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ICSE Class X Prelims 2023 : Mathematics (J.S.S. International School (JSS IS), Dubai)

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J.S.S. International School (JSS IS), Dubai
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, JSS INTERNATIONAL SCHOOL, DUBAI GRADE: 10 Marks: 80 MOCK I EXAMINATION DATE: 27-10-2022 MATHEMATICS Duration: 2 Hrs Answers to this Paper must be written on the paper provided separately. You 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 head of this Paper is the time allowed for 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 and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Section A (Attempt all questions from this section) [15] Question 1 Choose the correct answers to the questions from the given options: i) If the cost of an article is 25,000 and CGST paid by the owner is 2250, the rate of GST is a)9% b)10% c)15% d)18% ii) If (2/3) is a root of the equation kx 13 x 10 = 0, the value of k is a) 1 b)2 c)3 3 4 7 ] X = [ ]. Write the order of the matrix X. iii) Given A = [ 8 5 6 a) 2 x 3 b)2 x 1 c) 1x 2 d) 3 x 2 Page 1 of 5 d)4 iv) Mr. Ramesh deposits Rs.250 per month for 1 year in a bank's recurring deposit account at the rate of 8% per annum, then the interest earned by him is . a)Rs65 b)Rs 120 c)Rs130 d)Rs260 2 1 v. If x is a negative integer, find the solution set of 3 + 3 ( + 1) > 0 a){-1,-2} b){-2,-3} c){-3,-4} d){-4,-5} vi)If the common difference of an AP is 5, then find 18 13 . a)5 b)15 c)25 d)10 vii)What should be subtracted from the polynomial 2x + 5x -11x 10 so that 2x+7 is a factor? a) -4 b)4 c)0 d)-1 viii) The roots of the quadratic equation 4 - 7x + 2 = 0 are 1.390, 0. 359.The roots correct to 2 significant figures are a) 1.39 and 0.36 b) 1.3 and 0.35 c) 1.4 and 0.36 d) 1.390 and 0.360 ix) If a rectangular sheet having dimensions 22 cm x 11 cm is rolled along its shorter side to form a cylinder. Then the curved surface area of the cylinder so formed is: (a) 968 cm (b) 424 cm 1 x) The value of 1+ + a) 0 1 1+ b) 2 (c) 121 cm (d) 242 cm c)1 d) -1 = . xi)A vertical pole is 12m high and the length of the shadow is 12 3 m. The angle of elevation of the sun is a)30 b)60 d) 3 c)45 xii)If the end points of a diameter of a circle are A (-2,3) and B(4,-5), then the coordinates of its centre are a)(2,-2) b)(1,-1) c)(-1,1) d)(-2,2) xiii) If the equation 3x - k x + 2k = 0 has equal roots, the value(s) of k is(are) . a)6 b)0 only c)24 only d)0 or 24 xiv)If (k-3),(2k+1) and (4k+3) are three consecutive terms of an A.P, find the value of k. a)1 b)0 c)2 d)3 xv) The third proportional to a+b and 2 a)a -b Page 2 of 5 b)a+b c)a +b d) a-b Question 2 +3 63 i) Using properties of proportion, find the ratio a:b , given +3 = 62 [4] ii) Vicky had a recurring deposit in a bank. He deposited Rs 300 per month for some months. If [4] he received Rs 525 as interest at 7% per annum find the duration of the deposit. iii)Prove that 1 tan + 1 = + [4] Question 3 i)A hollow metal sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a solid cone of base radius 4cm.Find the height and slant height of the cone correct to two [4] significant figures. ii) A (2,5), B (-1,2) and C (5,8) are the vertices of a triangle ABC.M is a point on AB such that [4] AM : MB = 1: 2. Find the coordinates of M. Hence, find the equation of the line passing through the points C and M. iii)Use graph paper to answer the following questions. Take 1cm =1unit on both axes. a) Plot the following points on your graph sheet: A (0,0), B (-4, -2), C (-2,0), D (-4,2), E (-2,2), F (0,4). b) Reflect the points B, C, D, E on Y axis as B , C , D , E respectively. c) Join the points A, B, C, D, E, F, E , D , C , B and A in order. d) Name the closed figure obtained. [5] Section B (Attempt any four questions from this section) Question 4 i) Find the value of p if equation (p+6) x + (p-2) x +1 =0 has equal roots. [3] ii) A two-digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number. [3] iii) If 7 +2 7 2 5 = ,use properties of proportion to find i) p: q 3 ii) 3 2 +2 3 2 2 [4] Question 5 i) If q is the mean proportional between p and r, prove that p q r (p+ q + r) = (p q + q r + p r) Page 3 of 5 [3] 3 5] ii) If Q = [ and Q - 5Q = k I where I is the identity matrix of order 2x2.Find the [3] 4 2 value of k. iii) Find the ratio in which the line joining A(6,5) and B(4,-3) is divided by the line y = 2.Also, find the coordinates of the point of intersection. [4] Question 6 2 4 i)If P = [ 0 1 0 ] = [ ]Find the value of x if PQ = QP. 2 5 ii) Find the equation of the line passing through the origin and the point of intersection of the lines 5x+7y = 3 and 2x 3y = 7. iii)A vertical pole and a vertical tower are on the same level ground. From the top of the pole, the angle of elevation of the top of the tower is 60 and the angle of depression of the foot of the tower is 30 .Find the height of the tower if the height of the pole is 20m. [3] [3] [4] Question 7 4 i)The 31st ,16th and the last terms of an AP are 1, 4, 5 respectively. Find the first term and the number of terms in the AP. ii) Prove the following identity: + + = iii) Three vertices of a parallelogram ABCD taken in order are A(3,6), B(5,10) and C(3,2) . Find : a) coordinates of the fourth vertex D b) equation of side AB of the parallelogram ABCD. c) Slope of BD. [3] [3] [4] Question 8 i) The equation of a line is 2x -2 3y - 3 = 0. Find i) gradient of the line ii) inclination of the line iii) y intercept of the line. [3] ii) Solve the quadratic equation ( 1)2 3 + 4 = 0 and give your answer correct to two significant figures. [3] iii) A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13cm and 5cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of the conical part is 12cm. Page 4 of 5 [4] Question 9 i)Solve the linear inequation and graph the solution set on a real number line. [3] 2 1 1 1 + < 4 , 3 3 3 ii)Mr Kumar a registered dealer purchased goods worth Rs 40000 from a dealer (within the same state) .If the rate of GST is 18%, a) Calculate the input CGST and Input SGST b)If he sold these goods to Mr Dev (within the state) for Rs50000, calculate Mr Kumar s output [3] CGST and output SGST. c)Calculate the CGST and SGST payable by Kumar. iii) A train travelling at a uniform speed for 360km, would have taken 48 minutes less to travel the same distance if its speed were 5km/hr more. Find the original speed of the train. [4] Question 10 i) a) A wholesaler buys a machine from the manufacturer for Rs 25000.He marks the price of the machine 20% above his cost price and sells it to a retailer at 10% discount on the marked price. If the rate of GST is 18% and assuming that all transactions occur within the same state, calculate a) the marked price of the machine. b) Retailers cost price inclusive of GST c) the CGST and SGST payable by the wholesaler to the government. ii) Prove that + ( + ) [3] = iii)Use the remainder theorem to factorise 2x + x - 13x + 6 ******************* Page 5 of 5 [3] [4]

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