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ICSE Prelims 2016 : Mathematics 2 (R. B. K. School (RBK), Mira Road)

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SECOND PRELIM EXAMINATION 2015-16 Std: X Date: 04/01/16 Subject: MATHEMATICS Marks: 80 Dur. : 2 hrs Section I ( 40 marks ) [Attempt all questions from this section] Question 1:A) On a certain sum of money, the compound interest for 2 years is Rs 2172. If the rates of interest for successive years are 6% and 8% per year, then find the sum. B) Solve the following linear inequation and graph the solution on the number line:1 15 - 7x > 2x 27 , x N (3) (3) C) A straight line passes through the points P(-1,4) and Q(5,-2). It intersects the co-ordinate axes at points A and B. M is the midpoint of the segment AB. Find :(4) i) the equation of the line. ii) the co-ordinates of A and B iii) the co-ordinates of M. Question 2:A) Solve the following quadratic equation using factorization method: (3) x + 5 = x + 3 B) In the following figure, PB and PA are two tangents drawn to the circle with centre O. BPA = 480. Find ASB (3) C) Arun has a Savings Bank a/c in Bank of Baroda. His passbook had the following entries:(4) Date Particulars Debit Credit Balance Jan 1 2004 By balance Rs 2800 Jan 8 2004 By cash Rs 2000 Rs 4800 Feb 18 2004 By cheque Rs 2500 Rs 2300 May 19 2004 By cash Rs 1700 Rs 4000 July 15 2004 To self Rs 500 Rs 3500 Oct 7 2004 By cash Rs 1000 Rs 4500 On October 30, 2004 he received his transfer order and closed the account. Find the interest and the amount he received on closing the account if the rate of interest is 5% per annum. Page 1 of 4 Question 3:A) Evaluate without using trignometrical tables: tan 50 tan 250 tan 300 tan 650 tan 850 (3) B) Factorise the given polynomial completely:x3 7x2 + 15x 9 (3) C) The marks of 20 students in math test were as follows:10, 12, 6, 9, 15, 14, 2, 6, 18, 13, 12, 13, 7, 14, 19, 12, 5, 7, 11, 9. Calculate the mean, mode and median. (4) Question 4:A) A box contains cards numbers 10 to 30. A card is drawn at random. Find the probability that the card drawn is :(3) i) a prime number ii) a number divisible by 4 iii) a factor of 15 B) PQRS is a rectangle with PQ = 21 cm and QR = 14 cm. Two quadrants with centres Q and P are cut as shown in the figure. Find the area of the remaining portion. (3) P 21cm Q 14 cm S R C) Use Graph paper for this question ( Take 1 cm = 1 unit on both the axes ). The point (2,3) is reflected to P in the X axis and O is the image of the origin O when reflected in the line PP . i) Give the co-ordinate of P and O ii) the length of the segments PP and OO iii) Give the geometrical name to OPO P iv) How many lines of symmetry does OPO P ? Name them. (4) Section II (40 marks) [ Attempt any 4 questions from this section ] Question 5:A) Solve the following quadratic equation and give your answer correct upto 2 significant figures :4x 1 = 6 x B) The simple interest on a sum of money for 2 years at 4% per annum is Rs 340. Find :i) the sum of money ii) the compound interest on this sum for one year payable half yearly at the same rate. (3) (3) C) A car covers a distance of 400 Km at a certain speed. Had the speed been 12 Km/hr more, the time taken for the journey would have been 1 hr 40 min less. Find the original speed of the car. (4) Page 2 of 4 Question 6:A) In what ratio is the line joining the points (4,2) and (3,-5) divided by the X axis? Find the coordinates of the point of intersection. (3) B) Find the matrix X :- 3 7 2 4 0 2 + 2X = 3I, where I is identity matrix of the order 2x2. 5 3 (3) C) The angles of depression of the top and the foot of a100 m high tower as seen from the top a cliff are 450 and 600 respectively. Find the height of the cliff. (4) Question 7:A) In the diagram given below two chords intersect each other externally at point P. Find the value of x. (3) B) Use the properties of proportion to find x:3x + 9x2 5 = 5 3x - 9x2 5 (3) C) Construct a regular hexagon ABCDEF of side 4 cm and inscribe a circle in it. Measure the radius of the inscribed circle and also draw all the lines of symmetry of regular hexagon. (4) Question 8:A) A metallic sphere of radius 10.5 cm is melted and ten recast into small cones each of radius 3.5 cm and height 3cm. Find the number of cones thus formed. (3) B) The catalogue price of a computer is Rs 48,000. The shopkeeper gives a discount of 10% on the listed price. He further gives an off-season discount of 5% on the balance. Sales tax of 10% is charged on the remaining amount. Find the final price paid by the customer for the computer. (3) C) Find the mean of the following distribution using step-deviation method:Class interval 100 - 110 110 - 120 120 130 130 - 140 Frequency 15 18 32 25 (4) 140 - 150 10 Question 9:A) A man invested Rs 45,000 in 15% Rs 100 shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8400. Calculate :- i) the number of shares he still holds ii) the dividend due to him on these remaining shares. (4) B) The marks obtained by 200 students in a history test paper are given in the following table. Draw an Ogive for the given distribution and estimate the following:i) the median. ii) the lower quartile. iii) the number of students who obtained more than 80% marks in the test. Page 3 of 4 (6) Marks obtaine d No of student s iv) the number of students who did not pass the test if the pass percentage is 35. 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90100 5 10 11 20 27 38 40 29 14 6 Question 10:A) Mr Acharya deposits Rs 300 per month in R.D account for 2 years. If the rate of interest is 7% p.a, find the amount received by him at the time of maturity. (3) B) Prove that :- cot A tan A = 2 cos2 A 1 sin A cos A C) A model of the ship is made to a scale of 1 : 200. i) The length of the model is 4m. Calculate the length of the ship. ii) The area of the deck of the ship is 160000m 2. Find the area of the deck of the model. iii) The volume of the model is 200 litres. Calculate the volume of the ship in m 3. Question 11:A) Let M x 1 1 = 1 2 , State the order of matrix M and hence find M. 0 0 (3) (4) (3) B) From a pack of 52 playing cards, a black jack, a red queen, and two black kings fell down. A card was then drawn from the remaining pack at random. Find the probability that the card drawn is i) a black card (3) ii) a king iii) a red queen. C) From a right circular cylinder of radius 10cm and height 12cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume and the surface area of the remaining solid. ( Take =3.14 ) (4) Page 4 of 4

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