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P1 ST. FRANCIS SCHOOL (ICSE), MT. POINSUR, BORIVALI (W), MUMBAI st Sub: MATHEMATICS 1 PRELIMINARY EXAMINATION 2020-21 Marks: 80 10 Class: X Time: 2 hrs Date: 11/02/2021 _____________________________________________________________________________________________________ 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 the loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. _____________________________________________________________________________________________________ SECTION A (40 marks) (Answer all questions from this section) Question 1 (a) Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets 1200 as interest at the time of maturity, find: (i) the monthly installment, (ii) the amount at the time of maturity [3] (b) Solve the following equation and give your answer correct to 2 decimal places. 5 x2 3 x 4 = 0 (c) Prove that: (1 + cot A cosec A) (1 + tan A + sec A) = 2 [3] [4] Question 2 (a) In the given figure, P ( 4, 3) divides AB in the ratio 3:2. Find the coordinates of A and B. Y [3] B P (-4, 3) X A O (b) In the given circle, diameter AB chord DC and ABC = 52 . Find BAC and AED. A E [3] D O C 52 B (c) Solve the following inequations and represent the solution set on the number line. 8 x 7 2 (2 x) , x W [4] Question 3 (a) A shopkeeper sells some edible oil for 7,200 at its MP. The shopkeeper pays GST of 120 to the Government. If the GST charged throughout is 5%, calculate the price paid by the shopkeeper for the oil inclusive of tax. [3] 4 cos 60 2 sin 30 2 cos 0 sin 90 (b) Evaluate: 5 6 6 5 [3] (c) In the given figure, AD BC and ABC = 90 = DCA , AB = 12 cm and BC = 16 cm. Find (i) CD and (ii) AD A 12 cm D B P1 Std 10 Mathematics 2020-21 16 cm C Page 1 of 13 [4] Question 4 (a) Find the number of terms in the A.P. given below: 18, 15 1 , 13 . ( 47) 2 [3] (b) If the mean of the following distribution is 15.5, find the value of p. Class Interval Frequency 0 5 2 5 10 7 10 15 18 15 20 10 [3] 20 25 p 25 30 5 (c) Water flows through a cylindrical pipe of internal diameter 7 cm at 5 m/s. Calculate: [4] (i) the volume, in litres of water discharged by the pipe in 1 minute. (ii) the time, in minutes the pipe would take to fill an empty rectangular tank 4 m by 3 m by 2.31 m SECTION B (40 marks) (Answer any four questions from this section) Question 5 (a) What should be subtracted from the polynomial 2 x3 + 5 x2 11 x 10 so that (2 x + 7) is a factor? [3] (b) AB is a diameter of the circle with centre O. BT is a tangent. AC produced meets tangent BT at T. If ABC = 38 , find T. [3] (c) The following table gives the expenditure of boys on sports equipments. Draw a histogram and estimate the mode. Expenditure ( ) No. of Students 200 250 6 250 300 9 300 350 17 350 400 15 400 450 6 [4] 450 500 3 Question 6 (a) Prove that: cot A cot A 2 sec A cos ec A 1 cos ec A 1 [3] (b) Plot ABC when A (3, 2), B (7, 5) and C (5, 0). Reflect ABC in the line x = 2 as A B C . Write the coordinates of A , B and C . What figure is formed by joining AA C C? [3] (c) Given M = 4 [4] 1 . Find k if, M2 6 M + k I = Null Matrix, where I is an identity matrix 1 2 of order 2 2. Question 7 (a) If a, b and c are in continued proportion, prove that 3 a 2 4 a b 5 b2 a 3 b2 4 b c 5 c2 c [3] (b) A (2, 3) and B ( 2, 5) are two given points. Find : (i) The gradient of AB (ii) The equation of AB (iii) The coordinates of the point, where AB intersects x-axis [3] (c) A piece of cloth costs 75. If the length of the cloth had been 2 m longer and each metre costs 10 less, the cost would have remained same. How long is the piece? [4] P1 Std 10 Mathematics 2020-21 Page 2 of 13 Question 8 (a) From a boat 300 metres away from a vertical cliff, the angles of elevation of the top and foot of a concrete pillar at the edge of the cliff are 55 40 and 54 20 respectively. Find the height of the pillar correct to the nearest metre. [4] (b) Use graph paper for this question. The table below shows the distribution of the monthly earnings of 120 workers in a building site. [6] Daily Earning ( ) No. of Workers 15 20 10 20 25 15 25 30 20 30 35 25 35 40 18 40 45 13 45 50 12 50 55 7 Taking a scale of 2 cm = 5 and 2 cm = 20 workers, draw an ogive and estimate: (i) the median (ii) the upper quartile (iii) the number of workers earning more than 47 Question 9 (a) ABCD is a cyclic quadrilateral, ADC = 80 and ACD = 52 . Find the value of ABC and CBD. D C 80 A [3] 52 52 B (b) Find the sum of all multiples of 7 lying between 500 and 800. [3] (c) A shopkeeper buys a printer at a discount of 30% on the marked price of 8,000. He sells the printer to a customer at marked price. GST charged at each stage is 18%. If the sales are intra-state, find: (i) the CGST and SGST paid by the shopkeeper. (ii) the price paid by the shopkeeper for the article inclusive of tax. (iii) the cost to the customer inclusive of tax. [4] Question 10 (a) The three vertices of a parallelogram ABCD, taken in order are A (3, 1), B (5, 6) and C (7, 3). Find the coordinates of the fourth vertex. (b) The total surface area of a right circular cone of slant height 13 cm is 90 cm2. Calculate : (i) its radius in cm (ii) its volume in cm3 in terms of (c) Shivangi deposits 500 every month in a recurring deposit scheme and receives 16,550 at the end of 2 years. Calculate the rate of interest given by the bank. Question 11 (a) Using the Remainder theorem, factorise the following polynomial: x3 + x2 4x 4 [3] [3] [4] [3] (b) In the given figure, ABCD is a trapezium in which AB DC and AB = 2 DC. Determine the ratio of the areas of AOB and COD. D [3] C O A B (c) There are 12 cards numbered 1 to 12. What is the probability that a card picked up randomly has: (i) a prime number [4] (ii) a number between 3 and 11 (iii) a perfect square (iv) a perfect cube ******************************** P1 Std 10 Mathematics 2020-21 Page 3 of 13 P1 Std 10 Mathematics 2020-21 Page 4 of 13 P1 Std 10 Mathematics 2020-21 Page 5 of 13 P1 Std 10 Mathematics 2020-21 Page 6 of 13 P1 Std 10 Mathematics 2020-21 Page 7 of 13 P1 Std 10 Mathematics 2020-21 Page 8 of 13 P1 Std 10 Mathematics 2020-21 Page 9 of 13 P1 Std 10 Mathematics 2020-21 Page 10 of 13 P1 Std 10 Mathematics 2020-21 Page 11 of 13 P1 Std 10 Mathematics 2020-21 Page 12 of 13 P1 Std 10 Mathematics 2020-21 Page 13 of 13
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