep on May 8th, 2009 said:

    what is the sylabus of 10th cbse english and social studies?

  19. 19 gurpreet on May 15th, 2009 said:

    i want to know that improtent questions and the annual half yearly and wuarterly all paper in addvance plzzzzzzzzzz and send me the 2009 paper not sample realy one plzzzzzzzzzzzz i will give money u send i will give u card number u take money

  20. 20 gurpreet on May 15th, 2009 said:

    i want the gometry and graph paper can u send me…………

  21. 21 dolma on May 25th, 2009 said:

    respected sir,
    actually its my heartiest desire to score 90% above in 10th cbse board examination.so its my request to suggest me some methods as soon as possible. thankyou!

  22. 22 Pranjal Singh on May 31st, 2009 said:

    Can I get the solved answers to the above mentioned sample papers.

  23. 23 rebekah on Jun 25th, 2009 said:

    oacb is a quadrant of a circle o & radius 3.5cm. if OD= 2cm. find the area of the 1> quadrant OACB. 2> area of the shade region