# Sample Paper Mathematics CBSE SA 2

SAMPLE PAPER / MODEL TEST PAPER

CBSE SA – 2 (II) 2012

SUBJECT – MATHEMATICS

SECTION-A

Question number 1 to 10 carry 1 mark each. For each of the question 1-10, four alternative choices have been provided of which only one is correct. You have to select the correct choice.

1. The sum of the first 15 multiples of 8 is:

(a) 920                 (b) 860                      (c) 900                     (d) 960

2. A target PQ at a point P of a circle of radius 5 meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is:

(a) 12 cm              (b) 13 cm                  (c) 8.5 cm              (d) root 119 cm

3. If y =3 is a root of the quadratic equation ky square + 3 – ky = 0, then the value of k is:

(a) ½                    (b) -1/2                       (c) 2                        (d) -2

4. A girl calculates that the probability of her winning the first prize in a lottery is 0. 08. If 6000 tickets are sold, how many tickets has she bought?

(a) 40 cm            (b) 240 cm                 (c) 480 cm                 (d) 750

5. A tree breaks due to storm and broken part bends so that the top of the tree touches the ground making an angle of 30 degree with ground. If the distance between the foot of the tree to the point where the top touches the ground is 8 m then the height of the tree is:

(a) 8/3 cm           (b) 3/8cm                  (c) 8 root 3 m             (d) 8/ root 3 m

6. A point P is 13 cm from the centre of a circle. Radius of the circle is drawn from P to the circle is:

(a) 10                  (b) 11                          (c) 12                            (d) 13

7. If tangents PA and PB from a point P to a circle with centre with O are inclined to each other at angle of 80 degree, angle POA is:

(a) 50 degree (b) 40 degree (c) 70 degree (d) 90 degrees

8. The circular ends of a bucket are of radii 35 cm and 14 cm and height of the bucket is 40 cm. Find the volume.

(a) 50080 cm cub    (b) 80080 cm cub       (c) 70080 cm cub        (d) 60080 cm cub

9. In two concentric circle, the length of tangent to inner circle is 8 cm. Find the radius of outer circle, if the radius of inner circle is 3 cm.

(a) 5 cm                      (b) 4 cm                      (c) 3 cm                      (d) 2 cm

10. The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is:

(i) 56 cm                     (ii) 42 cm                    (iii) 28 cm                   (iv) 16 cm

SECTION – B

11. Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0. 62. What is the probability of Reshma winning the match?

Or

In a lottery there are 20 prizes and 30 blanks. Find the probability of getting a prize

12. An equilateral triangle has two vertices at the points (1, 1) and (-1, -1), Find the coordinates of the third vertex.

13. Find the roots of the quadratic equation 1/ x – 3 – 1/x + 5 = 1/6; x does not equal 3, -5.

14. If 9th term of an A.P. is zero prove that its 29th term is double the 19th tern.

15. Prove that parallelogram circumscribing a circle is a rhombus.

16. a road which is 7 m wide surrounds a circular park whose circumference is 352 m.

Find the area of the road.

17. A drinking glass is in the shape of a frustum of a cone of height 14 cm. the diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. (Use PI = 22/7)

18. Find the coordinates of the points which divide the line segment joining A ( -2, 2) and B ( 2, 8) into four equal parts.

SECTION – C

19. A chord of a circle of radius 15 cm subtends an angle of 60 degree at the centre. Find the area of the corresponding minor and major segments of the circle.

(User PI = 3. 14 and root 3 = 1.73)

20. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.

21. Find the roots of the quadratic equation:

x+3/x+2 = 3x – 7 / 2x – 3; x does not equal -2, 3/2

Or

The sum of two numbers is 17 and the sum of their squares is 157. Find the numbers.

22. The first and the last term of A.P. are 4 and 81 respectively. If the common difference is 7, how many terms are there in the A.P. and what is their sum?

23. If A (x , 3 ), B ( 3, 0 ) , ( 0, -4 ) and D ( 4, y ) are the vertices of a rhombus, taken in order. Find the value of x and y.

24. Prove that the lengths of tangents drawn from an external point to a circle are equal.

Or

ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.

25. Find the area of square , if coordinates of its vertices are ( 1, 2) , ( 6 , 3),  ( 5, 8) and ( 0, 7) taken in order.

26. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. find the total surface area of the toy.

27. A bunch of 10 books contains 3 books on Mathematics, 2 books on Physics and the remaining are on

Chemistry. One book is selected at random. Find the probability that:

(i) it is a chemistry book                            (b) it is a physics book.

28. The angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

29. A triangle ABC is drawn to circumscribe a circle of radius 4 cm, such that the segments BD and  DC into which BC is divided by the point of contact D are of length 8 cm and 6 cm respectively. Find the sides AB and AC.

30. The angle of elevation of a cloud from a point 60 m above a lake is 30 degree and the angle of depression of n the reflection of the could is 60 degree. Find the height of cloud.

31. Sum of the areas of two squares is 468 m square .If the difference of their perimeters is 24 m, find the sides of the two squares.

32. A right triangle, whose sides are 15 cm and 20 m is made to revolve about its hypotenuse. Find the volume and the surface area of the double one so formed. (Take PI = 3.14)

33. A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 14/3 m and the diameter of hemisphere is 3.5 m. calculate the volume and the internal surface area of the internal surface area of the solid.

34. A metallic right circular cone 45 cm  high and whose vertical angle is 60 degree is cut into two parts in the ratio 1 : 2 from the vertex of the cone by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1 cm, find the length of the wire.

CBSE SA 2 Sample Paper / Model Test Paper

Sample Paper Mathematics CBSE SA 2
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3.

1. sandip says:

find no. of sides if all the angles are in a.p of a polygon a=120 and d=5.

2. ishita says:

ur ans fr 2nd ques is wrong.. its root 119 dis same ques is in ncert check it out yr..

3. vaibhav says:

there is no nilesh in 10B APS ok CHATUR

4. huda khan says:

kysquare + 3 – ky = 0, y=0 k 3square + 3 – 3k = 0 9k + 3 – 3k = 0 6k + 3 = 0 6k = -3 k = -3/6 k = -1/2

5. anjali bajaj says:

please give me answers of sample paper given here

6. Gourav says:

Sir Iam student of class 10 Sir I want all subject sample paper of your.. PLEASE sir send me all sample papers with answer please sir

7. shreya says:

what is the answer of……. x+3/x+2 = 3x – 7 / 2x – 3; x does not equal -2, 3/2 ???

8. anjana says:

If from any point on the common chord of 2 intersecting circles,tangents be drawn to the circles,prove that they r =

9. solution of this question paper says:

10. vishy95 says:

a=120 d=5 l=360 360 = 120 + (n-1)5 360 – 120 / 5 = n – 1 48 = n-1 Therefore n = 49 sides

11. saima kousar says:

hii guyz this a good platform…we can discuss que….if any 1 wanna discuss online que than my id on facebook is juverhhea.kousar1996@gmail.com and many of u r giving board…n some are having their xms b4 24th march….den guys plz gimme copy of ur xm que paper…a sincere request..plz do if possible..

12. saima kousar says:

NO … optionc) is correct 8root3m….the ht of the total tree or the ht of the original tree..

13. pranav says:

let angle APO be theta so sin theta = oppo side divided by adj side therefore r divide by 2r =1 divided by 2 =sin 30 angle BPO = 30 degree since centre lies on the bisector other 2 angles are equal angle oppo to equal sindes are equal

14. saima kousar says:

C=c+c’ 2pi R=36pi+20pi 2piR=56pi R=28………

15. saima kousar says:

under root 424 or 20.59126

16. saima kousar says:

at 1st draw the base BC of 6 cm with the help of scale 2.from point B of 6 cm . 3.divide BC into two parts as we MEdian divide it into 3=3 BD=3 4.from point D cut an arc of 4 cm as AD=4cm the point of intersection of arcs will be A NOw join AB,AC,AD..UR TRIANgLe Is formed..

17. saima kousar says:

y=3,ky sqare-ky+3=0 just put the value of y and u ll get the ans k=-1/2 ans

18. saima kousar says:

GIVEN:-pt is tangent with center O and PAB is a secant. CONSTRUCTION:- Join OT and OA,OP and draw OM perpendicular to AB PROOF:- OT is perpendicular to PT since the tangent is perpendicular to the radius of the circle at the pt of contact In right triangle OTP OT*2=OT*2+PT*2(pythagoras th*m) PT*2=OP*2-OT*2 =OM*2=PM*2-OA*2(by pythagoras thorem in triangle OMP .OT=OA) OA*2-AM*2+PM*2-OA*2 (in rt triangle OMA) PM*2-AM*2 (PM+AM)(PM-AM)((a-b)*2=(a+b)(a-b)) PM+AM(PM) PT*2=PB*PA PT*2=PA*PB…. HENCE PROVED.

19. sameer says:

your website is to goob. and vary healp ful in my exame

20. "mess"i ! says:

how do you solve this question- this is a 9th class ka rd sharma se question.chapter- constructions. Q. construct a triangle ABC such that BC=6cm, AB= 6cm, and Median AD=4cm plz email me the steps of construction.- if not the teacher then the 10th students.. plz positively by today evening cuz 2morrow is my test,…. waiting.

21. ritu rani says:

A lottery there are 20 prize and 30 blanks. find the probability of getting a prize .

22. vikram says:

if y =3 is a root of the quadratic equation ky square + 3 – ky = 0, then the value of k is:

23. kaakl says:

by god, very intelligent

24. kaakl says:

mad boy,such a easy question you doesn’t know. mad boy

25. CHATUR says:

R U NILESH TIWARI OF 10 B APS,,,, WELL Q’S R GOOD……

26. sheeba khan says:

give me the answer of question:4,6,8,9,11,34

27. sheeba khan says:

the radius of the circle whose circumference is equal to the sum of the two circles with diameter 36cm and 20cm is:

IF u think all this r hard…. then try on this,its an arithmatic progression- find the number of sides in a polygon whose least angle is 120 degree and the common difference is 5 degree.

29. venkat says:

take it as A(5,7) B(6,6) & C(2,-2) as three ptss on circle. Take O as centre and solve by distance formula OA=OB=OC

yaar 8th ka sample papers kyu nahin dete

31. sarath says:

IN Triangle abc let the third vertecs be (x,y) ie ,c,the find the distance between AB ,BC,AC ,the equate ,by squaring the you will surely get ans

32. fazil says:

can u see me the answer of qest no 2?

33. Sreedev says:

what is the answer of question no.28

34. aiswarya says:

hi, i want to kno how to do this sum.please help.. find the centre of a circle passing through the pts. (5,7) , (6,6) and (2,-2). also find the radius. hope u tell me soon…..

35. Navneeta Shiwani says:

nth term of AP is 4n-10 1st term = 4*1-10 = -6 2nd term = 4*2-10 = -2 So, 1st term = -6 and common difference = -6+(-2)= -6-2 = -8 Sn = n/2(2a+(n-1)d) = 10/2(2*-6+(10-1)(-2) = 5(-12+(9)(-2) = 5(-12+(-18) = 5(-12-18) = 5*-30 = -150

36. ananya says:

VERY EASY ONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

37. ananya says:

YES……………………………………S!!!!!!!!!!!!!

38. ananya says:

Good sample papers! but can anyone knows how to do question number 12?

39. baala says:

@ ELDHO: IS 6HT QUESTION COMPLETED OR NOT?

40. baala says:

@ ELDHO: EVEN I HAVE THE SAME DOUBT. IS 6TH QUESTION CORRECT?

41. kamya says:

hello!anamika well both these qstions r frm rd shrma…thy r prtty easy.

42. Eldho says:

Is 6th question is correct or not.

43. Kdas says:

r u sure it is PA X PB??or PA +PB?and plz solve it 4 me

44. Kdas says:

2nd and 7th is already answered by navneeta nw 12th question’s ans:the answer to the 12th question is (1,-1),it becums easy if u draw the diagram and look.take the ratio of AB by wich it is divided by the origin and get the point at wich the y axis divide AK (if K Is the third vertex,u’ll get (0,-1))and by section formula u’ll get the coordinates of K the vertex.if any doubts i’ll clear.

45. Kdas says:

the answer to the 12th question is (1,-1),it becums easy if u draw the diagram and look.take the ration of AB by wich it is divided by the origin and get the point at wich the y axis divide AK (if K Is the third vertex,u’ll get (0,-1))and by section formula u’ll get the coordinates of K the vertex.if any doubts i’ll clear.

46. Dreamy says:

i think this question is in complete. A tangent is a line not a line segment. So it can not have a fixed length. if m correct……..!!!!

47. Dreamy says:

I guess the question is incomplete

48. Dreamy says:

Volume=56.145 m cube(approx.) Surface area=70.5834 m square(approx.)

49. Dreamy says:

The angle of elevation of the top of a tower standing on a horizontal plane A is @. After walking a distance “d” towards the foot of the tower the angle of elevation is found to be #. What is the height of the tower? (a)d/(cot@+cot#) (b)d/(cot@-cot#) (c)d/(tan#-tan@) (d)d/(tan#+tan@)

50. Dreamy says:

I want solution to some of my questions.

51. Neeraja says:

replace n with 1, u get first term and so on…

52. Neeraja says:

i guess that the options of the fifth questions are not right. the height of the tree still standing would be 8/root3 but the total height of the tree would be 8(2+1/root3)m.. that 12th question is not reaching anywhere. my brother says the question is wrong. the coordintes of the third points are (1,1) when i calculate.. is it wrong, i mean my answer? if it is… pls reply to my comment…

53. rishikesh says:

is 6th question wrong?

54. latha says:

(a-3d)(a-d)(a+d)(a+3d) let these be the 4 numbs.. and (a-3d)(a+3d)_ 7 (a-d)(a+d) – 15 now cross multiple n solve it ull get the AP…

55. ashwarya sat says:

the queston no; r 32, 33, 34 plz itssssssssss reallyyyyyyyyy urgenttttttt plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

56. ashwarya sat says:

pls slove the questipons no given below . question no; 32,33,34

57. rishiraj says:

they should also give us solutions so that we can check that we have done or solved question is correct or not.

how do i know that the answers i get are correct . Please give me the answers

59. himanshu says:

u can get sample papers frm me

60. purab says:

give me the solution

61. sreevani says:

i want 8 class paper

62. purnima says:

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 14/3 m and the diameter of hemisphere is 3.5 m. calculate the volume and the internal surface area of the internal surface area of the solid.

63. sandeep says:

sir/madam can i get solutions for the above questions

64. AKHILA A.A says:

PUZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZLE

65. AKHILA A.A says:

WHAT IS THE MEAN VALUE OF1000 PRIME NUMBERS

66. ANJALI says:

HOW HYPOTENUSE IS A LONGEST SIDE OF RIGHT TRIANGLE

67. garima says:

we have to put 1,2,3… in place of n. Then we will get an AP like if n=1 4*1-10=-6 4*2-10=-2 we will get sum of first 10 terms. n=10, a=-6, d=4

68. garima says:

pls send cbse latest sample papers for class x as soon as possible.

69. Dimple sharma says:

can any1 suggest me some questions 2 score full marks in sa2 board exams

70. mehnaj says:

i waant sample paper along with answers. please tell me 4 terms of an a.p {general form}

71. Faize says:

Suppose in a figure PT is a tangent and PAB is a sectant Prove that PT*2 = PA X PB

72. Faize says:

Easy questions!!! Well try out this Suppose in a figure PT is a tangent and PAB is a sectant Prove that PT*2 = PA X PB

73. zayesha says:

were r d answers????????

74. shikha merchan says:

i like the question but some que r difficult

75. Zain says:

wow…these are really easy……i hope this kind of paper comes

76. nilesh says:

if u think these questions are so simple then plz don’t solve them and plz don’t comment.

77. pratik says:

sir/madam where we will get the solutions of these question…..

78. Abhisekh says:

In an A.p. the sum of first n terms is 3n2/2+5n/2. Find its 20th term

79. JOWHAR says:

CAN SM 1 SAY HW TO DO 12 TH QUESTION….PLZ..

80. Navneeta Shiwani says:

stastistics is not in syllabus of second summetive assessment

81. fathima says:

dear sir/madam, could you please post all the sample papers so that it would be easir to attempt my exams??i need the sa2 cbse sample papers for class ten.please send it as soon as possible.thankyou

82. devansh says:

1) ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle. 2)A right triangle, whose sides are 15 cm and 20 m is made to revolve about its hypotenuse. Find the volume and the surface area of the double one so formed. (Take PI = 3.14)

83. GYANDEEEP says:

2 2 2 [5] +[5] +[5] =?

84. r kaushik says:

yes arushi u r correct

85. shubham dwivedi says:

i want to know that whether only this kind of sample paper will come in exam or more difficult than that?

86. shubham dwivedi says:

i want to know that whether othis kind of sample paper will come in exam or more difficult than that?

87. Nazzii says:

cool questions …..

88. deepak sikarwar says:

sir, why the statistics chapter made .what is the reason behind this chapter. thanks for helping us by providing these sample papers earlier. your,obediently deepak sikarwar morar(gwalior)

89. tanu says:

how can we make the data of a frequency distribution table continuous in chapter 14 statistics

90. jerin says:

28. The angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

91. Kevin says:

Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that ∠APB = 2 ∠OAB

92. SANDEEP TIWARI says:

in two concentric circle with centre O.PQ is the diameter of outer circle and QS is the tangent line to the inner circle touching it in R and outer circle in S. find the length of PR if radius of to circle are 13cm and 8cm

93. sanjana says:

the nth term of an A.P. is 4n-10. Find the sum of first 10 terms

94. anamika sharma says:

the questions r nt so bad…

95. javneet says:

12. An equilateral triangle has two vertices at the points (1, 1) and (-1, -1), Find the coordinates of the third vertex.

96. somnath says:

the cylinder and cone are in ratio of 5:9 if their h and r are equal then find ratio of their volumes

97. DEENA THOMAS says:

GIV US SOLUTION AISO

98. DEENA THOMAS says:

PLS GIVE US SOLUTION ALSO PLSSSSSSSSSSSSS

99. Abhishek says:

Nice question paper

thank you

101. Raji says:

I want the solution for these questions.

102. Raji says:

will we get a hard question paper for preparative test?? will we get these types of question???

103. pooja solanki says:

nice paper………..

104. kshitij says:

wat do u get cbse by irritating us by seeting these tough ques???

105. mridula says:

oplz send the ans

106. mridula says:

wow so easy paper

107. KOMAL says:

plzzzzzzzzzzzzzzzzzz give d answer of the question

108. SHUBHI says:

PLEASE GIVE US SOLUTION ALSO…………..

109. vidit says:

sum of n terms -2(sum of n-1 terms]+sum of n-2 terms

110. anamika sharma says:

could u plzz send me some gud sample papers online….

111. surbhi says:

can i get the solution also

112. surbhi says:

would this type of question paper come

113. Ayushi says:

answer of ques. 33 is volume=77.375 internal surface area=34.333333 =34.34(approx.)

114. gunjan says:

plzzzzzzzzzz give me ans of q.no 33

115. Gautam says:

Dont ask such easy qeustions…

116. Navneeta Shiwani says:

Please enter the terms

117. Navneeta Shiwani says:

The diametre passes through the centre of the circle .So, it is the longest chord

118. Navneeta Shiwani says:

2.(b)13cm (by using pythagoras theoram find hypotenuse i.e. PQ) 7.(a)50 degree

119. Navneeta Shiwani says:

1. If PA and PB are two tangents drawn to a circle with centre O.Let OP meets the point P in circle at Q. Join OA and AQ. Then, angle OAP = 90 degree (OA is perpendicular to AP) Thus, Q is midpoint of hypotenuse OP of triangle OAP So, Q is equidistance from O, A and P Therefore, QA=OQ=OP=r Thus, OA=OQ=QA=r Therefore, triangle AOQ is equilateral So, angle AOQ=60 degree and angle APO=30 degree Angle APB=2 angle APO =2*30 degree =60 degree Also, PA=PB angle PAB=angle PBA=60 degree Hence, the triangle ABP is equilateral 2.Given-PQ and RS are two parallel tangents to a circle with centre O and AB is tangent to a circle at a point C, intersecting PQ and RS at A and B respectively. To Prove- angle AOB=90 degree Proof- Since PA and PB are tangents to a circle at P and R respectively and POR is a diameter of the circle, we have angle OPA= 90 degree and angle ORB=90 degree angle OPA+angle ORB=180 degree PAis parellel to RB We know that tangents to a circle from an external point are equally inclined to the line segment joining this point to the circle. therefore, angle 2=angle 1(angle PAO=angle2 and angle OAB=angle1) and angle 4=angle 3 (angleABO=angle3 and angleROB=angle4) Now,PA is parallel to RB and AB is a transversal. Therefore, angle PAB+angleRBA=180 degree (angle1+angle2)+(angle3+angle4)=180degree 2angle1+2angle3=180degree 2(angle1+angle3)=180degree angle1+angle3=90degree From triangle AOB,we have angle AOB+angle1+angle3=180degree angleAOB+90degree=180degree angleAOB=90degree proved.

120. apoorva says:

ah ! finally i found a gud sample paper

121. anish says:

Kindly send me the ans of cbse sa ii maths paper 2011

122. zaid says:

thankx aftr all i fund sample papers

123. neeraj das says:

how diametre is the longest chord

124. sakshiaggarwal says:

divide 32 into four parts such that they r in A.P & the ratio of product of first term & fourth term = product of second & third terms is equal to7/15.

125. sakshiaggarwal says:

sum of terms of A.P is 36 and its product is 1296. find A.P

126. my name is sarah contact me 9465850727 says:

zainab ihave also same prblm

127. my name is sarah contact me 9465850727 says:

hi !everybody answer my question plzzzzzzzzzzzzzzzzzzzz q.2,7,12

128. answer of 2 ,7,12 says:

oh wow!answer me my questions plzzzzzzzzzzzzzzzzz

we will going to do the same

130. zainab says:

dear sir/madam, could you please post all the sample papers so that it would be easir to attempt my exams??i need the sa2 cbse sample papers for class ten.please send it as soon as possible.thankyou zainab

131. vignesh says:

sir from which date 9th class annual papers are starting

132. parvathi s mohan says:

sa 2 sample question paper answer

133. venkat ramana says:

i think these papers are more eazy. Will u give surity that this kind of paper will come in exam………

134. anamika sharma says:

1.From a point p,two tangents PA & PB are drawn to a circle with centre O. If OP= diameter of the circle show that triangle ABP is equilateral. 2.Prove that the intercept of the tangent between two parallel tangents to a circle subtends a right angle at the center ?

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