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ICSE Board Exam 2016 : Mathematics

8 pages, 59 questions, 59 questions with responses, 392 total responses,

Srujan Deshpande
Sri Chaitanya Techno School, Bangalore
XI-XII PCM, IP, English

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MATHEMATICS (Two hours and a hatfl Answers b You rhis Paper must be written on the paper provided separately. 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 heqd of this Paper is the time allowedfor 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 und must be done on the same sheet as the rest oflhe ansbter. Omission of essential working will result in loss of marks, The intended marks for questions or parts of questions are given in brackets I J. Mathematicol tables are provided. SECTION A (40 Marks) Attempt all questions from this Section. Question (a) I Using remainder theorem. find the value of k if on dividing 2x3 by x (b) (c) - Given 2, leaves a remainder o=[!, 9] + 3x2 - kx *5 7. .ro': [l ?] "ro 42= eA + mt. Find The mean of following numbers is 68. Find the value of m. t4l 'r'. t3] 45, 52, 60, x, 69, 70, 26, 8 I and 94. Hence estimate the median. This paper consists of 8 printed pages. T16 511 Copyright reserved. @ t3l Turn over Question 2 (a) The slope of a line joining P(6, k) and Q( l -3k, 3) is (i) k (ii) Midpoint (b) of PQ, using the value of 'k' found in (i). t4l Without using trigonometrical tables, evaluate: cosec257o (c) 13I ]. rinA - ten233" * cos44"cosec46" - 'l2cos45' - tanz 60" A certain number of rnetallic cones, each of radius 2 cm and height 3 cm are melted t3l and recast into a solid sphere of radius 6cm. Find the number of cones. Question 3 (a) Solve the following inequation. write the solution set and represent it on the number t3l line. -3(x (b) -7) > 1s - 7x )+,x e R In the figure given below. AD is a diameter. O is the centre of the circle. AD is parallelto BC and t4l I CBD: 320. Find: (i) zoBD (ii) zAoB (iii) zBED. (c) T16 511 If (34 + 2b): (54 + 3b) = 1,8:?9.Find o : b. t3l Question 4 (a) A game of numbers has cards marked with I 1,12,13,..... , 40.A card is drawn at t3] random. Find the Probability that the number on the card drawn is: (i) A perfect square (ii) Divisibleby (b) 7 Use graph paper for this (Take 2 question. cm: I unit along I4l both x and y axis.) Plot the points O (0, 0), A (-4, 4). B (-3, 0) and C (0, -3) (i) Reflect points A and B on the y axis and name them A' and B' respectively. Write down their coordinates. (ii) (iii) f ' (c) Name the figure OABCB'A'. State the line of symmetry of this figure. two t3] * 3(x + 3) = 0; Give vour answer correct to t3l Mr. Lalit invested t5000 at a certain rate of interest, compounded annually for ,ears. At the end of first year it amounts to t5325. Calculate (i) The rate of interest. (ii) The amount at the end of iecond year, to the nearest rupee. SECTION B (40 Marks) Attempt any four questions from this Section auestion 5 xz F- ,TJ:J::;:ffiiJuation T16 5u Turn Over (b) A page from the savings bank account of Mrs. Ravi is given below. Withdrawal Particulars Date April 3'd 2006 April April 7ih l5th Deposit Balance (o m m 6000 B/F By cash 2300 8300 By cheque 3500 I 1800 20th June lOth By cash June l5th To self August l3th By cheque August 25th To self September 6th 2006 7600 4200 To self By cash May t4l 3 100 1 000 3400 0300 r r300 3900 7400 2000 She closed the account on 30th September, 2006. r 1 5800 5900 Calculate the interest Mrs. Ravi eamed at the end of 30th September, 2006 at 4.5oh per annum interest. Hence, find the amount she receives on closing the account. (c) In what time will Rs.l500 yield Rs.1996.50 as compound interest at lUYo per t3l annum compounded annually? Question 6 (a) Construct a regular he5.agon of side 5 cm. Hence construct all its lines of symmetry t3l and name them. (b) In the given figure PQRS is a cyclic quadrilateral PQ and SR produced meet at T. (i) - ATRQ. (ii) Find SP if TP: l8cm, RQ :4 Prove ATPS (iii) Find area of quadrilateral T16 511 cm and TR:6cm. PQRS if area of APTS :27 cm'. t4l (c) civen matrix o : If [njjlor9" _:,"j3;"] : t3l [lJ AX:B (i) Write the order of matrix X. (ii) Find the rnatiix Question (a) and u 'X'. 7 An aeroplane at an altitude of 1500 metres finds that two ships are sailing it in the same direction. The angles of depression towards t4] as observed from the aeroplane are 45o and 30o respectively. Find the distance between the two ships. (b) The table shows the distribution of the scores obtained by 160 shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution. (Take 2cm: l0 scores Scores 0- l0 on the X axis and 2cm : t6l 20 shooters on the Y-axis). l0-20 20-30 30-40 40-50 50-60 i 60-70 70-80 80-90 90-100 I No. of l3 9 shooters 20 30 26 22 I l0 15 8 7 I I l Use your graph to estimate the following: (i) The median (ii) The interquartile range. (iii) The number of shooters who obtained a score of more than g5%. Question 8 (a) ff! t; = =';show that *.t; * i (b) Draw a line AB : t3l =# 5 cm. Mark a point C on AB such that AC :3 cm. Using a ruler and a compass only, construct: (i) A circle of radius 2.5 cm, passing through A and C. (ii) Construct two tangents to the circle from the external point B. Measure and record the length ofthe tangents. T16 511 Turn Over t4l (c) A line AB meets X-axis at A and Y- axis at B. P(4, -l) divides AB in the ratio l:2' (i) Find the coordinates of A and B. (ii) t3l Find the equatioh of the line through P and perpendicular to AB. Question 9 (a) A dealer buys an article at a discount of 30Yo from the wholesaler, the marked price t3] being t6,000. The dealer sells it to a shopkeeper at a discount of l0o/o on the marked price. If the rate of VAT is 6%, find (i) The price paid by the shopkeeper including the tax. (ii) The VAT paid by the dealer. (b) The given figure represents a kite with a circular and a semicircular motifs stuck on it. The radius of circle is 2.5 cm and the semicircle is 2 cm. tf diagonals AC and BD are of lengths 12 cm and 8 cm respectively, find the area of the: (i) shaded part. Give your answer correct to the nearest whole number. (ii) unshaded T16 511 part. t4] (c) A model of (i) a ship is made to a scale I : 300 t3t The length of the model of the ship is 2 m. Calculate the length of the ship. (ii) The area of the deck ship is 180, 000 m2. Calculate the area of the deck of the model. (iii) The volume of the model is 6.5 m3. calculate the volume of the ship. Question l0 (a) Mohan has a recurring deposit account in a bank for 2 years at 6 Yo p.a. simple interest. If he gets t (i) the monthly insralment (ii) (b) t3l 1200 as interest at the time of maturity, find: the amount of maturity. The histogram below represents the scores obtained by 25 students in a t4l Mathematics mental test. Use the data to: (i) Frame a frequency distribution table. (ii) To calculate mean. (iii) To determine the Modal class. 1 .E :ii:i-i r.rlt.,r-,. 1 s L ,,', 1' {I lt.' ,- ] rl :.i: rlI i:. l: l i Ir i ))i: Iti.iirl .: lii', .:i l r;, ' :-.1,i-i 1l.i:i :. ! i ,.t. .'- I I ,r,1jl a a'i;] i.:, 1 .-i .l-j i i i -t..".i-r'i"' i t ijli,: .r.i "'t i-i . ::-i l .n ;.r- ':i, ,'j (c) A bus covers a distance gets reduced by of ..i I l t1':-.:_tl i-: ,.. Il IIi ( .:lif, ! I : _i rqnxrl ltl rji 240 km at a uniform speed. Due to heavy rain its speed l0 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform sp'eed to be 'x' km/h, form an equation and solve it to evaluate 'x'. T16 511 Turn Over t3l Question 11 (a) Prove ttrat (b) Use ruler and compasses only for the following question. # t3l * tunA = secA' All construction lines t4] and arcs must be clearlY shown' (i) :60o' Construct a A ABC in which BC: 6'5 cm, ZABC AB: 5cm ' (ii)Constructthelocusofpointsatadistanceof3.5cmfromA. (iii)ConstructthelocusofpointsequidistantfromACandBC. (iv) Mark 2 points X and Y which are at a distance of 3.5cm from A and also equidistant from AC and BC' Measure XY' (c) Ashok invested { 26,400 on l2o/o, {25 shares of a company' dividend of t2,475,find the: (i) (ii) T16 number of shares he bought Market value of each share 5lr If he receives a [3]

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