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ICSE Prelims 2017 : Mathematics

3 pages, 34 questions, 19 questions with responses, 43 total responses,

Shikhar Agarwal
Presidency School, Bhiwandi

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10th I.C.S.E. Kewal Sir & Dhaval Sir Rudra s Academy Mathematics Preliminary Exam [Time: 2.5 hrs] [Marks: 80] [Set - 3] Section I All Questions are Compulsory Q.1) a] Show that 2 x 3 is a factor of 2 x3 19 x2 38x 21 .Hence factorise 2 x3 19 x2 38x 21 b] Two isosceles triangles have equal vertical angles and their areas are in the ratio 16:25. Find the ratio of their corresponding heights. c] Following toy is made by joining the three solid parts, a cone, a cylinder and a hemisphere. Mr. Pranit initially completely painted all three parts individually and then joined them as shown in the figure. If the cost of painting is Rs 19/- per sq.mm then how much could he save by first joining and then painting. [3] [3] [4] Q.2) a] In circle with center O, find x. [3] b] Mr. Vansh owns a tractor whose diameter of a fore wheel is 1.26 m, and diameter of the rare wheel is double the diameter of fore wheel. How far he would travels in 500 revolutions of rear wheel? How many revolutions are made by fore wheel during the journey? c] A x : 7 x 3 18x 51, x I and B x : 25 2 x 8x 19, x R . Find the range set A B & A B and represent it on a number line. Q.3) a] Mrs. Krishna has an account with The Bank of India. The following entries are from her pas book: Withdrawals Deposits Balance Date Particulars Rs P Rs P Rs P 08.02.06 B/F 8500.00 11.02.06 NEFT 6000.00 -------18.02.06 To Self 14000.00 -------12.04.06 By Online 2638.00 -------19.05.06 To LIC 941.00 -------31.05.06 LIC Maturity 11247.50 -------15.06.06 To Self 5000.00 -------08.08.06 By Cash 6000.00 -------Complete the above page of her pass book and calculate the interest for the six months, from February 2006 at 4.5%p.a. b] Socks of Mr. Darshil are observed from two points A and B 120 m apart on the either side of the tree. The sine of the angle of elevation from points A and B are 0.707 and 0.5 respectively. Find the height at which his socks are hanging. c] Find the co-ordinate of circumcenter of a triangle with vertices ( 2, 0), (2, 0) and (0, 2 3 ). ****Best of Luck**** Kewal Sir & Dhaval Sir [3] [4] [3] [3] [4] Page 1 10th I.C.S.E. Kewal Sir & Dhaval Sir Rudra s Academy Mathematics Preliminary Exam [Time: 2.5 hrs] [Marks: 80] [Set - 3] Q.4) a] Prove that: sec 1 sin sec tan 1 b] A box contains cards with numbers 10 to 1000. What is the probability that a number selected at random by Ms. Shreya has exactly one of the digit as 3. 5 0 1 2 2 2 and B c] Verify whether, A B A B A B where, A . 3 1 0 5 [3] [3] [4] Section II Attempt Any Four Questions Q.5) Q.6) Q.7) Q.8) 2 3 Find the values of x and y , if A and A2 I . x y b] Mr. Raj computed mean of 23 numbers as 17. Later on he found that he considered three wrong numbers as 10, 19 and 135. So, he immediately changed those numbers with the correct one. Finally he got the correct mean as 16. Find the mean of the three correct numbers which were initially missed. c] Mr. Kundan invests a sum of money in Rs 999 shares, paying 1.11 % dividend quoted at 20% premium. If his annual dividend is Rs 32190, calculate: i) His total investment ii) The rate of return on his investment. a] The equations 2 x2 kx 19 0 and 6 x2 36 x 57 0 have common roots. Find the product of the factors of k . b] Solve the inequation and represent the solution set on the number line. 2x 125 9 7 x 32 2 x, where x N . 3 3 c] Identify the type of quadrilateral form by joining the points A(1, 3), B(2, 6), C(5, 7), D(4, 4). Also draw its reflection about the origin and common line of symmetry, if any. [3] [3] [4] a] a] Prove that: sec4 sec2 tan 4 tan 2 b] Draw a quadrilateral whose vertices are equidistance from pair of adjacent sides of a quadrilateral with vertices A(15, 5), B(45, 5), C(10, 25), D(40, 25). c] A two digit natural number is such that the sum of its digit is 10. Sum of square of the digits is less than 78. Find the sum of all the numbers satisfying given condition. 2a 1 2 a 1 2a 1 2 a 1 b] The following table gives the weekly wages of workers in a factory owned by Mrs. Vidya: Weekly wages (in Rs.) 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 No. of workers 5 2 11 10 9 16 12 8 Calculate: Q3, P25, D5, P75. c] Mr. Shikhar borrows Rs.19250 at 10% p.a., compounded annually. If he repays Rs.1125 at the end of first year and Rs.12550 at the end of second year, find the amount of loan outstanding against him at the end of third year. a] If x2 4ax 1 0 , prove that x ****Best of Luck**** Kewal Sir & Dhaval Sir [3] [3] [4] [3] [3] [4] [3] [3] [4] Page 2 10th I.C.S.E. Kewal Sir & Dhaval Sir Rudra s Academy Mathematics [Time: 2.5 hrs] Preliminary Exam Q.9) [Marks: 80] [Set - 3] a] A sum of Rs 1950 is divided among J, K, D and M such that: J s share K s share J s share 2 K s share D s share M s share 3 b] Find the area of region enclosed by the line 2 x 5 y 10 , 2 x 6 and both the axes. c] In circle with center O, OE // BC. Prove that: i) AD = CD, ii) BE bisects B, iii) If BEO = 35 , find CAO, iv) If AC = 24, DE = 2, find area of circle. [3] [3] [4] Q.10) a] Draw a histogram to represent the following data: Class 9-19 19-29 29-39 39-49 49-59 59-69 Grade obtained 4 7.8 16.5 2 9 12 b] Find the equation of a straight line that has x-intercept 4 and is perpendicular to straight line joining (2, 3) and ( 4, 12). c] In circle with center O, point C is foot of perpendicular. B C Q and A P O Q. Prove that: i) QCP = BAP, ii) APCB is cyclic. iii) AB = AC [3] [3] [4] Q.11) a] Mr. Kewal applies for an examination whose 5 digit application is randomly generated. First three digits are alphabets whereas the last two digits are prime number. The code once generated cannot be reassigned. What is the maximum number registration Mr. Kewal has to do before getting his favorite id KDM37 . [3] b] Mr. Krishna, Mr. Darshan purchased the following goods: Item Quantity Rate Pads 8 pairs Rs 189 each Balls 25 Rs 144 each Bats 4 Rs 2049 each Helmets 4 Rs 4989 each Shoes 6 pairs Rs 5999 Shocks 12 pairs Rs 41 each pair Thigh pads 4 pairs Rs 149 each Glows 8 pairs Rs 876 each pair Giving importance to safety of batsmen, government has wiped out all taxes on helmets. If the sales tax is charged at 9%, find the total amount paid by Mr. Krishna and Mr. Darshan of them if they decide to pay in the ratio 6:4. [3] c] Inscribe a cyclic rhombus in the circle inscribed in a regular hexagon of side 5 cm. [4] ****Best of Luck**** ****Best of Luck**** Kewal Sir & Dhaval Sir Page 3

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