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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

publish, print or convey (by any means) to any person not authorised by the board in this

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.

MA2-041

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SECTION – A

1 8 1

Question numbers 1 to 8 carry 1 mark each. In each question, select one correct option out of the given four.

1. 4412 32 5 7

(A) (B)

(C) (D) 2

The decimal expansion of number 441

2 32 5 7

has :

(A) a terminating decimal (B) non-terminating but repeating

(C) non-terminating non repeating (D) terminating after two places of decimal

2. f (x)(x2)24

(A) 1 (B) 2 (C) 0 (D) 3

The number of zeroes that the polynomial f(x)(x2)24 can have is : (A) 1 (B) 2 (C) 0 (D) 3

3. ABC AB6 DEBC AE

1

4AC AD

(A) 2 (B) 1.2 (C) 1.5 (D) 4

If in ABC, AB6 cm and DEBC such that AE1

4AC, then the length of AD is :

(A) 2 cm (B) 1.2 cm (C) 1.5 cm (D) 4 cm

4. AB90 sin A

3

4 sec B

(A) 3

4 (B)

4

3 (C)

1

4 (D)

1

3

If AB90 ; sin A3

4, then sec B is :

(A) 3

4 (B)

4

3 (C)

1

4 (D)

1

3

5. x y

(A) x10 ; y14 (B) x21 ; y84 (C) x21 ; y25 (D) x10 ; y40

Page 4 of 9

The values of x and y in the given figure are :

(A) x10 ; y14 (B) x21 ; y84 (C) x21 ; y25 (D) x10 ; y40

6. x4 y3

(A) (B) (3, 4)

(C) (D) (4, 3)

The pair of equations x4 and y3 graphically represents lines which are :

(A) parallel (B) intersecting at (3, 4)

(C) coincident (D) intersecting at (4, 3)

7. AB 14 tan B

(A) 4

3 (B)

14

3 (C)

5

3 (D)

13

3

In the given figure, if AB 14 cm, then the value of tan B is :

(A) 4

3 (B)

14

3 (C)

5

3 (D)

13

3

8. 20 22

(A) 20 (B) 26 (C) 22 (D) 21

The mean and median of a data are respectively 20 and 22. The value of mode is :

(A) 20 (B) 26 (C) 22 (D) 21

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/ SECTION-B

9 14 2

Question numbers 9 to 14 carry 2 marks each.

9.

241 241 m n4000 2 5 m n m, n

If 241 241

m n4000 2 5 , find the values of m and n where m and n are non-negative integers.

Hence write its decimal expansion without actual division.

10. k 4 x2x(2k2)

For what value of k, the number 4 is a zero of the polynomial x2x(2k2). Also find

the other zero.

11. ABCD B90 AD2AB2

BC2CD2 ACD 90

In a quadrilateral ABCD, B90. If AD2AB2

BC2CD2, prove that ACD 90

12. 3 tan 3 sin sin2 cos2

If 3 tan 3 sin , then find the value of sin2 cos2 .

13. 2 3

3

2

Find the quadratic polynomial whose zeros are 2 3 and 3

2

.

14. 100

: 0 – 5000 5000 – 10000 10000 – 15000 15000 – 20000 20000 – 25000

: 8 26 41 16 3

The monthly income of 100 families are given below :

Income (in Rs.) : 0 –

5000 5000 – 10000

10000 – 15000

15000 – 20000

20000 – 25000

Number of families: 8 26 41 16 3

Calculate the modal income.

/OR

200 400 600 800 1000 1200

10 50 130 270 440 500

Construct a frequency distribution table for the data given below :

Daily wages : Below

200 Below

400 Below

600 Below

800 Below 1000

Below 1200

No. of workers : 10 50 130 270 440 500

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SECTION-C

15 24 3

Question numbers 15 to 24 carry 3 marks each.

15. 36 : 25

Two isosceles triangles have equal vertical angles and their areas are in the ratio 36 : 25. Find the ratio of their corresponding heights.

16. 21x2 x 2 2 2

If and are the two zeros of the polynomial 21x2 x 2. Find a quadratic polynomial whose zeros are 2 and 2 .

17. 312 27 (HCF) (LCM)

Find the HCF of 312 and 27 using Euclids Division Algorithm. Find LCM and verify that

LCMHCFProduct of 2 given numbers.

/OR

14 600 280

The LCM of 2 numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one

number is 280, then find the other number.

18. x

2 22 2sec 59 cot 31 2 4 sin 90 3 tan 56 tan 34

3 3 3

x

.

Find the value of x if 2 2

2 2sec 59 cot 31 2 4 sin 90 3 tan 56 tan 34 3 3 3

x

.

19. x22x2 x4

3x37x2

x13

Check whether x22x2 is a factor of x4

3x37x2

x13 or not.

20. x y 2 2 2 ; a b a b

a b

yxx y

Solve the following pair of linear equations for x and y : 2 2 2 ; a b a ba b

yxx y

/OR

15x7y66 7x2y15

Check whether the following pair of linear equations has a unique solution. If yes, find the

solution. 15x7y66, 7x2y15.

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21.

160 – 163 163 – 166 166 – 169 169 – 172 172 – 175

15 118 142 127 18

The following is the distribution of heights of students of a class in a school.

Height (in cm) : 160 – 163 163 – 166 166 – 169 169 – 172 172 – 175

No. of students 15 118 142 127 18

Find the median height.

22. PQBA PRCA PD12 BDCD

In the given figure PQBA ; PRCA. If PD12 cm. Find BDCD.

/ OR

Prove that the area of the equilateral triangle described on one side of a square is half the area of the equilateral triangle described on its diagonal.

23. 2 2 21 1 1 sintan tan 2

2cos cos 1 sin

Prove that 2 2 21 1 1 sin

tan tan 22cos cos 1 sin

24. 62.8 x

0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120

5 8 x 12 7 8

The mean of the following frequency distribution is 62.8. Find the value of x.

Class : 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120

Frequency : 5 8 x 12 7 8

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/ SECTION-D

25 34 4

Question numbers 25 to 34 carry 4 marks each.

25. 2 3 5

2 3 5 . 2 3 5

Prove that 2 3 5 is an irrational number. Also check whether

2 3 5 . 2 3 5 is rational or irrational.

26.

2x3y1 ; 4x3y10 .

(2, 3)

Solve the following pair of linear equations graphically. 2x3y1 ; 4x3y10 . Does the point (2, 3) lie on any one of the lines formed by the above given equations ? If yes, write the equation of the line.

27. AB90

2 tan A tan B tan A cot B sin B tan A

2sin A sec B cos A

If AB90, prove that 2 tan A tan B tan A cot B sin B

tan A2sin A sec B cos A

28. 16 a b 70

: 0 – 5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40

: 12 a 12 15 b 6 6 4

The median of the following data is 16. Find the missing frequencies a and b if the total

frequency is 70.

Class : 0 – 5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40

Frequency : 12 a 12 15 b 6 6 4

29. 2x49x3

5x23x1 2 3

2 3

Find all the zeroes of the polynomial 2x49x3

5x23x1 if two of its zeros are 2 3

and 2 3

/OR

9 : 7 4 : 3

2000

The ratio of monthly incomes of two persons is 9 : 7 and the ratio in their expenditure is 4 : 3.

If each person can save Rs. 2000 per month, then find their monthly incomes.

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30.

Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.

/OR

Prove that 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.

31.

tan sec 1 1 sin

tan sec 1 cos

Prove that tan sec 1 1 sin

tan sec 1 cos

32. ABC A BC BC D DB3 CD

2 AB22 AC2

BC2

The perpendicular from A on the side BC of a ABC intersects BC at D such that DB3 CD.

Prove that 2 AB22 AC2

BC2

33. cos m

cos

cos

nsin

2 2 2 2m n cos n

If cos

mcos

, cos

nsin

, show that 2 2 2 2m n cos n .

34.

5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65

6 11 21 23 14 5

The following table shows the ages of patients admitted in a hospital during a month.

Age in years 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65

No. of patients 6 11 21 23 14 5

Convert the above distribution into a “less than type” cumulative frequency distribution and draw its ogive. Also find the median from this ogive.

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