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Oxford International School (ICSE) Preliminary Examination- I (2020 2021) Sub.: Mathematics Marks: 80 Time: 2 hrs 30 min Date:13/01/2021 --------------------------------------------------------------------------------------------------------Section A (40 Marks) (All questions are compulsory) Question 1: a) A = 7 3 4 and B = . Is A X B possible? Give reason. If so, find the product. 5 6 8 (3) b) Solve the following in equation and represent the solution set on the number line: 4x 19 < -2 + x, x R. ( Graph paper not required) c) In the figure, DBC = 58 . BD is a diameter of the circle. Calculate: i) ) ) iv) BCD (3) (4) Question 2: a) Find the value of x: = (3) b) Using the Remainder Theorem, factorize each of the following completely: 4 + 7 36x 63 (3) c) In the given figure AX : XB = 3 : 5 (4) Find: i) the length of BC, if length of XY is 18 cm. ii) ratio between the areas of trapezium XBCY and triangle ABC. Question 3: a) The line segment joining the points (5, -4) and (2, 2) is divided by the point Q in the ratio of 1 : 2. Does the line x 2y = 0 contain Q? (3) b) The marks of 20 students in a test were as follows: 2, 6, 8, 9, 10, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, and 20. Calculate (3) i) the mean ii) the median iii) mode c) A box contains 180 bulbs out of which 25% bulbs are defective. It is not possible to just look at a bulb and tell whether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is: (4) i) A good one ii) A defective one. Question 4: a) Calculated the mean of the distribution by Step deviation method. Marks 11-20 21-30 31-40 41-50 51-60 61-70 obtained No. of 4 7 9 12 9 6 students b) Prove the identity: (sin + cos ) (tan +cot ) = sec + cosec . c) Solve: + (3) 71-80 3 = (3) (4) Section B (40 Marks) (Attempt only 4 questions out of 7 questions) Question 5: a) An architect charges Rs.34000/- for his services to his client. If GST is 18%, what is the total amount to be paid by his client? b) Rs.6500/- were divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs.30 less. Find the original number of persons. c) At a particular time, when the sun s altitude is 30 , the length of the shadow of a vertical tower is 45 m. Calculate: i) Height of the tower ii) The length of shadow of the same tower, when the sun s altitude is 60 . (3) (3) (4) Question 6: a) The angles of a triangle form an arithmetic progression. If the largest angle is twice the least, find all the angles of the triangle. b) Jayesh opens a recurring deposit account in a bank of Rs.450/- per month. How many installments does he have to pay to get a maturity of Rs.8613 if the bank pays a simple interest of 8% p.a. (3) (3) c) A cone of height 20 cm and radius 6 cm is cut through the midpoint of vertical axis. Find the volume of the conical part. (4) Question 7: a) Two poles 20 m and 80 m high are 100 m apart. Find the height of the intersection of the lines joining the top of each pole to the base of opposite pole. b) The following table gives daily wages of some employees in a firm. Find the missing frequency p if the mean is Rs.78. (3) Daily wages (in Rs.) 50-60 60-70 70-80 80-90 90-100 100-110 No. of employees 1 8 10 p 4 2 c) Plot P(2, 4), Q(-2, 1) and R(5, 0). Reflect points P and Q in x-axis to get P and Q . i) Write their co-ordinates. ii) Give a geometrical name to the figure formed by joining the points PQQ P R. Find its area and perimeter. iii) Name its axis of symmetry and write its equation. iv) Name two points from the figure which are invariant on reflection in x- axis. (4) Question 8: 1 3 5 = , find the values of x and y. 8 2 1 b) Find the sum of all odd numbers between 100 and 400. c) A manufacturer sells binoculars for Rs.3750/- to a wholesaler, who sells it to a retailer at a profit of 12%. The retailer sells it to the customer at 15% profit. If the rate of GST is 18%, find the i) GST paid by the wholesaler to the Government. ii) Price paid by the retailer inclusive of tax. iii) Total GST received by the Government. iv) Price paid by the customer. a) Given (3) (3) (4) Question 9: a) In a two digit number, the unit s digit exceeds its ten s digit by 1, and the product of the given number and its ten s digit is 280. Find the number. (3) b) Solve the following inequation, write the solution set and represent it on the number line: -1 < (3) , x R. ( c) Prove that: )( ) = sec A (4) Question 10: a) TP and TR are tangents to the circle with centre O. If POQ = 150 and PTR = 50 . (3) Calculate: i) TPR ii) QPR b) If a : b = c : d, then prove that: = (3) c) Mr Krunal opened a recurring deposit account in a bank. He deposited Rs.2500/per month for two years. At the same time of maturity he got Rs.67500/-. Find i) The total interest earned by Mr Krunal. ii) The rate of interest per annum. (4) Question 11: a) In the adjoining figure, P(-4, 3) divides AB in the ratio 3 : 2. Find the co ordinates of A and B. (4) b) The following table shows the daily expenditure on food of 100 families in a colony, Daily Expenditure (in Rs.) No. of families 100150 150200 200250 250300 300350 350400 400450 450500 3 8 14 20 22 18 12 3 Draw an Ogive for the given distribution on a graph sheet. Use a scale of 2 cm = Rs.50 on one axis and 2 cm = 10 families on the other. Use the ogive to estimate the: i) Median ii) The upper quartile iii) The number of families who spend less than Rs.175 iv) The number of families who spend more than Rs.425. Note: e-mail id: For 10th A: 10a.mathprelim1papers@gmail.com For 10th C: 10c.mathprelim1papers@gmail.com (6)
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