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ICSE Class X Sample / Model Paper 2020 : Mathematics

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Summer Mock MATHEMATICS Grade: 10 Max. Marks: 80 Date: 03.08. 2020 Duration: hours 1. Answer all questions from Section A and any four questions from Section B. 2. All working, including rough work, should be done on the same sheet and adjacent to the answer 3. The intended marks for questions or parts of questions are given in brackets[ ] 4. The time stated above is the time allowed for writing the examination In addition, the first 15 minutes will be the time given for reading the question paper. Section A (40marks) Answer all the questions from this section Question 1 [3 + 3 + 4] a) Find the values of x and y if [ 3 2 5 ][ ]=[ ] 4 1 12 b) A man has a recurring deposit account in a post office for 3 years at 12 % p.a. simple interest. If he gets 10206 at the time of maturity, find the value of his monthly instalments. c) Hundred identical cards are numbered from 1 to 100. The cards are shuffled well and then a card is drawn. Find the probability that the number on the card is i. ii. iii. iv. A multiple of 5 A multiple of 6 The number on the card is between 40 and 60 The number on the card is less than 48 Page 1 of 6 Question 2 [3 + 3 + 4] a) How many cubic meters of earth must-be dug out to make a well 28 m deep and 2.8 m in diameter? Also, find the cost of plastering its inner surface at 4.50 per square meter. b) Meena has a cumulative deposit account of 400 per month at 10% per annum simple interest. If she gets 30100 at the time of maturity, find the total time for which the account was held. c) The mean of the following distribution is 52 and the frequency of the class interval 30 40 is f. Find f. ClassIntervals Frequency 10 - 20 20 - 30 30 - 40 40 50 50 - 60 60 - 70 70 - 80 5 3 f 7 2 6 13 Question 3 [3 + 3 + 4] a) If (x 2) is a factor of the expression 2x3 + ax2 + bx 14 and when the expression is divided by (x 3), it leaves a remainder of 52, find the values of a and b . +4 b) Given that: x Z, solve the inequation: 3 + 2, also graph it on a 2 3 number line. c) Find the mean by step deviation method: Class 63 - 70 Interval Frequency 9 70 - 77 77 - 84 84 - 91 91 - 98 13 27 38 32 Question 4 98 - 105 105 - 112 16 15 [3 + 3 + 4] a) Given: A = {x : - 8 < 5x + 2 17, x I}, B = {x: - 2 7 + 3x <17, x R} where R = {real numbers} and I = {integers}. Represent A and B on two different number lines. Write down the elements of A B. Page 2 of 6 b) ABC is a right-angled triangle with = 90. S is a point on PQ and ST is perpendicular to PR, Prove that :i) ii) iii) PST~ PRQ If PR = 13 cm, QR = 5 cm and PT = 4 cm, find ST and PS. Find Area ( PST) : Area(quad. QRTS) c) Solve the quadratic equation x2 3(x + 3) = 0; Give your answer correct to two significant figures. SECTION B (40 Marks) Attempt any four questions: Question 5 a) If [ [3 + 3 + 4] 4 2 4 3 3 ] [ ] + 2[ ] = 5 [ ] 6 2 2 4 find the values of x and y. b) In the diagram given below if AF = 21 cm, CE = 30 cm and FB = 7 cm. Find the volume of the figure. C 21 cm 30 cm F E 0 7 cm c) Attempt this question on graph paper. Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes. Reflect A and B in the x-axis to A' and B' respectively. Plot these points also on the same graph paper. Write down: (i) The geometrical name of the figure ABB'A' (ii) The measure of angle ABB' (iii) The image of A'' of A, when A is reflected in the origin. (iv) The single transformation that maps A' to A''. Page 3 of 6 Question 6 [3 + 3 + 4] a) Using properties of proportion, find the value of x: 3 + 3 3 2 +1 2 b) If A = [ 0 = 341 91 1 4 1 3 2 ], B = [ ], C = [ ] find A2 + AC 5B 2 3 2 1 4 c) In ABC, DE BC. Find EC and AD in the given figure. Question 7 a) If x = -3 and x = [3 + 3 + 4] 2 3 are the solutions of the quadratic equation mx2 + 7x + n = 0, find the values of m and n. b) Calculate the arithmetic mean, correct to one decimal place, for the following frequency distribution. Marks 20-30 30-40 40-50 50-60 60-70 No of students 7 20 18 12 3 c) In the diagram, QPR RPS. Use the given side lengths to find the length of RS. Question 8 [3 + 3 + 4] a) The following observations have been arranged in ascending order. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 If the median of the data is 63, find the value of x. Page 4 of 6 b) Solve for x using the properties of proportion: 3 + 9 2 5 =5 3 9 2 5 c) An aeroplane travelled a distance of 400 Km at an average speed of x km/hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for: i. The onward journey ii. The return journey If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value. Question 9 [3 + 3 + 4] a) A recurring deposit account of 1200 per month has a maturity value of 12440. If the rate of interest is 8% and the interest is calculated at the end of every month; find the time (in months) of this Recurring Deposit Account. b) In the given figure, D is a point on BC such that BAD = ACD, AB = 7 cm and BD = 4 cm. i. Prove that ABD ~ CBA, ii. Also find, area ABC : area ADC c) A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which is exactly coincides with the hemisphere is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 10 cm. how much water in cm 3, will be required to fill the vessel completely. Question 10 [3 + 3 + 4] a) If (x + 1) and (x 2) are the factors of x3 + (a + 1) x2 (b 2)x 6, find the values of a and b. then factorise the expression completely. Page 5 of 6 b) If a bag contains 12 balls out of which x are black. i. If a ball is drawn at random, what is the probability that it will be a black ball? ii. If 6 more black balls are put in the bag, the probability of drawing a black ball will be double than that of (i), find the value of x. c) Using a graph paper draw a histogram for the given distribution showing the number of runs scored by 50 batsmen. Estimate the mode of the data: Runs scored No of batsmen 30004000 4 40005000 18 50006000 9 60007000 6 70008000 7 80009000 2 900010000 4 Question 11 [4 + 6] a) The following figure shows a PQR in which XY // QR. If PX : XQ = 1 : 3 and QR = 9 cm, find the length of XY. b) The monthly income of a group of 320 employees in a company is given below: Monthly income(in thousands) No. of employee 6-7 7-8 8-9 9 - 10 20 45 65 95 10 - 11 11 - 12 60 30 12 -13 5 Draw an ogive of the distribution on a graph paper taking 2 cm = 1000 on one axis and 2 cm = 50 employee on the other axis. From the graph determine: i. The median wage ii. Number of employee whose income is below 8500 iii. If salary of a senior employee is above 11500 find the number of senior employee in the company. iv. The upper quartile. ***************************************************************************************** Page 6 of 6

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