KENDRIYA VIDYALAYA GILL NAGAR CHENNAI -96 SUMMATIVE ASSESSMENT TERM I MODEL QUESTION PAPER CLASS X MATHEMATICS TIME: 3 HOURS MAXIMUM MARKS: 90 General Instructions: 1. All Questions are compulsory. 2. The Question paper consists of 34 questions divided into 04 sections A, B,C,D.Section A comprises of 8 questions of 01 mark each, section B comprises of 06 questions of 02 marks each, section C comprises of 10 questions of 03 marks each and section D comprises of 10 questions of 04 marks each. 3. Question nos.01-08 in section A are multiple choice questions where you are to select correct one correct option out of the 04 options. 4. There is no overall choice. However internal choice has been provided in one question of 02 marks each, 03 questions 03 marks each and 02 questions of 04 marks each, you have to attempt only one of the alternatives in all such questions. 5. Use of calculator is not permitted. SECTION A (1 Mark Questions) 1. The least number exactly divisible by 12,15, and 20 is A) 240, B) 540 C) 60 D) 120 2. Which of the following is not a solution of the pair of linear equations 3x-2y =4 and 6x - 4y = 8. A) x =2, y = 1 B) x= 4,y= 4 C) x = 6, y = 7 D) x= 5,y = 3 3. Value of cosec (67 0 + ) - sec (23 0 - ) is: A) 2 B) -2 C) 0 D) Cannot be determined. 4. Which of the following is not an expression for co A) B) (cos C) D) 5. If are the zeros of the polynomial 7x 3 + x 2 13 x +8 the value of is: A) B) C) D).
6. If the sum of the two numbers is 35 and their difference is 13, then the numbers are: A) 23,12 B) 25,10 C) 24,11 D ) 22,15 7. The median of a frequency distribution can be determined graphically from: A) Histogram, B) Frequency polygon C) Ogive D) Frequency curve. 8. In PQR and DEF if.then Ar( is A) 9 : 16 B) 16 :9 C) 3 : 4 D ) 4: 3 SECTION B (02 Mark Questions) 9. In the following figure PQRS is a trapezium. With PQ ll SR and and PQ= 4 cm, find the value of SR. M P Q O S R 10. Is 7x6x5x4x3x2x1 +5 a composite number? Justify your answer. 11. Find the HCF and LCM of 36 and 48 by prime factorization method. 12. If are the zeros of the polynomial x 2 m(x+1) n.express ( in terms of n. 13. If sin =, where 0,find cot and sec If cos3 = cos30 0 sin60 0 - sin30 0 cos60 0, then find the value of 14. The average weight of A, B, C is 45kg.If average weight of A and B is 40 kg and that of B and C is 43 kg.find the weight of B. SCTION C (03 mark Questions) 15. Rocha s mother is five times as old as her daughter Rekha. Five years later, Rocha s mother will be three times as old as her daughter Rekha. Find the present age of Rekha and her mother's age. Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4: 5. Find the numbers.
16. If sin =, find the value of 17. Find unknown entries a, b, c, d, e, and f in the following distribution of heights of students in a class and if the total number of students in the class are 50. Height in c.m 150-155 155-160 160-165 165-170 170-175 175-180 Frequency 12 b 10 d e 2 Cumulative Frequency a 25 c 43 48 f 18. Find the mean of the following frequency distribution. 1 C.I. 0-100 100-200 200-300 300-400 400-500 f 2 3 5 2 3 1 19. Prove that = 1 + sec. cosec Evaluate : 20.In fig, DE BC and AD : DB = 5:4, find 21.If are zeroes of polynomial 6x 3 + 3x 2-5x + 1, then find the value of.
22. Show that 6 + is irrational. Prove that 5 - is an irrational. 23. In PQR, PD QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d and a, b, c, d are positive units, prove that (a + b) (a- b) =(c+d) (c-d). 24.Solve for x and y: SECTION D ( 04 MARK QUESTIONS) 25.Using Euclids division lemma show that the square of any positive integer is of the form 3m or 3m+1 for any integer q. 26. State and Prove Basic proportionality theorem. Prove that ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides. 27.Prove that: 28.Solve the following equations graphically: x -y = 1 and 2x + y = 8. Shade the region between the two lines and y -axis.
29.Prove that: Without using trigonometric tables evaluate : 30 The median of the following data is 525.Find the values of f1 and f2 if total frequency is 100. C.I 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 800-900 900-1000 frequency 2 5 f1 12 17 20 F2 9 7 4 31.If the remainder on division x 3 + 2x 2 + kx + 3 by x - 3 is 21, find the quotient and the value of k. Hence, find the zeroes of the cubic polynomial x 3 + 2x 2 + kx - 18. 32.Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 33.Prove that = sin A + cos A 34.For the data given below draw less than ogive graph and find the median. Marks 0-10 10-20 20-30 30-40 40-50 50-60 Number of students 7 10 23 51 6 3