Class 10 - Sample Question Paper (Mathematics) I – SA-I Time allowed: 3 hours Maximum marks: 80 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections – A, B, C and D. (iii) Section A contains 10 questions of 1 mark each, which are multiple choice type questions, section B contains 8 questions of 2 marks each, section C contains 10 questions of 3 marks each and section D contains 6 questions of 4 marks each. (iv) There is no overall choice in the paper. (v) Use of calculators is not permitted. Section – A Question numbers from 1 to 10 are of one mark each. 1. Let be a rational number, such that the prime factorization of q is of the form 2n5m, where n, m are non-negative integers. Then the decimal expansion of x is a) Terminating b) Non-terminating recurring c) Non-terminating non recurring d) None 2. Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where r satisfies a) 0 <r < b b) 0 < r ≤ b c) 0 ≤r < b d) 0 ≤r ≤ b 3. The sum of the zeroes of the quadratic polynomial is a) – b) c) – d) Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 1 4. The lines a) Intersecting lines b) Parallel lines c) Coincident lines d) Perpendicular lines are 5. The sides of two similar triangles are in the ratio will be a) 2:5 b) 4:25 c) 25:4 d) 5:2 then the ratio of their areas 6. A ladder 13 m long is placed against a vertical wall of height 12m. The distance between the foot of the ladder and the wall is a) 5 m b) 10 m c) 7 m d) 8 m 7. If a) b) c) d) where 2A is an acute angle then 8. a) 1 b) 0 c) d) 9. a) b) c) d) Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 2 10. If the mode and median of a data are 27.8 and 26.7 then its mean is a) 26.51 b) 27.15 c) 26.15 d) 27.51 Section – B Question numbers 11 to 18 carry 2 marks each. 11. Given that HCF (306, 657) = 9, find LCM (306, 657). 12. Find the zeroes of the quadratic polynomial, relationship between the zeroes and the coefficients. 13. Solve the equations and verify the using substitution method. 14. The diagonals of a quadrilateral intersect each other at O such that . Show that ABCD is a trapezium. 15. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower. 16. Prove that 17. Write the formula to find the median for grouped data and explain each term. 18. Find the mode of the following data: Class Frequency 0–9 6 10 – 19 9 20 – 29 14 30 – 39 21 40 – 49 16 50 – 59 8 Section – C Question numbers 19 to 28 carry 3 marks each. 19. U Eu l d’ d v l mm h w h h qu r of the form 3m or 3m + 1 for some integer m. 20. Show that √ f y positive integer is either is irrational. Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 3 21. Divide by and verify the division algorithm. 22. Solve 23. State and prove basic proportionality theorem. 24. In rhombus ABCD, prove that 25. Prove that 26. Evaluate 27. Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method. Daily wages 100 – 150 150 – 200 200 – 250 250 – 300 300 – 350 Number of workers 10 15 22 17 6 28. Find the median weight of the following students shown in the distribution table. Weight 35 – 40 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 No. of 2 8 14 21 4 1 Students Section – D Question numbers 29 to 34 carry 4 marks each. 29. Obtain all the zeroes of the polynomial if two of its zeroes are √ and √ . 30. A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water. 31. BL and CM are medians of a right angled at . Prove that Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 4 32. If then show that 33. Prove that . . 34. The mean of the distribution of daily wages of 50 workers of a factory is 145.2, find the missing frequencies. Daily Wages (in Rs) 100 – 120 120 – 140 140 – 160 160 – 180 180 – 200 Number of Workers 12 8 10 For solutions, please visit: www.learnnext.com/sample-papers.htm Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 5 Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 6

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