Practice Paper Mathematics (ICSE grade X), Exams of Mathematics

Download Practice Paper Mathematics (ICSE grade X) and more Exams Mathematics in PDF only on Docsity! 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 1 10th ICSE Mathematics 2023 Prediction Paper ICSE X Marks: 80 Subject: Mathematics Time: 2 Hours 30 Min Section A (Attempt all questions from this section) Question 1. 1. The CGST paid by a customer to a retailer for an article costing Rs. 2,000 is Rs. 180. The rate of GST charged is (a) 5% (b) 9% (c) 12% (d) 18% 2. The roots of the quadratic equation 2x 2 – 3x + 4 = 0 are (a) Real and equal (b) Real and unequal (c) Not Real (d) Irrational 3. If (x – 2) is a factor of 3x 3 + 2ax 2 – x – 2, find a. (a) –2 (b) –2.5 (c) –4 (d) 5 4. A2  3  B3  m = C2  1 then m = (a) 1 (b) 2 (c) 3 (d) Matrices can’t be multiplied 5. The 5th term from the end of 3, 7, 11, 15, ……, 99 is (a) 75 (b) 79 (c) 83 (d) 87 6. The point invariant in the line x = 2 is (a) (3, 2) (b) (–2, 1) (c) (2, 4) (d) (0, 2) 7. If  ABC ~  DEF, find DF (a) 5 cm (b) 18 cm (c) 30 cm (d) 40 cm 8. Volume of a cylinder with same radius and height as a cone is 30 cm3, then the volume of cone is (a) 10 cm3 (b) 15 cm3 (c) 30 cm3 (d) 90 cm3 PRIME PRIVATE TUITION 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 2 9. The solution set for the given inequation is: –5 < 3x + 1 < 13, x  Z (a) {1, 2, 3, 4} (b) {0, 1, 2, 3, 4} (c) {–1, 0, 1, 2, 3} (d) {–1, 0, 1, 2, 3, 4} 10. Which of the following cannot be probability of an event? (a) 20% (b) 3 7 (c) –0.5 (d) 0.75 11. If [ 2 −3𝑥 −1 0 ] + 2 [ 1 𝑦 4 1 ] = [ 𝑦 5 7 2 ] then x is (a) 4 (b) –1 (c) 1 (d) –4 12. The midpoint of line joining points (2a, 3) and (4, a – 3b) is (–6, 2) then b is (a) –2 (b) 1 (c) –3 (d) 2 13. In the given figure, PQ = QR, RQP = 68º, PC & CQ are tangents to the circle with centre O. PCQ = (a) 56 (b) 68 (c) 72 (d) 112 14. If tn = 2n – 3, then the first three terms of the AP are (a) –3, –1, 1 (b) –1, 3, 7 (c) –1, 1, 3 (d) –2, 0, 2 15. In grouped frequency distribution mode is found using (a) Bar Graph (b) Histogram (c) Ogive (d) Both (b) and (c) Question 2. (a) A man had a recurring deposit account for 1 year at 14% p.a. simple interest. If he gets Rs. 6,455 at the time of maturity, find the monthly installment. [4] (b) If 2, 6, p, 54 and q are in continued proportion, find the values of p and q. [4] (c) [4] Question 3. (a) A toy is in the shape of a cone surmounting a hemisphere. The height and radius of the base of the conical part are 4 cm and 3 cm respectively. Find the volume of the toy correct to four significant figures. [4] 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 5 (c) [4] Question 8. (a) [3] (b) Find the mean of the following distribution using step deviation method: [3] Price (Rs.) 80 – 90 90 – 100 100 – 110 110 – 120 120 – 130 No. of days 12 10 8 15 5 (c) [4] Question 9. (a) If the speed of an aeroplane is reduced by 40 km per hr it takes 20 mins more to cover 1200 km. Find the speed of the plane. [4] (b) [6] 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 6 Question 10. (a) If √3𝑥 + 1 + √𝑥 + 1 √3𝑥 + 1 − √𝑥 + 1 = 4, use properties of proportion to find x. [3] (b) Using ruler and compasses, construct a regular hexagon of side 4 cm. Hence construct a circle inscribing the hexagon. Measure and write down the length of in-radius. [3] (c) As observed from the top of a 80 m tall light house, the angles of depression of two ships on the same side of the light house in horizontal line with its base are 30º and 40º respectively. Find the distance between the two ships. Give your answer correct to the nearest meter. [4] In case of any doubts whatsapp on 9819547699 All the Best 24 Hr Phone Helpline from 10 am 9 March (Thu) to 10 am 10 March (Fri) You may call or whatsapp anytime to clear your doubts 7 Answers: MCQs 1d, 2c, 3b, 4a, 5c, 6c, 7c, 8a, 9d, 10c, 11c, 12c, 13b, 14c, 15b 2a) Rs. 500 b) 18, 162 c) You can send it on given number to verify 3a) 94.29 cm³ b) A = (6, 0), B = (0, -3), 2x + y – 7 = 0, x – 2y = 0 c) Q’ = (0, -5), R = (-3, 1), P’ = (3, -1), R’ = (-3, -1), Hexagon 4a) 18,290 + 2,432 = Rs. 20,722 b) 1.30, -2.30 c) Rs. 42, Modal Class is 40 - 45 5b) P is common angle and PTQ = PRT [Angles in alternate segments], 3 cm c) 2, 5, (x + 1) (x – 2) (x + 3) 6a) (-2, 1), Equation of BD: y = 1 b) You can send it on given number to verify c) n = 41, Sn = 5,412 7a) 1/8; 32 Balls in the bag b) 54 c) 54°, 27°, 27°, 153° 8a) {x : –3 < x < 4, x  R} b) Rs. 103.20 (2 decimals because final answer is in Rs.) c) 10 cm 9a) 400 kmph b) (i) 43 (ii) 60 – 28 = 32 (iii) 10 10a) 8g c) 43.15 m