Mathematics - Class IX 2012 - Exam - Set 39, Exams of Mathematics

Download Mathematics - Class IX 2012 - Exam - Set 39 and more Exams Mathematics in PDF only on Docsity! Page 2 of 10 SUMMATIVE ASSESSMENT – II, 2012 II, 2012 MATHEMATICS / 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 3 4 2 (v) 45010 Page 3 of 10 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. The equation of a line parallel to y-axis is : (A) x1 (B) x y0 (C) y0 (D) y1 y- (A) x1 (B) x y0 (C) y0 (D) y1 2. In a triangle ABC, D, E and F are the mid-pts of sides BC, CA and AB respectively, then : (A) ar (BDEF) 1 4 ar (ABC) (B) ar (AFE) 1 2 ar (ABC) (C) ar (DEF) 1 2 ar (ABC) (D) ar (BFEC) 3 4 ar (ABC) ABC , BC , CA AB D, E F (A) ar (BDEF) 1 4 ar (ABC) (B) ar (AFE) 1 2 ar (ABC) (C) ar (DEF) 1 2 ar (ABC) (D) ar (BFEC) 3 4 ar (ABC) 3. In the given figure, ADBC and BCA40. The measure of DBC is equal to : (A) 50 (B) 80 (C) 40 (D) 20 ADBC BCA40 DBC Page 6 of 10 6 3 cm 11. A class consists of 50 students out of which 30 are girls. The mean of marks scored by girls in a test is 73 and that of the boys is 71. Find the mean score of whole class. 50 30 73 71 12. The table given below shows the marks obtained by 80 students of a class in a test with maximum marks 100 : Marks 020 2040 4060 6080 above 80 No : of students 8 16 40 10 6 A student is chosen at random. Find the probability that he gets : (i) less than 40 marks. (ii) 60% or more marks. 80 100 020 2040 4060 6080 80 8 16 40 10 6 (i) 40 (ii) 60% 13. In the given figure, in a circle with centre O, AOC80, B and D are two other points on the circle. Find ABC and ADC. O AOC80 B D ABC ADC OR If a line intersects two concentric circles with common centre O, at A, B, C and D, prove that ABCD. O A, B, C D ABCD. 14. Find the mean of first seven multiples of 9. 9 7 Page 7 of 10 SECTION-C / Question numbers 15 to 24 carry three marks each. 15. Express y in terms of x in the equation 2x3y12. Find the points where the line represented by the equation 2x3y12 cuts the x - axis and y – axis. 2x3y12 y x 2x3y12, x - y – 16. Show that the diagonals of a parallelogram divide it into four triangles of equal area. 4 17. Draw a ABC in which BC6 cm, AB5.2 cm and AC4.8 cm. Draw the perpendicular bisector of BC. Does it pass through A ? (Use ruler and compass only). ABC BC6 cm AB5.2 cm AC4.8 cm BC A 18. A solid cube of side 30 cm is cut into eight cubes of equal volume. What will be side of the new cube ? Also find the total surface area of each of these 8 cubes. 30 cm OR The diameter of a roller 140 cm long is 150 cm. If it takes 800 complete revolutions to level a playground, determine the cost of levelling it at the rate of Rs. 2 per square metre. (roller) 150 cm 140 cm 800 2 19. Find the mean for the following data : x 4 6 8 10 12 f 4 8 14 11 3 x 4 6 8 10 12 f 4 8 14 11 3 OR The score of 15 students in an examination out of 10 marks is as below : 3 , 9 , 7, 5 , 6 , 3 , 7 , 6 , 7 , 4 , 7 , 7, 4 , 8 , 2 Find the mean, mode and median for the each. 15 10 3 , 9 , 7, 5 , 6 , 3 , 7 , 6 , 7 , 4 , 7 , 7, 4 , 8 , 2 20. Write 7 2 y x as a linear equation of the form 0 ax by c   . Also write the values corresponding to a, b, c. Does the graph of this linear equation pass through origin ? Give your answer in yes or no. Page 8 of 10 7 2 y x 0 ax by c   a, b, c OR Solve the equation 2x33x1 and represent the solutions (i) on the number line (ii) in the Cartesian plane. 2x33x1 (i) (ii) 21. A capsule of medicine is in the shape of a sphere of diameter 3.5 cm. How much medicine (in mm3) is needed to fill the capsule. (Use   22 7 ). 3.5 cm m3  22 7 22. Prove that the quadrilateral formed by joining the mid-points of the consecutive sides of a rectangle is rhombus. 23. ABCD is a parallelogram. P and Q are points on DC and AB respectively, such that DAPBCQ. Show that AQCP is a parallelogram. ABCD P Q DC AB DAPBCQ AQCP 24. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes : Outcome 3 heads 2 heads 1 head 3 tails Frequency 23 84 71 22 Find the probability of getting (a) 3 heads (b) no heads (c) at least 2 heads 200 3 2 1 3 23 84 71 22 (a) 3 (b) (c)