Class 10 - Sample Question Paper (Mathematics) II – 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. A composite number has at least ________ factors a) 1 b) 2 c) 3 d) None 2. If the HCF of 96 and 404 is 4 then its LCM is a) 6969 b) 9696 c) 9966 d) 6699 3. The remainder when a) b) 48 c) – d) is divided by Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. is Page 1 4. If a pair of linear equations has unique solution then the lines are a) Intersecting lines b) Parallel lines c) Coincident lines d) None of these 5. Two right triangles ABC and DEF right angled at B and E respectively are similar. If then a) b) c) d) 6. The maximum value of a) 0 b) 1 c) d) 7. If a) b) c) d) 8. The value of is then √ at is 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 mean of 4, 5, a) 5 b) 15 c) d) 8, p is 5 then p = Section – B Question numbers 11 to 18 carry 2 marks each. 11. Without actually performing the long division, state whether the will have a terminating decimal expansion or a non-terminating repeating decimal expansion. 12. Find a quadratic polynomial with √ as the sum and product of its zeroes respectively. 13. The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number. 14. If AD d PM re med PQR, prove that f r gle ABC d PQR re pe vely where Δ ABC ~ Δ . 15. Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD. 16. If and √ then find A and B. 17. The mean of 10 observations is 15 and the mean of 15 observations is 10. Find the mean of 25 observations. 18. Write the formula of median for grouped data and explain each term. Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 3 Section – C Question numbers 19 to 28 carry 3 marks each. 19. U e Eu l d’ d v lemm to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8. 20. Show that √ is irrational. 21. Verify that 3, –1, are the zeroes of the cubic polynomial p(x) , and then verify the relationship between the zeroes and the coefficients. 22. Solve the following system of linear equations graphically and find the area of the region bounded by these lines and the x-axis. 23. State and prove Pythagoras theorem. 24. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals. 25. Find the mode of the given data: Age 5 – 15 15 – 25 25 – 35 Number of 8 22 32 patients 26. If tan θ 27. If 35 – 45 26 45 – 55 12 Ev lu e ( then prove that 28. Find the mean of the following data: Classes 0 – 19 20 – 39 40 – 59 Frequency 5 18 25 60 – 79 16 Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. ) 80 – 99 6 Page 4 Section – D Question numbers 29 to 34 carry 4 marks each. 29. If the sum of the squares of zeroes of the polynomial 𝑘 is 6 findthe value of k. 30. Solve for x and y 𝑎 [ 𝑎 𝑏 𝑎 𝑏 ] 𝑏 [ 𝑏 𝑎 𝑏 𝑎 ] 𝑎 𝑎 𝑏 ;𝑏 𝑎 𝑎 𝑏 31. In an equilateral triangle ABC, D is a point on side BC such that BD = BC. Prove that 9AD2 = 7AB2 32. Two ships are sailing in the sea on the either side of the light house, the angles of depression of two ships as observed from the top of the lighthouse are 60° and 45° respectively. If the distance between the ships is height of the lighthouse. 33. If e √ √ , find the then show that 34. In a talent test conducted by a trust, 1000 students appeared and the marks scored by them are given in the following distribution table. Draw an ogive and use it to answer the following : a) Find the median. b) How many students scored less than or equal to 45 marks Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 5 For solutions, please visit: www.learnnext.com/sample-papers.htm Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 6 Copyright © 2013. Next Education India Pvt. Ltd. All rights reserved. Page 7

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