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ST. JOHN S UNIVERSAL SCHOOL FORMATIVE ASSESSMENT 1 2020-2021 CLASS: X SUBJECT: MATHEMATICS MARKS: 50 TIME: 1 hr 50min. DATE: 17/08/2020 Answers to this paper must be written on a ruled sheet. First 10 minutes are to be spent in reading the question paper. The time given at the head of this paper is for writing and uploading the paper. The Answer Sheet should have the following details mentioned- Date, Full Name, Class & Division, Subject. The pages should be numbered appropriately. . Attempt all questions from section A and any THREE questions from section B. All working, including rough work must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. Section A (20 marks) (Attempt all questions from this section) Question 1 a) Given x R, solve the inequation and graph the solution on the number line: 3 4 2 + 2 3 b) Two dice are rolled together. Find the probability of getting: i) A doublet ii) the product of the numbers as 4 or 5. [3] [3] c) Ramesh has a recurring deposit account in a bank for three and a half years at 9.5 % p. a. If he deposits 1200 per month, find the interest paid by the bank and the maturity value of the account. [4] Question 2 a) Find the value of k for which the given equation has real and equal roots: 2 2( + 1) + 2 = 0 [3] b) The marks scored by 16 students in a class test are as below: 3, 6, 8, 13, 15, 5, 21, 23, 17, 10, 9, 1, 20, 21, 18, 12. Find the median and mode. [3] c) Find vertex M of parallelogram LMNO, where L (10, -6), N (-4, -2) and O (4, -2). [4] Section B (30 marks) (Attempt any three questions from this section) Question 3 a) E is a point on side AD produced of a parallelogram ABCD and BE intersects CD at F. Prove that ABE ~ CFB. If AD = 4 cm, DE = 2 cm; find AB : CF. [3] b) Kiran deposits 200 per month for 36 months in a bank under recurring deposit scheme. If she receives 8421 at the time of maturity, find the rate of interest paid by the bank. [3] c) The triangle OAB is reflected in origin to triangle OA B . A and B have the co-ordinates (-3, -4) and (0, -5) respectively. i) Find the co-ordinates of points A and B. ii) Write the special name of the figure ABA B . Also name two invariant points under reflection in Y- axis. [4] Question 4 a) In a collection of funds for flood hit victims, 200 people in a colony contributed some money. The following table shows the distribution: Contribution 500600 in ( ) No of people 6 600700 12 700800 16 800900 34 9001000 40 10001100 36 11001200 28 12001300 14 13001400 8 14001500 6 Draw the ogive and use it to answer the following: (i) Estimate the median. (ii) Find the lower quartile. (iii) If the top 10% of the contributors were to attend an official program, what would be the lowest contribution to qualify for the program. [6] b) If P is the solution set of -3x + 4 < 2x 3, x N, and Q is the solution set of 4x - 5 < 12, x W. Find (i) P Q (ii) Q P [4] Question 5 a) There are 16 red balls and some white balls in a box. If the probability of getting a red ball is two-third of getting a white ball, how many white balls are there in the box? [3] b) Solve and give your answer correct upto two decimal places: 3 2 32 + 12 = 0 [3] c) In PQR, the medians QA and RB intersect at C. Prove that: RC = 2BC. Also, find the ratio of areas of QRC and ABC. [4] Question 6 a) The point P(4, -7) on reflection in x-axis is mapped onto P followed by reflection in y-axis and mapped onto P . Find the co-ordinates of P and P . Write down the single transformation that maps P onto P . [3] b) If A and B are two points having co-ordinates (-2, -2) and (2, -4) respectively, 3 find the co-ordinates of point P such that AP = 7 AB. [3] c) The measures of the diameters of the heads of 150 screws is given in the following table. Diameter 32 - 36 37 - 41 42 - 46 47 - 51 52 - 56 57 - 61 62 - 66 (in mm) No of 15 17 14 25 29 20 30 screws Find the mean using step deviation method. Give your answer to nearest mm. [4]
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