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SUMMATIVE ASSESSMENT – II, 2012
II, 2012
MATHEMATICS /
Class – IX / IX
Time allowed : 3 hours Maximum Marks : 90
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 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.
(i)
(ii) 34 8
(iii) 1 8
(iv) 2 3
(v)
SECTION–A /
Question numbers 1 to 8 carry one mark each. For each questions, four alternative choices have
been provided of which only one is correct. You have to select the correct choice.
1. Any solution of linear equation 2 x 0 y 9 0 in two variables is of the form.
(A)
, m 2
(B)
n, 2
(C)
(D) (9, 0)
2 x 0 y 9 0
(A)
, m 2
(B)
n, 2
(C)
(D) (9, 0)
2. In the given figure, ABCD is a parallelogram. F and E are midpoints of CD and AB respectively. If
area (BEC) a sq. units, then the area (ABCD) (in sq. units) is equal to :
(A) 2 a (B) a (C) 3 a (D) 4 a
ABCD F E CD AB ar
(BEC)a area (ABCD)
(A) 2 a (B) a (C) 3 a (D) 4 a
3. In the given figure, O is the centre of the circle. ABCD is a trapezium in which ABDC and
ADC 110 . The measure of ACD is equal to :
(A) 35 (B) 70 (C) 20 (D) 55
O ABCD ABDC ADC 110 ACD
SECTION-B /
Question numbers 9 to 14 carry two marks each.
9. In the given figure, ABED is a parallelogram in which DEEC. Show that area (ABF)ar (BEC).
ABED DEEC ar (ABF)ar (BEC)
10. (^) The edge of a cube is 10.5 mm. Find its total surface area in cm^2.
एक घन का दकनाया 10.5 चभ.भी.है। सेभी^2 भं घन का कुर ऩृष्ठीम ऺेत्र पर ऻात कीजजए।
If the mean of five observations x , x 2, x 4, x 6, x 8 is 13, then find the value of x.
मदद ऩॉॊि प्रेऺ णों x , x 2, x 4, x 6 तथा x 8 का भाध्म 13 है तो x का भान ऻात कीजजए।
12. A die is tossed 100 times and the data are recorded as below :
Outcomes 1 2 3 4 5 6
Frequency 20 15 20 15 20 10
The die is tossed again. Find the probability of getting
(a) an odd number
(b) a prime number
(a)
(b)
13. In the given figure, ABC 69 and ACB 31 , find BDC
ABC 69 ACB 31 BDC
OR
In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at E such that
BEC 130 and ECD 20 . Find BAC.
A, B, C D AC BD E BEC 130
ECD 20 BAC
14. (^) From the following observations
(i) (^) Calculate the Mode
(ii) (^) Calculate the Range
चनम्न प्रेऺ णों से (i) फहुरक ऻात कीजजए (ii) ऩरयसय ऻात कीजजए।
SECTION-C /
Question numbers 15 to 24 carry three marks each.
15. Show that the points A (1, 2), B (1, 16) and C (0, 7) lie on the graph of the linear equation
y 9 x 7.
A (1, 2), B (1, 16) C (0, 7) y 9 x 7
16. PQRS is a parallelogram and O is a point in the interior of the parallelogram. Show that
ar (POS)ar (QOR)
ar (PQRS).
PQRS O
ar (POS)ar (QOR)
ar (PQRS)
17. Draw a triangle ABC, in which base BC8 cm, B 45 and ABAC3.5 cm.
22. PQRS is a parallelogram and PL and RM are perpendiculars drawn from the vertices P and R of the
parallelogram on diagonal SQ. Show that
(a) PLQ RMS
(b) PLRM
PQRS P R SQ PL RM
(a) PLQ RMS
(b) PLRM
23. (^) Show that the median of a triangle divides it into triangles of equal area. 24. (^) 1500 families with 2 children were selected randomly, and the following data were recorded :
Number of girls in a family 2 1 0
Number of families 475 814 211
Compute the probability of a family, chosen at random, having
(i) 2 girls (ii) No girl
(i) 2 (ii)
SECTION-D /
Question numbers 25 to 34 carry four marks each.
25. Diagonals AC and BD of quadrilateral ABCD intersect at O in such a way that ar(AOD)ar(BOC).
Prove that ABCD is a trapezium.
ABCD AC BD O ar(AOD)ar(BOC)
ABCD
26. Construct a triangle in which base is 4.1 cm, base angle is 45 and sum of other two sides is
6.7 cm.
OR
Construct a XYZ in which Y 30 , Z 90 and XYYZZX11 cm
XYZ Y 30 , Z 90 XYYZZX 11
27. (^) Give the geometrical representation of 2 x 13 0 as an equation in :
(i) One variable (ii) Two variables
2 x 13 0
(i)
(ii)
28. (^) Lead spheres of diameter 6 cm each are dropped into a cylindrical beaker containing some water
and are fully submerged. If the diameter of the beaker is 18 cm and water level rises by 40 cm,
find the number of lead spheres dropped in the water.
29. (^) In the given figure, O is the centre of the circle. Prove that BOC 2 BAC.
O BOC 2 BAC
30. Show that the bisectors of angles of a parallelogram enclose a rectangle.
Number of balls Team A Team B
एक दक्रकेट भैि की प्र थभ 42 र्ंदं भं दो टीभं A तथा B द्वाया फनामी र् ई दौड़े
दौड़ं की सॊख्मा टीभ A टीभ B
