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Atul Vidyalaya Maths paper 1

4 pages, 32 questions, 32 questions with responses, 74 total responses,    0    0
Chirag Kamath
Atul Vidyalaya, Valsad
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ATUL VIDYALAYA THIRD PRELIMINARY EXAMINATION (2014-15) MATHEMATICS STD: X DATE: 06/01/2015 SESSION: I B MM: 80 TIME: 2 hrs GENERAL INSTRUCTION (Two and half hours) Answers to this paper must be written on the paper provided separately. You will NOT allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. This question paper is divided into two sections. Attempt all questions from Section A and any four questions from Section B. The intended marls for questions or parts of questions are given in the brackets [ ]. All working, including rough work , must be clearly shown and should be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. Mathematical tables are provided. SECTION A [40 Marks ] Question 1. (a) Ram purchased a shirt for Rs 300, a cup set for Rs 6700 and a pair of shoes for 1 8 1 2 Rs 1200. Sales tax was charged at the rate of 5%, 8 % & 7 % respectively If the shopkeeper allowed 5% rebate on the bill, what was the amount paid? (b) Find the value of k if ( x k ) is a factor of the polynomial x 3 (k 2 1) x + 2 . Also factorise it further. (c) If 3a + 8b : 3c + 8d = 3a 8b : 3c 8d, then show that a, b, c, d are in proportion. Question 2. 1 1 1 1 = sec tan cos cos sec + tan (a) Prove that: [3] [3] [4] [3] (b) The area enclosed between two concentric circles is 770 sq cm. If the radius of the outer circle is 21 cm. Calculate the radius of the inner circle. [ = 22 ] [3] 7 (c) Point P ( k, m) is reflected in the x-axis to P ( 5, -2). Write down the values of k and m. P is the reflection of P when reflected in the y axis. Write down the co-ordinates of P . Name a single transformation that maps P to P . Question 3. (a) If the mean of the following distribution is 7.5, find the missing frequency f. Variable 5 6 7 8 9 10 11 20 17 f 10 8 6 7 [3] 12 Frequency [4] 6 (b) A rectangular playground has two semicircles along its widths, which also act as diameters. If the sides of the rectangle are 120 m and 21 m, then find the area of the playground. (c) If [m n ] m n [3] = [25] , (i) find all the positive integers m and n (ii) find all the integers m and n Question 4. [4] 1 3 2 (a) Find the nature of the roots of x + 2 x + = 0 and solve it. [3] (b) Find the value of x given that A2 = B [3]

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