I, 2012 SUMMATIVE ASSESSMENT – I, 2012
MA2-021
/ MATHEMATICS X / Class – X 3
90
Time allowed : 3 hours
Maximum Marks : 90
(i) (ii)
34
8
1
6
3
10
(iii)
1
2
10
4
8
(iv)
2 3
4
3
2
(v)
General Instructions: (i) (ii)
(iii) (iv)
(v)
All questions are compulsory. 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. 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. 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. Use of calculator is not permitted.
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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.
3 8 (A) 0.125 (B) 3 in decimal form is : 8 (A) 0.125 (B)
0.0125
(C)
0.0375
(D)
0.375
0.0125
(C)
0.0375
(D)
0.375
(D)
23, 24
(D)
23, 24
2
p(x)54x 212x19 3 3 3 3 (A) , (B) 2 ,2 (C) 3, 4 2 2 2 2 2 The zeroes of the polynomial p(x)54x 212x19 are : 3 3 3 3 , (B) 2 ,2 (C) 3, 4 (A) 2 2 2 2
3.
DABC ~ DPQR
x (A)
2.5
(B)
3.5
(C)
2.75
(D)
3
(C)
2.75 cm
(D)
3 cm
(C)
0
(D)
2ab
(D)
2ab
In the given figure if DABC ~ DPQR
The value of x is : (A) 2.5 cm 4.
(B)
x5a cosu, y5b sinu (A)
1
(B)
3.5 cm b2x21a2y22a2b2 21 2 2
2 2
2 2
If x5a cosu, y5b sinu, then b x 1a y 2a b is equal to : (A) 1 (B) 21 (C) 0
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5. 111 125
(A)
(B)
127 8
19
(C)
3
9 455
(D)
2
5 32 A rational number which has non terminating decimal representation is : 19 111 127 9 (B) (C) (D) (A) 3 2 125 8 455 5 32
6.
x5a, y5b
x2y52
a
x1y54
b
(A) 3, 5 (B) 5, 3 (C) 3, 1 (D) 21, 23 If x5a, y5b is the solution of the pair of equation x2y52 and x1y54, then the respective values of a and b are : (A) 3, 5 (B) 5, 3 (C) 3, 1 (D) 21, 23 7.
2
2
sin 6082sin 308 (A)
1 4
(B)
1 2
The value of sin26082sin2308 is : 1 1 (A) (B) 4 2 8.
(C)
3 4
(D)
2
1 2
(C)
3 4
(D)
2
1 2
(C)
17.5
(D)
15
(C)
17.5
(D)
15
10 – 25 (A) 17 (B) 18 The class mark of the class 10 – 25 is : (A) 17 (B) 18
/ SECTION-B 9
14
2
Question numbers 9 to 14 carry two marks each. 9.
255
867
Find the HCF of 255 and 867 by Euclid division algorithm. 10.
2
f(x)52x 27x13
p, q
2
p 1q
2
If p, q are zeroes of polynomial f(x)52x227x13, find the value of p21q2. 11.
PQR KR58
ÐQPR5908, PQ524
QR526
DPKR
ÐPKR5908,
PK
In the given triangle PQR, ÐQPR5908, PQ524 cm and QR526 cm and in DPKR, Page 4 of 9
ÐPKR5908 and KR58 cm find PK.
12.
3 2cot2A21 2 3 2 If sinA5 , find the value of 2cot A21. 2
13.
2
sinA5
2 2
Find the quadratic polynomial whose zeroes are
2 and 2 2 .
14. 0–6
6 – 12
12 – 18
18 – 24
24 – 30
7 5 10 12 6 Find the mean of the following frequency distribution : Class : 0–6 6 – 12 12 – 18 18 – 24 24 – 30 Frequency : 7 5 10 12 6 /OR 0–6
6 – 12
12 – 18
18 – 24
24 – 30
7 5 10 12 6 Find the mode of the following frequency distributions : Class : 0–6 6 – 12 12 – 18 18 – 24 24 – 30 Frequency : 7 5 10 12 6 SECTION-C 15
24
3
Question numbers 15 to 24 carry three marks each. 15. Prove that the sum of squares on the sides of a rhombus is equal to sum of squares on its diagonals. 1 2
16.
23 2
4x214x23
1 23 and are the zeroes of the polynomial 4x214x23 and verify the 2 2 relationship between zeroes and co-efficients of polynomial.
Show that
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17.
423 2 Prove that 423 2 is an irrational number. /OR a b
0.3178
Express the number 0.3178 in the form of rational number
a . b
18. cos508 4 ( cosec 2 598!2 tan 2 318 ) 2 1 2 tan128 tan788.sin908 2 2sin408 3 3tan 458 Find the value of the following without using trigonometric tables :
cos508 4 ( cosec 2 598!2 tan 2 318 ) 2 1 2 tan128 tan788.sin908 2 2sin408 3 3tan 458
19.
b
3
2
2x 19x 2x2b
(2x13)
Find the value of b for which (2x13) is a factor of 2x319x22x2b 20.
3x25y520, 6x210y14050 Using graph, find whether the pair of linear equations 3x25y520, 6x210y14050 is consistence or inconsistent. Write its solution. /OR x
y
6 3 2 51 x 21 y 22 5 1 1 52 , x¹ 1, y ¹ 2 x 21 y 22 Solve for x and y : 6 3 2 51 x 21 y 22 5 1 1 5 2 , where x¹ 1, y ¹ 2 x 21 y 22
21.
27 0 – 10
10 – 20
p 20 – 30
30 – 40
40 – 50
8 p 12 13 10 If the mean of the following distribution is 27, find the value of p : Class : 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 Frequency : 8 p 12 13 10 22. If the areas of two similar triangles are equal, then prove that they are congruent. /OR Page 6 of 9
ABC
DBC
BC
PQ??BA
PR??BD
QR??AD.
In the given figure, two triangles ABC and DBC lie on same side of BC such that PQ??BA and PR??BD. Prove that QR??AD.
23.
sin3u5cos(u268), 3u u268 u If sin3u5cos(u268), where 3u and u268 are both acute angles, find the value of u.
24. 0 – 10
10 – 20
20 – 30
30 – 40
8 16 36 34 Find mean, and median for the following data : Class : 0 – 10 10 – 20 20 – 30 30 – 40 Frequency : 8 16 36 34
40 – 50 6 40 – 50 6
/ SECTION-D 25
34
4
Question numbers 25 to 34 carry four marks each. 25.
3n
3n11
By Euclid division algorithm, show that square of any positive integer is of the form 3n or 3n11. 26.
k 3x1y51 (2k21)x1(k21)y52k11 For what value of k will the pair of equations have no solution ? 3x1y51 (2k21)x1(k21)y52k11 Page 7 of 9
27.
(secA2tanA)2(11sinA)512sinA Prove that (secA2tanA)2 (11sinA)512sinA
28. 20 – 30
30 – 40
40 – 50
50 – 60
60 – 70
70 – 80
8
10
14
12
4
2
Draw ‘less than’ and ‘more than’ ogives for the following distribution : Scores : 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 Frequency : 8 10 14 12 4 2 Hence find they median. Verify the result through calculations. 29.
p(x)58x4114x322x218x212
4x213x22 4
3
2
p(x)
2
What must be subtracted or added to p(x)58x 114x 22x 18x212 so that 4x 13x22 is a factor of p(x) ? /OR x
y 133x1 87y5353 87x1133y5307
Solve for x and y 133x1 87y5353 and 87x1133y5307 30.
DABC
AB
AC
BC
P
Q
AD
PQ
BC
A
PQ
In DABC, P and Q are the points on the sides AB and AC respectively such that PQ is parallel to BC. Prove that median AD drawn from A to BC bisects PQ also. /OR ABC
AD^BC
2
2
3AB 54AD .
In an equilateral DABC, AD^BC. Prove that 3AB254AD2. 31.
sinu1cosu5m
secu1cosecu5n,
2
n(m 21)52m
2 If sinu1cosu5m and secu1cosecu5n, then prove that n(m 21)52m
32. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides. 33.
tanu!1 sinu secu!1 1 5 tanu!2 sinu secu!2 1 tanu!1 sinu secu!1 1 5 Prove that : tanu!2 sinu secu!2 1
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34.
65
f1 0 – 20
20 – 40
40 – 60
60 – 80
80 – 100
100 – 120
6
8
f1
12
6
5
6, 8, f1 12 Find the value of f1 from the following data if its mode is 65 : Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Frequency 6 8 f1 12 6 where frequency 6, 8, f1 and 12 are in ascending order.
100 – 120 5
-oOo-
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