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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.

MA2-063

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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. 2 8

(A) 10 (B) 16 (C) 28 (D) 3 2

2 8 equals to :

(A) 10 (B) 16 (C) 28 (D) 3 2

2. 1 x2kx5 k

(A) 4 (B) 4 (C) 0 (D) 5

If 1 is the zero of the quadratic polynomial x2kx5, then the value of k is :

(A) 4 (B) 4 (C) 0 (D) 5

3. AD

(A) 10 (B) 26 (C) 24 (D) 25

In the figure given below, length of AD is :

(A) 10 cm (B) 26 cm (C) 24 cm (D) 25 cm

4. sincos 0 90

(A) 30 (B) 90 (C) 0 (D) 45

If sincos, 0 90 then is equal to :

(A) 30 (B) 90 (C) 0 (D) 45

5. 6

1250

(A) 1 (B) 4 (C) 3 (D) 2

The decimal representation of 6

1250 will terminate after how many places of decimal ?

(A) 1 (B) 4 (C) 3 (D) 2

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6. 2x5y7 4x10y14

(A) x6, y1 (B) x1, y1 (C) x 7

2, y0 (D) x3, y1

Which of the following is not a solution of the pair of equations 2x5y7 and 4x10y14 ?

(A) x6, y1 (B) x1, y1 (C) x 7

2, y0 (D) x3, y1

7. (secAtanA)(1sinA)

(A) tan2A (B) sec2A (C) cosA (D) sinA (secAtanA)(1sinA) on simplification gives :

(A) tan2A (B) sec2A (C) cosA (D) sinA

8. 8 8

(A) 10 (B) 8 (C) 7 (D) 8 If the mode of a distribution is 8 and its mean is also 8, than its median is : (A) 10 (B) 8 (C) 7 (D) 8

/ SECTION-B

9 14 2

Question numbers 9 to 14 carry two marks each.

9. 7n n 0

Show that 7n cannot end with the digit zero, for any natural number n.

10.

1

3 p(x)3x3

5x211x3

Find whether 1

3 is a zero of the polynomial p(x)3x3

5x211x3 or not.

11. AB ADBE DEAB

In the given figure AB and ADBE. Show that DEAB.

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12. cos45 1

sec30 sec60

Evaluate : cos45 1

sec30 sec60

13. x3, f(x)x36x2

10xb b

If x3 is a factor of f(x)x36x2

10xb, find the value of b.

14. 80

10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80

5 10 25 12 10 08 10

Following distribution shows the marks obtained by a class of 80 students :

Marks 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80

Number of students 5 10 25 12 10 08 10

Find the Mode of above distribution.

/OR

x y

0 – 8 15 15

8 – 16 x 28

16 – 24 15 43

24 – 32 18 y

32 – 40 09 70

Find x and y from the following cumulative frequency distribution :

Classes Frequency Cumulative frequency

0 – 8 15 15

8 – 16 x 28

16 – 24 15 43

24 – 32 18 y

32 – 40 09 70

SECTION-C

15 24 3

Question numbers 15 to 24 carry three marks each.

15. ABC AD AD ADE

(ADE) : (ABC)3 : 4.

AD is an altitude of an equilateral triangle ABC. On AD as base another equilateral triangle ADE is constructed. Prove that ar(ADE) : ar(ABC)3 : 4.

16. f(x)3x25x2

(i) 2

2 (ii) 3

3

If and are the zeroes of the quadratic polynomial f(x)3x25x2, then evaluate

(i) 2

2 (ii) 3

3

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17. 5 3 5

Prove that 5 3 is irrational, given that 5 is irrational.

/OR

445, 572 699 4, 5 6

Find the greatest number that will divide 445, 572 and 699 to leave the remainders 4, 5 and 6 respectively.

18. tan 30

Find the value of tan 30 geometrically.

19. 3x2x3

3x5 x1x2

Divide 3x2x3

3x5 by x1x2 and verify the division algorithm.

20. x y

1 1 2

2 3

yxy

,

1 1 1

2 4

yxx

Solve for x and y : 1 1

22 3

yxy

,

1 1 1

2 4

yxx

/OR

k x2y5, 3xky150

(i) (ii)

For what value of k, will be pair of equations x2y5, 3xky150 have (i) unique solution (ii) no solution

21.

135 – 140

140 – 145

145 – 150

150 – 155

155 – 160

160 – 165

165 – 170

170 – 175

4 9 18 28 24 10 5 2

Using step deviation method find the mean of the following data :

Classes 135 – 140

140 – 145

145 – 150

150 – 155

155 – 160

160 – 165

165 – 170

170 – 175

Frequency 4 9 18 28 24 10 5 2

22. ABC BC D BD

1

3BC

9AD27AB2.

In an equilateral triangle ABC, D is a point on side BC such that BD1

3BC. Prove that

9AD27AB2.

/OR

ABC DBC BC AD BC O

ABC AO

DO DBC

ABC and DBC are two triangles on the same base BC. If AD intersects BC at O show that

ar ABC AO

ar DBC DO

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23.

tanA cotA 1 secA . cosecA

1 cotA 1 tanA

Prove that : tanA cotA

1 secA . cosecA1 cotA 1 tanA

24. 120

141 – 150 151 – 160 161 – 170 171 – 180 181 – 190

6 28 48 30 8 120

The frequency distribution of the weights of 120 birds is shown below :

Weight (in grams) 141 – 150 151 – 160 161 – 170 171 – 180 181 – 190 Total

Number of Birds 6 28 48 30 8 120

Find the median weight of a bird.

/ SECTION-D

25 34 4

Question numbers 25 to 34 carry four marks each.

25. n, n2 n4 3 n

Show that one and only one out of n, n2, n4 is divisible by 3, where n is any positive

integer.

26. 2xy6 2xy20 x-

Draw a graph of 2xy6 and 2xy20 shade the region bounded by these lines and

x-axis. Find the area of the shaded region.

27. sectanp

2

2

p 1 sin

p 1

If sectanp, show that 2

2

p 1 sin

p 1

28.

10 0

30 10

50 25

70 43

90 65

110 87

130 96

150 100

Find the median for the following data :

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Marks Number of students

Less than 10 0 Less than 30 10 Less than 50 25 Less than 70 43 Less than 90 65 Less than 110 87 Less than 130 96 Less than 150 100

29. f(x)4x42x3

2x2x1 g(x)x2

2x3

What must be added to f(x)4x42x3

2x2x1 so that the resulting polynomial is

divisible by g(x)x22x3

/OR

10% 20% 60

5% 5% 10

On selling a tea set at 10% loss and a lemon set at 20% gain a shop keeper gains Rs. 60. If he

sells tea set at 5% gain and lemon set at 5% loss he gains Rs. 10. Find the cost price of the

Tea set and the lemon set.

30.

Prove that if a line is drawn parallel to one side of triangle to intersect the other two sides in

distinct points, the other two sides are divided in the same ratio.

/OR

Prove that in a right triangle the square of the hypotenuse is equal to the sum of the squares

of other two sides.

31.

2 2

2

3cos43 cos37 cosec53 sin 35

sin47 tan5 tan25 tan45 tan65 tan85 cos 55

Evaluate : 2 2

2

3cos43 cos37 cosec53 sin 35

sin47 tan5 tan25 tan45 tan65 tan85 cos 55

32. D E ABC C CA CB

(AE2BD2)(AB2

DE2)

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C.

Prove that : (AE2BD2)(AB2

DE2)

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33. AB90

2

2

tanA tanB tanA cotB sin B tanA

sinA secB cos A

If AB90 then prove that : 2

2

tanA tanB tanA cotB sin B tanA

sinA secB cos A

34. 60

`

120 – 140 4 140 – 160 6 160 - 180 10 180 – 200 16 200 – 220 12 220 – 240 9 240 – 260 3

The following distribution gives the daily wages of 60 workers of a factory :

Daily wages (in `) Number of wokers

120 – 140 4 140 – 160 6 160 - 180 10 180 – 200 16 200 – 220 12 220 – 240 9 240 – 260 3

Convert the above distribution into Less than type cumulative frequency distribution. Draw its ogive and find the median.

- o O o -