(Not to be printed with the question paper) 8 of 11 23. ABC AB AC BA D AD AB BCD Triangle ABC is an...
Transcript of (Not to be printed with the question paper) 8 of 11 23. ABC AB AC BA D AD AB BCD Triangle ABC is an...
Page 1 of 11
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.
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paper being administered to the examinees.
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I, 2012
SUMMATIVE ASSESSMENT – I, 2012
/ MATHEMATICS
IX / Class – IX
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.
MA1-042
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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. 9
p
q p q q 0
(a) 2999
1000 (b)
19
10 (c) 3 (d)
26
9
The value of 2. 9
in the formp
q, where p and q are integers and q 0, is
(a) 2999
1000 (b)
19
10 (c) 3 (d)
26
9
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2. abc0 a3b3c3
(a) abc (b) 3abc (c) 2abc (d) 4abc
If a b co, then a3 b3 c3 is equal to :
(a) abc (b) 3abc (c) 2abc (d) 4abc
1
3. f(x)2x27x3 x 2
(a) 19 (b) 3 (c) 3 (d) 0
Value of f(x) 2x2 7x 3 at x 2 is :
(a) 19 (b) 3 (c) 3 (d) 0
1
4. 52524752
(a) 100 (b) 10000 (c) 50000 (d) 100000
Value of 5252 4752 is : (a) 100 (b) 10000 (c) 50000 (d) 100000
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5. 130
(a) 45 (b) 65 (c) 75 (d) 35
An exterior angle of a triangle is 130 and its two interior opposite angles are equal. Each of the interior angle is equal to : (a) 45 (b) 65 (c) 75 (d) 35
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6.
(a) 15 (b) 25 (c) 30 (d) 35
In a right angled triangle, if one acute angle is half the other, then the smallest
angle is :
(a) 15 (b) 25 (c) 30 (d) 35
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7. ( 3, 9) x
(a) (3, 9 ) (b) (9, 3 ) (c) (3, 9 ) (d) (3, 9)Mirror image of point ( 3, 9) on x axis is : (a) (3, 9 ) (b) (9, 3 ) (c) (3, 9 ) (d) (3, 9)
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8.
(a) I (b) II
(c) III (d) IV
A point both of whose co-ordinates are positive will be in : (a) I Quadrant (b) II Quadrant (c) III Quadrant (d) IV Quadrant
1
/ SECTION-B
9 14 2
Question numbers 9 to 14 carry two marks each.
9. 5 8 2 32 2 2
Simplify : 5 8 2 32 2 2
2
10. 2x3 11x2 4x 1 2x1
Show that 2x1 is a factor of 2x3 11x2 4x 1
2
11. x33x2
3x1 (x 1)
Find the remainder, when x3 3x2 3x 1 is divided by (x 1)
2
12.
State fifth postulate of Euclid.
2
13. (3x58) (x 38) x
If (3x 58) and (x 38) are supplementary angles, find x and the angles.
/ OR
PQR QP RQ S T
SPR 135 PQT110 PRQ
2
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In the figure sides QP and RQ of PQR are produced to points S and T
respectively. If SPR 135 and PQT 110 find PRQ.
14. 3 : 4 : 5 144 cm
The length of sides of a right angled triangle are in the ratio 3 : 4 : 5 and perimeter is 144 cm. Find its sides and area.
2
/ SECTION-C
15 24 3
Question numbers 15 to 24 carry three marks each.
15. 7 5.
Represent 7 5. on the number line geometrically.
/ OR
11 11 433 3281 (64 125 )
Evaluate :
11 11 433 3281 (64 125 )
3
16.
5 3 5 3
7 4 3 7 4 3
Simplify : 5 3 5 3
7 4 3 7 4 3
3
17. x3 3x29x5
Factorize : x3 3x2 9x 5
/ OR
3 3 32 2 a 16 2 b c 12abc
Factorize : 3 3 32 2 a 16 2 b c 12abc
3
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18. px2 5x r (x2) (2x1) pr
If both (x 2) and (2x1) are factors of px2 5x r show that p r
3
19.
POQ OR PQ OS, OP OR
1
ROS QOS POS2
In figure POQ is a line. Ray OR is to PQ. OS is another ray lying between OP
and OR.
Prove that
1
ROS QOS POS2
/ OR
OP RS, OPQ110 QRS130 PQR
In figure if OP RS, OPQ 110 and QRS 130, then determine PQR.
3
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20. ABC ABAC B C O
A O
(i) OBOC (ii) A AO
In an Isosceles triangle ABC, with AB AC, the bisectors of B and C
intersect each other at O. Join A to O. Show that (i) OB OC, (ii) AO bisects A
3
21.
l m p q
ABC CDA
l and m are two parallel lines intersected by another pair of parallel lines ‘p’ and
‘q’ (see figure ). Show that ABC CDA
3
22.
PQR QR S PQQRRP > 2 PS
In figures is any point on QR of PQR. Prove that PQ QR RP >2PS
3
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23.
ABC ABAC BA D
ADAB BCD
Triangle ABC is an isosceles triangle AB AC. Side BA is produced to D, such
that AD AB. Show that BCD is a right angle.
3
24. 3 : 5 : 7 300 m
The sides of a triangular park are in the ratio 3 : 5: 7 and the perimeter is 300 m. Find its area and the length of perpendicular drawn on the biggest side.
3
/ SECTION-D
25 34 4
Question numbers 25 to 34 carry four marks each.
25.
2 6 6 2 8 3
2 3 6 3 6 2
Simplify : 2 6 6 2 8 3
2 3 6 3 6 2
/ OR
2 5
a 2 5
2 5b
2 5
(ab)3
If 2 5
a 2 5
, and 2 5
b 2 5
then find (a b )3
4
26. a8 3 7 b
1
a a2
b2
If a 8 3 7 and b 1
a, what will be the value of a2 b2 ?
4
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27. 2x33x2
17x30
Factorize : 2x3 3x2 17x 30
4
28. k2 x3kx2
3kxk ( x3) k
k 0
Find the value of k ( k 0) if ( x3 ) is a factor of k2 x3 kx2 3kx k.
4
29.
(ab)3(bc)3
(ca)33(ab) (bc) (ca)2(a3
b3c3
3abc)
Prove that :
(ab)3 (bc)3 (ca)3 3(ab) (bc) (ca) 2(a3 b3c3
3abc)
4
30. PQRS P(4, 0), Q(1, 0), R(1,5)
S
Three vertices of a square PQRS are P(4, 0), Q (1, 0) R(1, 5). Plot the points.
Also find the co-ordinates of the missing vertex S.
4
31.
PQR QR S PQR PRS T
QTR1
2QPR
The side QR of PQR is produced to point S. If the bisector of PQR and PRS
meet at point T, then prove that QTR 1
2QPR.
4
32. PQR S SQSR < PQPR
S is any point in the interior of PQR. Show that SQ SR < PQ PR.
/ OR
4
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ABC AB, BC AM PQR PQ, QR
PN
(i) ABM PQN, (ii) ABC PQR
Two sides AB, BC and median AM of one ABC are respectively equal to sides PQ, QR and median PN of PQR. Prove that : (i) ABM PQN (ii) ABC PQR
33.
ABCD O OAOC D, O B
In a rhombus ABCD, O is any interior point such that OA OC. Then prove that D, O and B are collinear.
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34.
ABC AB AC BE CF
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