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SUMMATIVE ASSESSMENT II, 2012 MA-1025 MATHEMATICS / II, 2012 Class IX / IX Time allowed : 3 hours Maximum Marks : 90 3 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 1 6 2 10 3 10 4 (iii) 1 8 (iv) 2 3 (v) 3 4 2 Page 2 of 10
SECTION A / Questions Number 1 to 8 carry 1 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 8 1 1. The graph of 3x y 9 intersects x-axis at the point. (A) ( 3, 0) (B) (3, 0) (C) (0, 9) (D) (0, 9) 3x y 9 x- (A) ( 3, 0) (B) (3, 0) (C) (0, 9) (D) (0, 9) 2. In given fig., ABCD is a parallelogram. If ar ( BFC) 40 cm 2 then ar ( AEB) is equal to : (A) 20 cm 2 (B) 40 cm 2 (C) 80 cm 2 (D) 10 cm 2 ABCD ( BFC) 40 cm 2 ( AEB) (A) 20 cm 2 (B) 40 cm 2 (C) 80 cm 2 (D) 10 cm 2 3. A chord of a circle is equal to its radius. (See given fig). BAC is equal to : (A) 90 (B) 60 (C) 30 (D) 45 BAC (A) 90 (B) 60 (C) 30 (D) 45 Page 3 of 10
4. Which of the following is a linear equation? (A) x 2 4x 3 (x 2 1) (B) x 2 3x 4 (C) x 1 5 (D) (x 1) 1 x x (A) x 2 4x 3 (x 2 1) (B) x 2 3x 4 (C) x 1 5 (D) (x 1) 1 x x 5. The class marks of a frequency distribution are 15, 20, 25,. The class corresponding to class mark 25 is : (A) 17.5 22.5 (B) 20 30 (C) 22.5 27.5 (D) 22 27 ( class marks) 15, 20, 25,. 25 (A) 17.5 22.5 (B) 20 30 (C) 22.5 27.5 (D) 22 27 6. A semi-circle is folded to form a cone, (See fig.). The radius OA will form : (A) height of the cone (B) slant height of the cone (C) Circumference of the base (D) half of the circumference of the base OA (A) (C) (B) (D) 7. The sum of probability of an event A and event not A is equal to : (A) 0 (B) 1 (C) 1 (D) 2 A A (A) 0 (B) 1 (C) 1 (D) 2 8. If diameter of a sphere is doubled then its surface area will be : (A) same (B) doubled (C) four times (D) eight times (A) (B) (C) (D) Page 4 of 10
SECTION-B / Question numbers 9 to 14 carry 2 marks each. 9 14 2 9. Show that the line segment joining the mid-points of opposite sides of a parallelogram, divide it into two equal parallelograms. 10. A cylinder 3 m high, is open at the. Top the circumference of its base is 22 m. Find its total surface area (take 22 7 ) 3 22 ( 22 7 ) 11. The following number of goals were scored by a team in a series of 10 matches : 2, 3, 4, 5, 0, 1, 3, 3, 4, 3. Find mode and median of the above data. 10 2, 3, 4, 5, 0, 1, 3, 3, 4, 3. 12. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes. Outcome : 3 heads 2 heads 1 head 3 tails Frequency : 24 70 75 31 Compute the probability of getting (i) less than 2 heads (ii) 3 heads 200 3 2 1 3 24 70 75 31 (i) (ii) 3 13. In adjacent Fig., two chords AB and CD of a circle intersect at right angle. If ABD 65, find the measure of CAB. AB CD Page 5 of 10
ABD 65 CAB In the figure, AB BP prove that DP DC. AB BP DP DC. 14. Calculate mean of first 5 prime numbers. SECTION-C / Questions numbers 15 to 24 carry 3 marks each. 15 24 3 15. Rohit is driving his car at a uniform speed of 80 km per hour. Draw time distance graph taking time along x-axis and distance along y-axis. 80 / x- y- 16. Prove that median of a triangle divides it into two triangles of equal area. 17. Draw an acute angled triangle ABC. Construct perpendicular bisectors of AB and BC intersecting each other at O. Measure OA, OB and OC. Are they equal? Page 6 of 10
OB OC AB BC O OA, 18. A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between. 4 cm A river 4 m deep and 60 m wide is flowing at the rate of 0.31 km/hour. How much water will fall into the sea in a minute? 4 m 60 m 0.31 km/hr 19. Find the mean of the following distribution : Variable (x) : 4 5 6 7 8 9 Frequency (f) : 12 10 8 7 8 5 (x) : 4 5 6 7 8 9 (f) : 12 10 8 7 8 5 The number of books in different shelves of a library are as follows : 25, 27, 32, 24, 28, 34, 20, 25, 28, 30, 20, 35, 25, 27, 31, 37, 22, 24, 27, 28, 27, 20, 36, 21, 20, 29 30, 29, 36, 30. Prepare a frequency distribution table with class size 4 for the data given above taking the first interval as 18 22. (22 not included) (shelves) 25, 27, 32, 24, 28, 34, 20, 25, 28, 30, 20, 35, 25, 27, 31, 37, 22, 24, 27, 28, 27, 20, 36, 21, 20, 29 30, 29, 36, 30. 4 18 22 22 20. Find three different solutions for the equation 6x 8y 32 0. 6x 8y 32 0 If the point (2, 4) lies on the graph of the equation 2y ax 10, find the value of a. Now express this as a linear equation in two variables. 2y ax 10 (2, 4) a 21. The outer diameter of spherical shell is 10 cm and the inner diameter is 8 cm. Find the volume of the metal contained in the shell. 10 cm 8 cm Page 7 of 10
22. Prove that a diagonal of a parallelogram divides it into two congruent triangles. 23. ABCD is a rhombus with ABC 50 Determine ACD. ABCD ABC 50 ACD 24. 30 plants were planted in each school out of 12 schools. After a month the number of plants that survived are given below. School : 1 2 3 4 5 6 7 8 9 10 11 12 Number of 22 15 12 24 27 10 13 22 17 9 20 25 plants survived : What is the probability of survival of : (i) more than 20 plants in a school (ii) less than 10 plants in a school (iii) exactly 22 plants in a school 12 30 1 2 3 4 5 6 7 8 9 10 11 12 22 15 12 24 27 10 13 22 17 9 20 25 (i) 20 (ii) 10 (iii) 22 SECTION-D / Question numbers 25 to 34 carry 4 marks each. 25 34 4 25. Prove that the bisectors of angles of a parallelogram encloses a rectangle. 26. Construct a triangle PQR such that R 75, Q 45 and PQ QR RP 11 cm. PQR R 75, Q 45 PQ QR RP 11 Construct a triangle ABC in which BC 8 cm, B 45 and AB AC 3.5 cm. ABC BC 8 cm B 45 AB AC 3.5 cm 27. Draw the graph of linear equation 5y 3x 18 on Cartesian plane. From the graph check whether ( 2, 4) is the solution of linear equation or not. 5y 3x 18 ( 2, 4) 28. What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material required for sticking purpose will be approx. 20 cm. (Take 3.14). Page 8 of 10
( 3.14 ) 3 m 6 m 8 m 20 cm 29. If a line intersects two concentric circles with centre O at A, B, C and D. Prove that AB CD. (See fig.) O A, B, C D AB CD. 30. ABC is a triangle right angled at C. A line through the mid point M of hypotenuse AB and parallel to BC intersects AC at D show that (i) D is the mid point of AC (ii) CM MA 1 2 AB. ABC C AB M BC D AC (i) AC D (ii) CM MA 1 2 AB. ABCD is a parallelogram and X and Y are points on the diagonal BD, such that DX BY. Show that (i) AYCX is a parallelogram (ii) CX AY. ABCD BD X Y DX BY (i) AYCX (ii) CX AY. Page 9 of 10
31. Give the geometrical representation of 4 (y 3) 2 y 5 as an equation (i) in one variable (ii) in two variables. 4 (y 3) 2 y 5 (i) (ii) 32. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side. 33. Twenty cylindrical pillars of a building are to be cleaned. If the diameter of a pillar is 0.5 m and height is 4 m, what will be the cost of cleaning them at the rate of Rs. 3 per m 2. (Take 3.14) 20 0.5 4 3 ( 3.14 ) 34. Draw a histogram representing the following frequency distribution. Marks : 0 10 10 20 20 30 30 40 40 50 50 60 No. of students : 3 5 8 10 7 2 0 10 10 20 20 30 30 40 40 50 50 60 3 5 8 10 7 2 - o O o - Page 10 of 10