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ICSE Class X Prelims 2021 : Mathematics

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MOUNT CARMEL SCHOOL PREBOARD EXAMINATION 2020-2021 MATHEMATICS CLASS- X TIME -2 1/2HRS MARKS : 80 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 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 brackets [ 1 Mathematical tables are provided. QI a) Section A (40 Marks) Attempt all questions from this Section. is 52? Which term of the A.P. 1+4+7 + 10 + (3) b) Solve the matrix equation : (3) 7 4 2 c) 6 (4) Prove that : sinA cosA = cosA + sinA 1 tanA I cotA Q2 a) 5, find x. If (4x + 4) : (9x 10) is the triplicate ratio of4 : (3) 1 b) Solve the following Inequation and write the solution (3) set. 12 c) 3x,xtR. 6 Represent the solution on a real number line. i) Write down the co-ordinates of the point P that in the divides the joining A(-4,1) and ratio 1:21 ii) iii) Q3 (4) Calculate the distance OP where O is the origin. In what ratio does the y-axis divide the line AB? a) Without solving the given quadratic equation, find b) The capacity and the base area of a right conical vessel are 9856cm 3and 616cm 2respectively. Find the curved surface area of the vessel. (3) c) Mr. Johnson saves Rs. 80 every month and puts in a recurring deposit paying 8% S.l. per annum. In order to receive a maturity amount of Rss 5,776, how many (4) monthly instalments must he deposit? the value of 'k' so that the equation x2- 4x + k = 0 has (3) equal roots. Solve the following equation by using formula: (3) 1 2 Give your answer correct to 2 decimal place. b) Two vertices of a triangle are (-1, 4) and (5, 2). If the co-ordinates of the centroid of the triangle are (O,3), find the co-ordinates of the third vertex (3) (4) Use graph paper for this question. c) The points A(l, 2), B(4, 8) and C(6, 8) are the vertices of AABC. i) Write down the co-ordinates of A', B' and C' if A A'B'C' is the image of A ABC, when reflected in the x-axis. ii) Write down the co-ordinates of A", B" and C" if A A" B"C" is the image of A A' BIC%when refleced in the origin. Mention the special name of the quardrilateral ABB'At and find its area. Section - B (10 Marks) Q5 a) Solve the following equation and give your answer correct to 2 decimal places: (3) 2X2 + $ X-5=0 b) When 00< 0 < 900, slove the following equation: cos0 cos0 I sine 1+sin0 c) 4 (3) The daily profits (in Rs.) of 100 shops in a market are distributed are follows: (4) Profit per 0-100 00-200 00-300 00-400 00-500 500-600 shop (in Rs.) No. of shops 12 18 27 20 17 6 Draw a histogram of the data given above, on graph paper, and estimate the mode. P(3, 4), Q(7, -2) and R(-2, -1) are the vertices of a triangle PQR. Write down the equation of the median of the triangle through R. (3) b) A dice is thrown once. What is the probability of getting a number (3) i) greater than 2 ? less than or equal to 2 ? The horizontal distance between two towers is 140m. c) The angle of elevation of the top of the first tower, when seen from the top of the second tower is 300. If the height of the second tower is 60m, find the height of the first tower correct to two decimal places. (4) Q7 Find the equation of the perpendicular bisector of a) the line segment obtained on joining the points (3) (6, -3) and (0, 3). b) In the adjoining figure AB is parallel to DC, LBCE=80 0 (3) and ZBAC=25 0. Find (i) ZCAD (ii) ZCBD (iii) ZADC c) c The marks obtained by 40 students in a short assesmentare given below, where a and b are two missing data Q8 Marks 5 6 7 8 9 No. of student 6 a 16 13 b a) If the mean of the distribution is 7.2, find a and b. If (2x+1) is a factor of both the expression 2x2-5x+p and 2x2+5x+q, find the value of p and q. b) The adjoiningfigure reprsents a conical block of wood. The diameter of their of bases is 6cm each and the slant height of the cone is 5cm. Calculate: (3) (i) the height of the cone (ii) the volume of the solid (Take 7t=3.14) 4 c) If two coins are tossed once, find the probability of (4) getting ii) at least one head i) 2 heads iii) both heads or both tails Q9 a) Using the properties of proportion, solve for x, given 17 2 (3) 8 2 b) Given A x 1 andB 2 1 4 o -1 (3) find x if AB = BA. c) A shopkeeper buys x articles for a total of Rs. 600. i) Write down the cost of one article in terms of x. If the cost per article was 5 more, the number of articles that can be bought for Rs. 600 would be 4 less. Write down the equation in x for the above situation and solve if for x. Q10 a) Find the amount of bill for the following intra-state transaction of goods/services. The rate of GST being 12%. b) MPR (in Rs.) 600 450 900 750 Discount % 40 32 20 30 (3) A bag contains 14 balls out of which x are white. (3) i) If one ball is drawn at random, what is the probability that it will be a white ball? If 6 more white balls are added to the bag, the probability of drawing a white ball is h. Find the value of value of x. 5 c) QII a) Show that (2x + 5) is a factor of 2x3+ 3x2- 9x - 10. Hence, factorise the expression 2x3+ 3x2 - 9x - 10 (4) completely, using the Factor Theorem. In the given figure, ABC is a triangle. DE is parellel to AD 3 DB 2 BC and (4) Determine the ratio i) AE EC Prove that A DEF is similar to A CBF. Hence, find What is the ratio of the area of DEF and CBF? iii) B b) Marks Use graph paper for this question. The marks obtained by 200 students in an examination are given (6) below: -10 0-20 0-30 0-40 0-50 0-60 0-70 0-80 0-90 0-100 54 No. of students 11 10 20 28 37 40 29 Draw an ogive for the given distribution taking 2cm=10marks on one axis and 2cm=20 student on the the other axis. Using the graph, determine following: 6 i) the median marks. the number of students who failed if minimum marks required to pass is 40. If scoring 85 and more marks in considered an grade one, find the number of students who secured grade one in the examination.

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