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ICSE Prelims 2017 : Mathematics (The Indian Public School, Dehradun)

5 pages, 42 questions, 35 questions with responses, 117 total responses,

Rashmi
The Indian Public School, Dehradun

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THE INDIAN PUBLIC SCHOOL, DEHRADUN PRE-BOARD-II 2016-17 MATHEMATICS/CLASS X TIME: 2Hrs30Mins MM: 80 RST: 35 DATE: 1/2/17 Answers to this paper must be written on the paper provided separately. You will not be allowed to write during first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is allowed for writing the answer. Answer 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) QUESTION 1. a) Mohini borrowed Rs. 20,000 for 3 years. The rate of interest for the three successive years was 8%, 9% and 10% respectively. If she repays Rs. 6600 at the end of the first year and Rs. 6350 at the end of the second year, find the outstanding amount at the end of third year. [3] b) Solve the following in-equation, write the solution set represent it on the number line. 3 x 4 x + 2, where x I . 2 3 [3] c) A jar contains 24 marbles, some green and others blue. If a marble is drawn at random from the 2 jar, the probability that it is green is . Find the number of blue marbles in the jar. 3 [4] QUESTION 2. a) Find the values of [ ][ ] [ ] x y ,if 2 x x 3 = 16 y 3y 2 9 b) Anjana has a recurring deposit account in a bank for [3] 3 1 2 years at 9.5% S. I. per annum. If she gets Rs. 78,638 at the at the time of maturity, find the amount of monthly installment. [3] c) Points A, B and C have coordinates (0, 3), (4, 4) and (8, 0) respectively. Find the equation of the line through A and perpendicular to BC. [4] QUESTION 3. a) Without using trigonometric tables, evaluate: 1 2 ( 2 2 tan 35 cot 55 sec 40 + 3 cot 55 tan35 cosec50 )( ) ( ) [3] b) Using the Remainder and Factor Theorem, factorize the following polynomial: 3 2 [3] 2 x +9 x + 7 x 6 c) In the figure, ABCD is a square of side 6 cm. Find the area of the shaded region. [Use = 3.14 and 3=1.732 ] [4] QUESTION 4. a) For the data: 6, 2, 5, 4, 3, 4, 4, 2, 3, calculate the mean of its median and mode. [3] b) The bisectors of the opposite angles P and R of a cyclic quadrilateral PQRS intersect the circle at the points A and B respectively. Prove that AB is a diameter of the circle. [3] c) Use graph paper to answer the following questions. (Take 2cm=1 unit on both axes) (i) Draw a triangle ABO with vertices A(0, 3), B(3, -2) and O(0, 0). (ii) Plot D the reflection of B in the y-axis, and write its coordinates. (iii) Give the geometrical name of the figure ABOD. (iv) Write the equation of the line of symmetry of the ABOD. [4] SECTION-B (40 MARKS) Attempt any four questions from this section. QUESTION 5. a) A shopkeeper buys an almirah at a discount of 10% from the wholesaler, the wholesale price of the almirah being Rs. 8,000, and the rate of sale tax 6%. The shopkeeper sells it to the buyer at the wholesale price and charges tax at the same rate. Find (i) The price at which the almirah can be bought by buyer; 2 The VAT paid by the shopkeeper. (ii) [3] a+1+ a 1 , using the properties of proportion show that 2 b) If x= x 2 ax+1=0 a+1 a 1 [3] c) The image of a tree on the film of a camera is of length 35 mm, the distance from the lens to the film is 42 mm and the distance from the lens to the tree is 6 m. How tall is the portion of the tree being photographed? [4] QUESTION 6. a) Show that the triangle PQR is a right-angled triangle if P(1, 3), Q(3, -1) and R(-5, -5) [3] b) Sumitra owns 500 shares of a company. The face value of each share is Rs. 2. The company declares a dividend of 20%. Calculate : (i) The amount of dividend that Sumitra will get; (ii) The rate of interest on her investment if she paid Rs. 40 for each share. [3] c) A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the sauce level in the inverted cone. [4] QUESTION 7. a) Find the mean of the following data by step-deviation method: Class- interval Frequency 45-50 5 50-55 8 55-60 30 60-65 25 [3] 65-70 14 70-75 12 b) In the figure, AB=7 cm and BC=9 cm. (i) Prove that ACD DCB. (ii) Find the length of CD. c) Let [ ] [ ] [ 75-80 6 [3] ] A= 4 2 , B= 0 2 C= 2 3 , find A 2 A+ BC . 6 3 1 1 1 1 [4] QUESTION 8. a) Construct a triangle ABC in which BC=6cm, AB=5.5cm and ABC =120 . (i) Construct a circle circumscribing the triangle ABC. (ii) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C. [4] b) The table below shows the distribution of the scores obtained by 120 shooters in a shooting competition. Using a graph sheet, drawn an ogive for the distribution. 3 Scores obtained Number of shooters 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 5 9 16 22 26 18 11 6 4 3 Use the ogive to estimate: (i) The median (ii) The interquartile range, and (iii) The number of shooters who obtained more than 75%. [6] QUESTION 9. a) According to a census, the population of a town was found to be 80,000. The census authority also found that the population of this particular town had a growth rate of 5% per annum. In how many years will the population of the town be 92,610? [3] b) Using the quadratic formula, solve the following for x: 2 [3] x ( 1+ 3 ) x + 3=0 . th c) Mrs. Aggarwal opened a saving account in a nationalized bank on 9 January, 2013. Her passbook entries for the year 2013 are given below: Date 2013, Jan. 9 Feb. 12 April 6 April 30 July 16 Aug. 4 Aug. 20 Dec. 12 Particulars By Cash By Cash To Cheque To Self To Cheque To self To Cheque By Cash Withdrawals ( in Rs.) ----------3,500 2,000 -----5,500 1,200 ------ Deposits (in Rs.) 10,000 15,500 --------6,500 ---------1,700 Balance (in Rs.) 10,000 25,500 22,000 20,000 26,500 21,000 19,800 21,500 Mrs. Aggarwal closed the account on 31st December, 2013. If the bank pays at 4% per annum, find the interest Mrs. Aggrawal received on closing the account. Give the answer correct to the nearest rupee. [4] QUESTION 10. a) A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 4 days, find the time taken by B to finish the work. b) In school the weekly pocket money of 50 students is as follows: [3] Weekly pocket money (in Rs.) 40-50 50-60 60-70 70-80 80-90 90-100 No. of students 2 8 12 14 8 6 Draw histogram and find the mode, using the histogram. [3] c) AB is a diameter of a circle with center O (-2, 5). If A (3, -7) find the length of AO and the coordinates of B. [4] QUESTION 11. 4 a) In the figure, AC is a transverse common tangent of two circles with centers P and Q and of radii 6 cm and 3 cm respectively. Given that AB=8cm, calculate PQ. [3] b) Provethat sin tan =( 1+ sec ) ( 1 cos ) . [3] c) From a lighthouse, the angles of depression of two ships on the opposite sides of the lighthouse were observed to be 30 and 45 . If the height of the lighthouse is 90m and the line joining the two ships passes through the foot of the lighthouse, find the distance between the two ships(give your answer correct to two decimal places.) [4] 5

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