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CBSE Sample Paper -02 SUMMATIVE ASSESSMENT I Class X Mathematics Time allowed: 3 hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper comprises of 31 questions divided into four sections A, B, C and D. You are to attempt all the four sections. c) Questions 1 to 4 in section A are one mark questions. d) Questions 5 to 10 in section B are two marks questions. e) Questions 11 to 20 in section C are three marks questions. f) Questions 21 to 31 in section D are four marks questions. g) There is no overall choice in the question paper. Use of calculators is not permitted. 1. SECTION A Is the triangle with sides 12 cm, 16 cm and 18 cm a right triangle? Give reason. 2. Express 0.6 as rational number in simplest form. 3. If sec 2 (1 + sin ) = k , then find they value of k. 4. Evaluate: tan 26o cot 64o SECTION B 1 , 0o 90o. sec 5. Find maximum value of 6. Find the HCF of 96 and 404 by prime factorisation method. Hence, find their LCM. 7. In a ABC , if C = 90o , prove that sin 2 A + sin 2 B = 1 . 8. Sum of two numbers if 35 and their difference is 13. Find the numbers. 9. The number of students absent in a school was recorded every day for 147 days and the raw data was presented in the form of the following frequency table. No.of students 5 6 7 8 9 10 11 12 13 15 18 20 1 5 11 14 16 13 10 70 4 1 1 1 absent No. of days Obtain the median and describe what information it conveys. 10. In an isosceles ABC , if AC=BC and AB 2 = 2 AC 2 then find C . Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks SECTION C n 1 + n + 1 is rational. 11. Show that there is no positive integer n for which 12. E and F are points on the sides PQ and PR respectively of a PQR . Show that EF||QR. If PQ=1.28 cm, PR=2.56 cm, PE=0.18 cm and PE=0.36 cm. 13. The taxi charges in a city comprise of a fixed charge together with the charge for the distance covered. For a journey of 10 km, the charge paid is Rs 75 and for a journey of 15 km, the charge paid is Rs 110. What will a person have to pay for travelling a distance of 25 km? 14. 3 If sin A = , Calculate cos A and tan A. 4 15. Let ABC be a triangle and D and E be two points on side AB such that AD = BE. If DP || BC and EQ || AC, then prove that PQ || AB. 16. Find the zeros of the polynomial f(u) = 4u2 + 8u and verify the relationship between the zeros and its coefficients. sin 2 20o + sin 2 70o sin(90o .sin cos(90o .cos + + cos 2 20o + cos 2 70o tan cot 17. Evaluate the following: 18. If the median of the distribution given below is 28.5, find the values of x and y. Class interval 10-20 20-30 30-40 40-50 50-60 Total Frequency 19. 0-10 5 x 20 15 y 5 60 Solve: ax + by = c bx + ay = 1 + c 20. If sec = x + 1 1 , prove that sec + tan = 2 x or . 4x 2x SECTION D 1 21. 2 Let a, b, c and pbe rational numbers such that p is not a perfect cube. If a + bp 3 + cp 3 = 0 , then prove that a = b = c = 0. Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks cos 2 B cos 2 A sin 2 A sin 2 B . = cos 2 B cos 2 A cos 2 A cos 2 B 22. Prove that: tan 2 A tan 2 B = 23. The perpendicular from A on side BC of a ABC intersect BC at D such that DB = 3CD (see Fig. 4.40). Prove that 2 AB 2 = 2 AC 2 + 2 BC 2 . 24. A frequency distribution of the life times of 400 T.V. picture tubes tested in a company is given below. Find the average life of a tube. Life time (in hours) Frequency Life time (in hours) Frequency 300-399 14 800-899 62 400-499 46 900-999 48 500-599 58 1000-1099 22 600-699 76 1100-1199 6 700-799 68 1 1 1 1 = . (cos ecx + cot x ) sin x sin x (cos ecx cot x ) 25. Prove that: 26. Find the values of a andb so that x4 + x3 + 8x2 + ax + b is divisible by x2 + 1. 27. Solve the following system of linear equations graphically. x y=1 2x + y = 8 Shade the area bounded by these two lines and y-axis. Also, determine this area. 28. In trapezium ABCD, AB || DC and DC = 2AB. A line EF drawn parallel to AB cuts AD in F and BC in E such that 29. BE 3 = . Diagonal DB intersects EF at G. Prove that 7FE = 10AB. EC 4 In a ABC, right angled at C and A = B, (i) Is cosA = cosB? (ii) Is tanA = tanB? What about other trigonometric ratios for A and B. Will they be equal? Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 30. A sweet seller has 420 kajuburfis and 130 badamburfis. She wants to stack them in such a way that each stack has the same number and they take up the least area of the tray. What is the number of burfis that can be placed in each stack for this purpose? 31. In a housing society, people decided to do rainwater harvesting. Rainwater is collected in the underground tank at the rate of 30 cm3/sec. Taking volume of water collected in x seconds as ycm3. a. Form a linear equation. b. Write it in standard form as ax + by + c = 0. c. Which values are promoted by the members of this society? Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks

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