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SUMMATIVE ASSESSMENT II, 2012 MA-1024 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 11
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. Equation of a line passing through origin is : (A) x y 1 (B) x 2y 4 (C) x y 0 (D) y x 1 (A) x y 1 (B) x 2y 4 (C) x y 0 (D) y x 1 2. x 4 is a line : (A) parallel to y 4 (B) parallel to x axis (C) passing through origin (D) parallel to x 4 x 4 (A) y 4 (B) x- (C) (D) x 4 3. Choose the correct statement : (A) Diagonals of a rectangle are perpendicular to each other (B) Diagonals of a rhombus are perpendicular to each other (C) A kite is a parallelogram whose adjacent sides are equal (D) Diagonals of a trapezium are always equal. (A) (B) (C) (D) 4. In given fig, AB DC. If A 50, then measure of ABC is : (A) 50 (B) 130 (C) 100 (D) 80 Page 3 of 11
AB DC A 50 ABC (A) 50 (B) 130 (C) 100 (D) 80 5. A cone and a hemisphere have equal bases and equal volumes. The ratio of their heights is : (A) 2 : 1 (B) 1 : 2 (C) 2 : 3 (D) 3 : 2 (A) 2 : 1 (B) 1 : 2 (C) 2 : 3 (D) 3 : 2 6. If probability of an event is represented by p then choose the correct statement : (A) p 0 (B) 0 < p 1 (C) 0 p 1 (D) 1 p 1 p (A) p 0 (B) 0 < p 1 (C) 0 p 1 (D) 1 p 1 7. If total surface area of a cube is equal to its volume then each side of the cube is : (A) 6 units (B) 1 unit (C) 2 units (D) 6 units (A) 6 (B) 1 (C) 2 (D) 6 8. Facts or information collected with a definite purpose are called : (A) median (B) mode (C) data (D) histogram (A) (B) (C) (D) SECTION-B / Question Numbers 9 to 14 carry 2 marks each. 9 14 2 9. If an angle of a parallelogram is two-third of its adjacent angle then find the measure of all the angles. 10. A square piece of paper of side 22 cm is rolled to form a cylinder. Find the volume of the cylinder. (Take 22/7) 22 22/7 Page 4 of 11
11. In fig, O is the centre of the circle. If AOB 80 then find the measures of ADB and ACB. O AOB 80, ADB ACB In given fig, ABCD is a parallelogram. BE AD. If BE 14 cm and AD 8 cm, find the area of DBC. DBC ABCD BE AD BE 14 AD 8 12. On a particular day, the number of vehicles passing through a crossing is given below : Vehicle : Two wheeler Three wheeler Four wheeler Frequency : 57 33 30 A particular vehicle is chosen at random. What is the probability that it is not a four wheeler? 57 33 30 Page 5 of 11
13. Arithmetic mean of terms 21, 16, 24, x, 29, 15 is 23. Find the value of x. 21, 16, 24, x, 29, 15 23 x 14. Read the bar graph. Find the percentage of excess expenditure on wheat than pulses and ghee taken together. SECTION-C / Question Number 15 to 24 carry 3 marks each. 15 24 3 15. Write the equation y 3 8x 3 in the form of ax by c 0. Check whether (0, 1) and ( 3, 9) are solutions of this equation. y 3 8x 3 ax by c 0 (0, 1) ( 3, 9) 16. In given fig, ABCDE is a pentagon. BD FC. Prove that (i) ar ( BDC) ar ( BDF) (ii) ar ( ABCDE) ar ( AFDE) Page 6 of 11
ABCDE BD FC (i) ( BDC) ( BDF) (ii) ( ABCDE) ( AFDE) PQRS is a quadrilateral If points A, B, C, D are mid points of sides PQ, QR, RS and SP respectively then show that ABCD is a parallelogram. PQRS A, B, C D PQ, QR, RS SP ABCD 17. Find three different solutions for the equation 3x 4y 12. 3x 4y 12 18. A shot-putt is a metallic sphere of radius 3.5 cm. If the density of the metal is 7.8 g per cm 3, find the mass of the shot-putt. (Take 22/7) (shot-putt) 3.5 7.8 3 19. The radius and height of a right circular cone are in the ratio of 5 : 12. If its volume is 314 cm 3, find the slant height and radius of the cone ( 3.14) 5 : 12 314 3 3.14 A box with lid is made out of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm and 15 cm respectively. Find the capacity of the box and volume of the wood used. 2 25 18 15 Page 7 of 11
20. Find the mean of the following distribution Variable (x) : 5 15 25 35 45 Frequency (f) : 6 4 9 6 5 5 15 25 35 45 6 4 9 6 5 Find mean, median and mode of the following data : 15, 17, 16, 14, 17, 16, 11, 15, 17, 14. 15, 17, 16, 14, 17, 16, 11, 15, 17, 14. 21. Construct an equilateral triangle of side 6 cm write the steps of construction. 6 22. Prove that equal chords of a circle subtend equal angles at the centre. 23. Two parallel lines l and m are intersected by a transversal p. Show that the quadrilateral formed by the bisectors of interior angles is a parallelogram. (see given fig.) p l m 24. Fifty seeds were selected at random from each of 5 bags of seeds and were kept under standardised conditions favourable to germination. After 20 days, the number of seeds germinated were counted and recorded as follows : Bag 1 2 3 4 5 Number of seeds germinated 42 45 48 41 38 What is the probability of germination of (i) more than 40 seeds in a bag? (ii) 49 seeds in a bag? (iii) less than 40 seeds in a bag? Page 8 of 11
20 50 1 2 3 4 5 42 45 48 41 38 (i) 40 (ii) 49 (iii) 40 SECTION-D / Question numbers 25 to 34 carry 4 marks each. 25 34 4 25. Draw the graph of linear equation 2x y 8 on Cartesian plane. Write the coordinates of the points where this line intersects x-axis and y-axis. 2x y 8 x y 26. In given fig. ABC is an isosceles triangle in which AB AC. AD bisects exterior angle EAC. If CD AB, show that. (i) DAC BCA (ii) ABCD is a parallelogram (i) (ii) ABC AB AC AD EAC CD AB DAC BCA ABCD Page 9 of 11
27. Bhavya has a piece of canvas whose area is 552 m 2. She uses it to make a conical tent with a base radius of 7 m. Assuming that all the stiching margins and the wastage incurred while cutting amounts to approximately 2 m 2. Find the volume of the tent that can be made with it (Take 22/7). 552 m 2 7 2 2 22/7 A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm and outer diameter is 5.0 cm. Find its (i) Inner curved surface area (ii) Outer curved surface area. (iii) Total surface area. 77 (cross-section) 4 (i) (ii) (iii) 5 28. In given fig., PQ is the diameter of the circle. If PQR 65, RPS 25 and QPT 60 then find the measure of (i) QPR (ii) PRS (iii) PSR (iv) PQT PQ PQR 65, RPS 25 QPT 60, (i) QPR (ii) PRS (iii) PSR (iv) PQT 29. Construct a triangle PQR such that Q 45, R 60 and PQ QR RP 20 cm PQR Q 45, R 60 PQ QR RP 20 Page 10 of 11
Construct a XYZ in which YZ 5 cm, Y 60, and XY XZ 9 cm. XYZ YZ 5 cm, Y 60 XY XZ 9 30. Give the geometrical representation of 3 (x 6) 2 x 7 as an equation (i) in one variable (ii) in two variables. 3 (x 6) 2 x 7 (i) (ii) 31. In given fig., AD is the median of ABC. E is the mid point of AD. DG BF. Prove that AC 3 AF AC 3 AF ABC AD AD E DG BF 32. A cylindrical container of base radius 28 cm contains sufficient water to submerge a rectangular block of iron with dimensions 32 cm 22 cm 14 cm. Find the rise in the level of the water, when the block is completely submerged. 28 32 22 14 33. If the non-parallel sides of a trapezium are equal, prove that it is cyclic. 34. For the following data, draw a histogram. Age (in years) : 0 6 6 12 12 18 18 24 24 30 30 36 Number of persons : 8 12 15 18 12 4 0 6 6 12 12 18 18 24 24 30 30 36 8 12 15 18 12 4 - o 0 o - Page 11 of 11