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ICSE Class X Prelims 2023 : Mathematics (GEMS Modern Academy, Dubai) Mock 1

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MOCK EXAMINATION 1 (2022 - 2023) MATHEMATICS Grade:10 Time: 2 Hours Date:06/02/2023 Max. Marks: 80 INSTRUCTIONS Answer all questions in Section A and any four questions from Section B Show all working including rough work clearly. The intended marks for questions are given in brackets [ ]. The time stated above is the time allowed for writing the examination. In addition, first 15 minutes will be the time given for reading the questions. Mathematical tables will be provided. This paper consists of 8 printed pages. Section A (Attempt all the questions from this section) Question 1 [15 M] Choose the correct answers to the questions from the given options: i. For a transaction of Rs. 80,000 in Delhi, if GST rate is 18%, then SGST is a) Rs 7200 b) Rs 14400 c) Rs 6400 d) Nil. ii. If 2 3 a) 1 is a root of the equation 2 13 10 = 0 , then value of k is b) 2 c) 3 d) 4 Page 1 of 8 iii. If x + 1 is a factor of 3 + 2 + 7 + 4 , then the value of a is a) 6 b) 0 c) 6 d) 4 iv. If ( 1 3 2 5 ) ( ) = ( ) , the value of x is 0 0 0 a) 1 b) 1 c) 2 d) 3 v. Which of the following point is invariant with respect to the line = 2 ? a) (2, -7) b) (-2, 7) c) (2, -2) d) (7, -2) vi. If two coins are tossed simultaneously, probability of getting at most one tail is a) 1 2 3 b) 4 1 c) 4 d) 1 vii. The 2 x 2 matrix whose elements are given by = 2 is 1 0 1 3 1 0 1 3 a) ( ) b) ( ) c) ( ) d) ( ) 3 2 0 2 0 3 3 2 viii. Which term of the A.P. 92, 88, 84 . is 0? a) 23rd b) 28th c) 24th ix. d) 27th In the following figure, ~ and their sides are of lengths (in cm) as marked along them. The length of side RQ is a) 12cm b) 9cm c) 24cm d) 30cm. x. The solution set for the inequation 8 2 < 8, is a) {-4,-3,-2,-1,0,1,2,3,4} b) {0,1,2,3,4} c) {0,1,2,3} d) {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8} xi. A cylindrical pencil sharpened at one edge is the combination of a) cone and a cylinder b) cylinder and hemisphere c) two cylinders d) cylinder and two cones Page 2 of 8 xii. The sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at P, the sides AD and BC are produced to meet at Q. If ADC=85o and BPC=40o, then CQD = ? a) 95o xiii. b) 55o c) 85o d) 30o The line segment joining P (-4,5) and Q (3,2) intersects the Y axis at R. PM and QN are the perpendiculars from P and Q on x axis. The ratio PR : RQ is a) 4:5 b) 3:4 c) 5:4 d) 4:3 xiv. The 10th term from the end of an A.P. 7, 10, 13, ., 184 is a) 157 b) 154 c) 160 d) 151 xv. The inclination of the line 3 + 2 3 = 0 is a) 0o b) 60o c) 30o Question 2 d) 90o [4+4+4] i. Mr. John has a recurring deposit account and deposits Rs. 750 per month for 2 years. If he gets Rs. 19125 at the time of maturity, find the rate of interest. ii. What least number must be added to each of the numbers 5, 11, 19 and 37 so that the resulting numbers are proportional? Page 3 of 8 iii. Prove that +1 + 1 = 1 Question 3 i. [4+4+5] In the figure, from a cuboidal solid metallic block of dimensions 15 cm x 10 cm x 5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block. ( = 22 7 ) ii. Calculate the ratio in which the line joining A ( 4, 2) and B (3, 6) is divided by point P (x, 3). iii. Using a graph paper, a) Plot the points A (6, 4) and B (0, 4). b) Reflect A and B in the origin to get the images A' and B'. c) Write the coordinates of A' and B'. d) State the geometrical name for the figure ABA'B'. e) Find its area. SECTION B (Answer any four questions from this section) Question 4 i. [3+3+4] Mr. Sunil visits the market and buys the following articles: Medicines costing Rs.950, GST @ 5% A pair of shoes costing Rs. 3000, GST @ 18% A laptop bag costing Rs.1000 with a discount of 30%, GST @ 18%. Page 4 of 8 a) Calculate the total amount of GST paid. b) The total bill amount including GST paid by Mr. Sunil. ii. Solve the quadratic equation 2 4 8 = 0 . Give your answer correct to three significant figures. iii. Using a graph paper, draw a histogram for the given distribution and estimate the mode of the data. Class 0 5 5 10 10 15 15 20 20 25 25 30 Frequency 2 5 18 14 8 5 Question 5 [3+3+4] 2 6 3 2 4 0 ), = ( ), = ( ). Find the matrix X such that 2 0 4 0 0 2 + 2 = 2 + . i. Given = ( ii. In the following figure ABC is a right-angled triangle with BAC = 90 , and AD is perpendicular to BC. a) Prove ADB ~ CDA. b) If BD = 18 cm, CD = 8 cm find AD. iii. If (x 2) is a factor of the expression 2 3 + 2 + 14 and when the expression is divided by (x 3), it leaves a remainder 52, find the values of a and b. Question 6 i. [3+3+4] Find the equation of the line through P and perpendicular to AB given A is (6,0), B is (0, -3) and P is (4, -1). Page 5 of 8 ii. If + = and + = , prove that ( 2 1) = 2 . iii. How many terms of the A.P. 7,11,15,19,23 must be taken to get the sum 250? Question 7 [3+3+4] i. Sixteen cards are labelled as a, b, c, m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is: a) a vowel. b) a consonant. c) none of the letters of the word 'median' ii. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled? iii. In the given figure TP and TQ are two tangents to the circle with centre O, touching at A and C respectively. If BCQ = 55 and BAP = 60 , find: a) OBA b) OBC Question 8 i. [3+3+4] Solve the following inequation and represent your solution on the number line. Page 6 of 8 ii. iii. If the mean of the following distribution is 24, find the value of a . Marks 0 10 10 20 20 30 30 40 40 50 Frequency 7 a 8 10 5 Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of PQR (see Fig.). Show that ABC ~ PQR. Question 9 [4+6] i. Rs. 6500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs. 30 less. Find the original number of persons. ii. 40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below: Use a scale of 2 cm = 1 m on one axis and 2 cm = 5 students on the other axis. Hence using your graph find: a) the median b) Upper Quartile 1 c) Number of students who cover a distance which is above 16 m. 2 Page 7 of 8 Question 10 [3+3+4] i. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30 , which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60 . Find the time taken by the car to reach the foot of the tower from this point. ii. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. iii. If = 6 + +3 , prove that ( 3 + +3 3 ) = 2 using properties of proportion. Page 8 of 8

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