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Important Instructions for the

School Principal

(Not to be printed with the question paper)

1) This question paper is strictly meant for use in school based SA-I, September-2012 only.

This question paper is not to be used for any other purpose except mentioned above under

any circumstances.

2) The intellectual material contained in the question paper is the exclusive property of

Central Board of Secondary Education and no one including the user school is allowed to

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regard.

3) The School Principal is responsible for the safe custody of the question paper or any other

material sent by the Central Board of Secondary Education in connection with school

based SA-I, September-2012, in any form including the print-outs, compact-disc or any

other electronic form.

4) Any violation of the terms and conditions mentioned above may result in the action

criminal or civil under the applicable laws/byelaws against the offenders/defaulters.

Note: Please ensure that these instructions are not printed with the question

paper being administered to the examinees.

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I, 2012

SUMMATIVE ASSESSMENT – I, 2012

/ MATHEMATICS

X / Class – X

3 90

Time allowed : 3 hours Maximum Marks : 90

(i)

(ii) 34 8

1 6 2 10

3 10 4

(iii) 1 8

(iv) 2 3 3 4 2

(v)

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A, B, C and D.

Section-A comprises of 8 questions of 1 mark each, Section-B comprises of 6 questions of 2

marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises

of 10 questions of 4 marks each.

(iii) Question numbers 1 to 8 in Section-A are multiple choice questions where you are required

to select one correct option out of the given four.

(iv) There is no overall choice. However, internal choices have been provided in 1 question of

two marks, 3 questions of three marks each and 2 questions of four marks each. You have to

attempt only one of the alternatives in all such questions.

(v) Use of calculator is not permitted.

MA2-025

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SECTION–A

1 8 1

Question numbers 1 to 8 carry one mark each. For each question, four alternative

choices have been provided of which only one is correct. You have to select the correct

choice.

1. 189

125

(A) 1 (B) 2

(C) 3 (D) 4

The decimal expansion of 189

125 will terminate after :

(A) 1 place of decimal (B) 2 places of decimal

(C) 3 places of decimal (D) 4 places of decimal

2. 3

(A) (B) (C) (D)

The maximum number of zeroes that a polynomial of degree 3 can have is :

(A) One (B) Two (C) Three (D) None

3. ABC PQR 60 36 PQ9

AB

(A) 6 (B) 10 (C) 15 (D) 24

The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If

PQ9 cm, then AB equals :

(A) 6 cm (B) 10 cm (C) 15 cm (D) 24 cm

4. sin

(A) 1

2 (B)

3

2 (C) 1 (D)

1

2

The maximum value of sinis :

(A) 1

2 (B)

3

2 (C) 1 (D)

1

2

5. 20 24

(A) 240 (B) 480 (C) 120 (D) 960

The least positive integer divisible by 20 and 24 is :

(A) 240 (B) 480 (C) 120 (D) 960

6. 3x2y6 y-

(A) (2, 0) (B) (0, 3) (C) (2, 0) (D) (0, 3)

The point of intersection of the lines represented by 3x2y6 and the y-axis is :

(A) (2, 0) (B) (0, 3) (C) (2, 0) (D) (0, 3)

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7. A, B C ABC tan

A B

2

(A) sinC

2

(B) cosC

2

(C) cotC

2

(D) tanC

2

If A, B and C are interior angles of a ABC, then tanA B

2

equals :

(A) sinC

2

(B) cosC

2

(C) cotC

2

(D) tanC

2

8. (20.5, 15.5)

(A) 36.0 (B) 20.5 (C) 15.5 (D) 5.5

If the „less than‟ type ogive and „more than‟ type ogive intersect each other at (20.5, 15.5),

then the median of the given data is :

(A) 36.0 (B) 20.5 (C) 15.5 (D) 5.5

/ SECTION-B

9 14 2

Question numbers 9 to 14 carry two marks each.

9. (867, 255)

Find the HCF (867, 255) using Euclid‟s division lemma.

10.

4

5

1

3

Write the quadratic polynomial whose zeroes are 4

5 and

1

3.

11. ABCD ABCDEF ,

AE BF

ED FC

In the given figure, if ABCD is a trapezium in which ABCDEF, then prove that

AE BF

ED FC .

12. 2 sin2 3 cos2

Find the value of cos2 if 2 sin2 3 .

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13. 4t25

Find the zeroes of the polynomial 4t25.

14.

10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70

1 3 5 9 7 3

Find the sum of lower limit of mediun class and the upper limit of model class :

Classes : 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70

Frequency : 1 3 5 9 7 3

/OR

50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 80

2 8 12 24 38 16

Convert the following data into more than type distribution :

Class : 50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 80

Frequency : 2 8 12 24 38 16

SECTION-C

15 24 3

Question numbers 15 to 24 carry three marks each.

15. ADBC AB2CD2

BD2AC2

In the given figure, if ADBC, prove that AB2CD2

BD2AC2

16. x26xa a 2

If and are zeroes of the polynomial x26xa, find a if 2.

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17. x, y z „y‟ „z‟ 'x'

Find the value of x, y, and z in the following factor tree. Can the value of 'x' be found without finding the value of „y‟ and „z‟, if yes, explain :

/OR

2

Prove that 2 is irrational.

18. cosec

13

12

2 sin 3 cos

4 sin 9 cos

If cosec13

12, then evaluate

2 sin 3 cos

4 sin 9 cos

.

19. ax25xc 10 „a‟ „c‟

If the sum and product of the zeroes of the polynomial ax25xc is equal to 10 each, find

the value of „a‟ and „c‟.

20.

x5y6 ; 2x10y12

Represent the following pair of linear equations graphically and hence comment on the

condition of consistency of this pair :

x5y6 ; 2x10y12

/OR

2x3y7 ; 2 x()y28

Find the value of and for which the following pair of linear equations has infinite

number of solutions :

2x3y7 ; 2 x()y28

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21.

0 – 20 20 – 40 40 – 60 60 – 80 80 – 100

25 16 28 20 5

Compute the mode of the following data :

Class : 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100

Frequency : 25 16 28 20 5

22. ABC AB AC D E BC

AD AE

AB AC

.

If a line segment intersects sides AB and AC of a ABC at D and E respectively and is

parallel to BC, prove that AD AE

AB AC

.

/OR

ABCD ABDC O AB2CD

AOB COD

The diagonals of a trapezium ABCD, in which ABDC intersect at O. If AB2CD, then find the ratio of areas of triangles AOB and COD.

23. sinA, tanA cosecA secA

Express sinA, tanA and cosecA in terms of secA.

24.

50 – 60 60 – 70 70 – 80 80 – 90 90 – 100

6 5 9 12 6

Draw the less than type ogive for the following data and hence find the median from it.

Classes : 50 – 60 60 – 70 70 – 80 80 – 90 90 – 100

Frequency : 6 5 9 12 6

/ SECTION-D

25 34 4

Question numbers 25 to 34 carry four marks each.

25. n n2n 2

Prove that n2n is divisible by 2 for every positive integer n.

26. x y : 2(3xy)5xy ; 2(x3y)5xy

Solve for x and y : 2(3xy)5xy ; 2(x3y)5xy

27. sec41.sin49cos49.cosec41

2

3tan20tan60tan703(cos245sin290)

Evaluate : sec41.sin49cos49.cosec412

3tan20tan60tan703(cos245sin290)

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28. 28.5 60 „p‟ „q‟

0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

5 p 20 15 q 5

The median of the following frequency distribution is 28.5 and the sum of all the frequencies is 60. Find the values of „p‟ and „q‟ :

Classes : 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

Frequency : 5 p 20 15 q 5

29. 2x3x2

13x6 3

Show that 3 is a zero of the polynomial 2x3x2

13x6. Hence find all the zeroes of this

polynomial.

/OR

5 3

9 3 2

67

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units

and the breadth is increased by 3 units. The area is increased by 67 square units if length is

increased by 3 units and breadth is increased by 2 units. Find the perimeter of the

rectangle.

30.

Prove that “The ratio of the areas of two similar triangles is equal to the ratio of squares of

their corresponding sides”.

/OR

Prove that “In a right angled triangle, the square of the hypotenuse is equal to the sum of

the squares of the other two sides”.

31. (sinAsecA)2(cosAcosecA)2

(1secAcosecA)2

Prove that (sinAsecA)2(cosAcosecA)2

(1secAcosecA)2

32.

If two sides and a median bisecting one of these sides of a triangle are respectively

proportional to the two sides and the corresponding median of another triangle, then prove

that the two triangles are similar.

33.

tanA tanA 2 cosecA

secA 1 secA 1

Prove that : tanA tanA

2 cosecAsecA 1 secA 1

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34. `

` < 100 < 200 < 300 < 400 < 500

12 28 34 41 50

Calculate the average daily income (in `) of the following data about men working in a company :

Daily income (in `) < 100 < 200 < 300 < 400 < 500

Number of men 12 28 34 41 50

- o O o -