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ICSE Class X Prelims 2021 : Mathematics (Clarence Public School (CPS), Bangalore)

5 pages, 31 questions, 3 questions with responses, 3 total responses,

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No of pages: 05 No. Of Questions-11 CLARENCE PUBLIC SCHOOL J. P. NAGAR, BENGALURU 78. SECOND PREPARATORY EXAMINATION MARCH -2021 Subject: MATHEMATICS Maximum Marks: 80 STD: X-ICSE Time: 2 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 allowed for writing the answers. _________________________________________________________________________ Attempt all questions from Section-A and any four questions from Section-B. All the 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 [ ]. __________________________________________________________________________ Section-A (40 Marks) (Attempt all questions) Question 1 [3+4+3] a)Solve and represent it on a number line x { } b) Find 16th term and sum of 20 terms of the given AP [7 , 11, 15, 19 ] c) The following numbers are arranged in descending order. 68, 60, 52, x-3, x-8, x-11, 30, 25 and 22. If their median is 39, find x and also find the mean. 1 Question 2 a) If (x [4+3+3] 1) and ( x + 5) are the factors of the polynomial Find a and b. ( b) Prove the identity ) c) Good are sold from Agra [UP] to Kanpur [UP] for Rs 30000 and then from Kanpur to Jaipur [Rajasthan]. If the rate of GST is 18% and the profit made in Kanpur is Rs 5000. Find (1) the net GST payable by the dealer in Kanpur. (2) The cost of the goods at Jaipur. Question 3 [4+3+3] a) Find the order and the matrix M, If M = [ ] b) Find the i) slope of the passing through A (-2, 3) and B (2 , 7). ii) The inclination of the line A iii) Find the equation of line AB c) In the given figure, (i) (ii) , BD is diameter of the circle. Calculate: (iii) Question 4 a) Solve the quadratic equation X2 4X places. [3+3+4] = 0 . Correct the answer to two decimal b) Find two numbers such that the mean proportional between them is 14 and third proportional between them is 112. 2 c) Find the mode of the following data, by drawing Histogram Class interval 10-14 15-19 20-24 25-29 30-34 35-39 frequency 10 17 12 10 8 15 SECTION B (40 Marks) [Answer any 4 questions] Question 5 [3+3+4] a) From a set of playing cards, a card is drawn at random. Find the probability of i) picking a red face card ii) a black or a diamond card ii) a number card b) Manu deposits Rs 2000 per month in a recurring deposit scheme for one and an half year. He gets Rs 38280 at the time of maturity. Find the rate of interest charged? c) Use graph paper, Plot the point A(2,3), Reflect it on X axis as B. Reflect B on origin and name it as C. Reflect A on origin and name it as D. Mark a point E(0,6). Name the figure ABDCE. Question 6 [4+3+3] a) Find the value of p , if the mean of the following distribution is 54 Class 0 20 20 40 40 60 60 80 80--100 Frequency 7 P 10 9 13 b) A solid cylinder of height 16cm and radius 12cm is melted and re-casted in to cones of height 4cm and radius 3cm. How many such cones can be made? c) Find the amount of bill for the following intra-state transaction if GST is 18% Article MRP in Rs Dis% A 5800 20% B 7500 30% C 6000 15% 3 Question 7 a) A = [ [3+3+4] ] and B = [ ] C =[ ] Find matrix X such that A + 2X = 2B + C b) In the given figure, O is the centre of the circle. Tangents at A and B meet at C. if , find (i) (ii) (iii) c) In a two digit number, the tens digit number is bigger. The product of the digits is 27 and the difference of two digits is 6.Find the number. Question 8 [3+3+4] ( a) Find the sum of this AP ( ( b) Find in what ratio the join of (4,3) and (2, ( divided by the X axis. Also find the point of intersection. c) Using factor theorem, Factorize completely 3X3 + 10X2 +X - 6 Question 9 [3+3+4] a) Prove the identity ( b) Given that ) ( ) ( ) using the properties of proportion, find m:n 4 c) In triangle ABC A = 90 . AP is drawn perpendicular to BC. Prove that AB2 = BP x BC. If BP=4cm and PC = 5cm, find the length of AB Question 10 [6+4] Attempt this question on graph. Wages of 160 workers are given Wages 0 10 frequency 12 10 20 20 30 30 40 40 50 50 60 60 70 70 80 20 30 38 24 16 12 8 Calculate a) median wage b) upper and lower quartile c) No of people who gets more than Rs 60 as their daily wage b) AB is a tower and two objects C and D are located on the ground, on the same side of the tower AB. When observed from top A of the tower, their angles depressions are 45 and 60. Find the distance between the objects, if height of the tower is 300m.(correct it to the nearest meter) Question 11 [3+4 +3] a) Find the maturity value of a recurring deposit, if a man deposits Rs 5000 per month for 2 years at 12% per annum interest . b) Given A = { x: 5 < 2x 1 11, X (i) Represent A and B on number lines and B = { x: --1 3 + 4x < 23, X R} I} (ii) Write down elements of A c) Find the value of P for which the following quadratic equation has real and equal roots (p 3)x2 4x + 1 = 0 5

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