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ICSE Class X Mid-term 2021 : Mathematics

5 pages, 46 questions, 4 questions with responses, 4 total responses,

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Booster Exam 2020 - 2021 SUBJECT: Mathematics GRADE: X (ICSE) DATE: 14/12/2020 MARKS: 80 TIME: 2 Hrs. Instructions: 1. Answers to this paper must be written on the paper. 2. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. 3. The time given at the head of this paper is the time allotted for writing the answers 4. Section A all Questions are compulsory 5. Section B attempt any four 6. Marks are indicated in [] Section A (All are compulsory) Question 1 a) Find x, if : [3 Marks] b) Two equal cones are touching each other completely at the base circle. Given that the distance between the two vertices is 16 cm and the diameter of the base circle is 12 cm, find the total surface area of the solid. [3 Marks] c) Solve the matrices A and B, where [ ] [ ] [4 Marks] Page 1 EISB/FA2/DEC 20/GRADE X/Mathematics Question 2 a) The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window, At a certain instant, the angle of elevation of a balloon from these window are observed to be 60 respectively . Find the height of the balloon above the ground [4 Marks] b) There are 25 discs numbered 1 to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box. [3 Marks] Find the probability that the number on the dice is i) An odd number ii) Divisible by 2 and 3 both iii) A number less than 16. c) Using properties of proportion solve for x, given [3 Marks] Question 3 a) Prove that: [3 Marks] b) Simplify : [3 Marks] [ ] [ ] c) In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below : [4 Marks] Marks 1 2 3 4 5 6 7 8 9 10 No of 1 2 3 3 6 10 5 4 3 3 students Calculate the following for the given distribution: i) Median ii) Mode Page 2 EISB/FA2/DEC 20/GRADE X/Mathematics Question 4 a) Given [ i) ii) ] where M is a matrix and I is unit matrix of order 2 2 State the order of matrix M. Find the matrix M. [4 Marks] b) Find the value of x, if the mean of the following distribution is 18. Date 13 15 17 19 20+x Frequency 8 2 3 4 5x [3 Marks] 23 6 c) The diameter of a closed cylinder is 7 cm and its height is 16 cm, Find : i. The lateral surface area of the cylinder ii. The total surface area of the cylinder [3 Marks] iii. The volume of the cylinder [take = 3 ] Section B (Attempt any four) Question 5 a) In Game of COD Modern warfare, the ratio of number of Pro player to the number of Player was 3:31 before a battle. In the battle 6 Pro player and 22 player were killed, the ratio between the number of Pro player and the number of Player now is 1:13, find the number of Pro player and Player in the Game before the battle. [3 Marks] b) What least number must be added to each of the numbers 6,15,20 and 43 to make them proportion [3 Marks] c) Two people standing on the same side of the tower in a straight line with it, measure the angle of elevation of the top of the tower as 25 respectively. If the height is 70 m, find the distance between the two people. [4 Marks] [use these value where required tan 25 ] Page 3 EISB/FA2/DEC 20/GRADE X/Mathematics Question 6 [3 Marks] a) Prove that b) Two dice are thrown simultaneously, find the probability of: [3 Marks] i. Obtaining a total of at least 9. ii. Getting a multiple of 2 on one dice and multiple of 3 on the other dice iii. Getting the sum of 3 as the sum c) Marks obtained by 40 students in a short assessment is given below, where A and B are two missing data. [4 Marks] Marks 5 6 7 8 9 Number of students 6 A 16 13 B If the mean of the distribution is 7.2, find A and B. Question 7 a) If [3 Marks] b) Using step deviation method, calculate the mean marks of the following distribution. [3 Marks] Class interval 50 55 55 60 60 65 65 70 70 75 75 80 80 85 85 90 frequency 5 20 10 10 9 6 12 8 c) Evaluate [4 Marks] ( Page 4 ) ( ) ( ) EISB/FA2/DEC 20/GRADE X/Mathematics Question 8 a) A bag contains 5 white balls, 6 red balls and 9 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is [3 Marks] i. A green ball ii. A white or red ball iii. Neither a green nor a white ball b) When a metal cube is completely submerged in water contained in a cylindrical vessel with diameter 30 cm, the level of water rise by 1 cm. Find [3 Marks] i. The length of edge of the cube ii. Total surface area of the cube c) Given [ ] [ ] [ ] [4 Marks] Question 9 a) [use graph paper for this question] [6 Marks] Marks 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 No of student 5 9 16 22 26 18 11 6 4 3 Draw the ogive graph and hence, estimate: i) ii) iii) The median marks The number of students who did not pass the test if the pass percentage was 50. The upper quartile marks. b) A man observes the angle of elevation of the top of the tower to be 45 . He walks towards it in a horizontal line through its base. On covering 20m, the angle of elevation changes to 60 . Find the height of the tower correct to 2 significant figure [4 Marks] Page 5 EISB/FA2/DEC 20/GRADE X/Mathematics

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