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ICSE Class X Prelims 2021 : Mathematics (Sri Aurobindo International School, Hyderabad)

6 pages, 30 questions, 3 questions with responses, 3 total responses,

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MATHEMATICS (Two and half hours) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the Question Paper. The time given at the head of this Paper is the time allotted for writing the answers. Attempt all questions from SectionA and any four 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(40 marks) Attempt all questions from this Section Question 1 A) Sandeep started a recurring deposit by paying some amount per month in a bank.It amounts to 1,31,184 at the end of 3 years.The rate of interest offered by the bank is 9% per year.What is the amount deposited by Sandeep in every month? [3M] B) Find the value of k so that 8k+4,6k-2 and 2k+7 will form an A.P [3M] C) Solve the inequation 2y 3 y+2 < 3y+5. Graph the solution on the number line if a)y R,b)y Z, c) y N [4M] Question 2: A) B) For what value of m, the roots of the equation (3m+1)x2 +(11+ m)x +9=0 are equal. [3M] (x+2) is a factor of 2x3 +9x2 +7x-6.Using Reminder or Factor theorem find other factors. [3M] 1 + C) If 7 = ,Use the properties of proportion, to find the value of 4 [4M] + Question 3: A) Find the amount of bill for the following intra state transaction of goods.The rate of GSTis 12% [3M] Goods Chocolate Doll Wall hangins Fancy Items 200 150 300 MRP 250 30 D% B) If A = 40 4 2 0 = 6 3 1 32 20 2 2 C= 1 1 3 1 Find the sum of Transpose of Matrix A, additive inverse of C and two times of matrix B [3M] C) Use Graph sheet to answer the following: [4M] 1.Plot the triangle whose points of the vertices A(5,4) B(7,5) C(-3,6) on a graph paper. 2.Draw the image of TriangleABC under reflection in the lineY=3and name and mark the coordinates as A ,B ,C respectively. Mark any two points invariant under this reflection. 3.Reflect A ,B ,C through origin and mention the points as A ,B ,C . Question 4: A) Find the Mean,Median and Mode of the following: [3M] 10,75,3,71,18,27,4,48,12,12,47,9,15 B)A dice has 8 face smarked by the given numbers as shown below: 3 -2 -1 0 -4 1 2 -3 3 3 2 The dice is thrown once. What is the probability of, C) i) ii) Getting an integer greater than -2 A positive integer iii) The smallest integer [3M] The time taken by the person to cover 150 Km. was 2.5 hours more than the time taken in return journey. If he returned at a speed of 10Km/h more than speed of going, what was the speed per hour in each direction? [4M] SECTION-II Answer any Four questions Question 5: A) Mrs.Bajaj has recurring deposit in a bank. She deposits Rs.900 per month for a period of 4 years. If she gets Rs.52,020 at the time of maturity, find the rate of interest. [3M] B) Goods and services are sold from Kota(Rajasthan) to Mumbai for Rs.20,000 then from Mumbai to Pune .If the rate of GST is 12% and profit made at Mumbai is Rs.5000.Find the net GST paid at Pune,if the dealer at Pune is end user. [3M] C) If a,b,c,d are in proportion show that (a-c) b2: (b-d)cd=(a2-b2-ab) : ( c2- d2- cd) [4M] Question 6: A) Solve the following equation and give your answer upto two decimal point. 2x2+11x+4=0 [3M] B) Solve the in equation; 2 + 2 1 4 2 5 3 4 +2x ; Where x 3 [3M] C) The sum of 30 terms of a series in A.P is 1635.Its last term is 98.Find the first term and common difference. Also find the sum of first 100 terms. [4M] Question 7: A) Answer the following using graph sheet i)The Point P(5,14) and Q(2,-1) is reflected along y axis as P and Q respectively. Mention the coordinates of P and Q ii)Join the points of P,Q,Q ,P . Name the quadrilateral formed. iii) Find the area of the quadrilateral from the figure. Let A = B) 1 5 2 0 2 2 = C= 3 3 1 1 [3M] 4 1 Find A2- A + BC [3M] The polynomials 2x3-7x2+ax-6 and x3-8x2+(2a+1)x-16 leave same reminder when divided by (x-2) .Find the value of a.[4M] C) Question 8: A) The age of 40 students are given below; Age in Years Frequency 12 13 14 15 16 17 18 2 4 6 9 8 7 4 Find the arithmetic mean. [3M] B) Two dice are thrown at once. Find the probability that sum of the two numbers appear on the top of the dice is i) 8 , ii)13 , iii)less than equal to 12 [3M] C) In a two digit number the ten s digit is bigger. The product of the number is 27 and the difference between two digit is 6.Find the number.[4M] 4 Question 9: A) From the following data draw the o give. Find the Median, Lower quartile ,upper quartile and also the students who secured more than 49 marks. Marks Frequency B) 0-10 5 10-20 20-30 30-40 40-50 50-60 60-70 70-80 25 40 70 90 40 20 10 [6M] 80 coins are placed in straight line on the ground. The distance between any two consecutive coin is 10meters.How far must a person travel to bring one by one to a basket placed 10m behind the first coin.[4M] . 10m 10m 10m 10m Question 10: A) Manish opened an R.D. Account with a bank and deposits Rs.600 per month for 20 months. Calculate the maturity value if the interest paid by the bank is 10% per annum. [3M] B) Find the value of x given that A2 = B A= C) 2 0 4 12 = 1 0 [3M] 1 A bag contains 100 identical cards numbered from 1 to 100. If one card is taken at random from bag, find the probability that it bears [4M] i) perfect square number ii) a number divisible by 5 iii ) a number factor of 20 5 Question 11: A ) Find Mode from following Calculations [3M] Age 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 No.of 50 70 100 180 150 120 70 59 persons B )What should be subtracted from 3x3-8x2+4x-3 so that the resulting expression has (x+2) as a factor [3M] C ) Solve the equation; 4 +2 1 +3 = 4 2 +1 6 [4M]

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