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ICSE Prelims 2017 : Mathematics

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Rashmi
The Indian Public School, Dehradun

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THE INDIAN PUBLIC SCHOOL, DEHRADUN PRE-BOARD-I 2016-17 MATHEMATICS/CLASS X TIME: 2Hrs30Mins MM: 80 RST: 35 Answers to this paper must be written on the paper provided separately. You will not be allowed to write during first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is allowed for writing the answer. Answer all questions from section A and any four questions from section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in the loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Section-A (40 Marks) Question 1. (a) On a certain sum of money, the difference between the compound interest for a year, payable half yearly, and the simple interest for a year is Rs. 128. Find the sum lent out, if the rate of interest in both case is 8%. [3] (b) Solve the following in equation and represent the solution set on the number line. 1 15 7 x >2 x 27 , x N [3] (c) A die has 6 faces marked by the given numbers as shown below: [4] 1 2 3 -1 -2 -3 The die is thrown once. What is the probability of getting? (i) (ii) (iii) A positive integer. An integer greater than -3. The smallest integer. Question 2. (a) If A= [ 1 0 1 7 ] , then find the value of k, so that A =8A+kI. 2 [3] (b) Sandhya has a 4 years recurring deposit account in State bank of India and deposits Rs.2500 per month. If she receives Rs.149400 at the time of maturity, find the rate of interest. [3] (c) (i) In the given figure, a right triangle BOA is given. C is the midpoint of the hypotenuse AB. Show that it is equidistance from the vertices O, A and B. (ii) If A (1, 0), B (5, 3), C (2, 7) are the vertices of a parallelogram ABCD, find the coordinates of the fourth vertex. [4] Question 3. (a) Without using trigonometric tables, evaluate: cos2 20 + cos2 70 tan 45 + tan 13 tan23 tan 30 tan 67 tan77 . sin2 25 + sin2 65 2 (b) Using factor theorem, factorize 3+ 7 x + x 10 . :2 x 2 ( ) [3] [3] (c) ABC is an equilateral triangle of side 6cm. A, B and C are the centers of circular areas of radius 3cm. Find the area of the shaded region correct up to 2 places of decimal. (use =3.142 and 3=1.732 ) [4] Question 4. (a) If P= 4 xy P+2 x P+2 y , find the value of + . X+y P 2 x P 2 y [3] (b) (i) A point P(a, b) on reflection in the y-axis is mapped onto P (-3,4). Write the values of a and b. (ii) P is the image of P when reflected in the x-axis. Write down the coordinates of P . (ii) P is the image of P when reflected in the line x=3, parallel to the y-axis. Write the coordinate of P . [3] (c) In the given figure, in right angled ABC, the perpendicular BD on hypotenuse AC is drawn, prove that. [4] 2 2 (i) AC x AD= AB (ii) AC x CD= BC SECTION-B (40 MARKS) Attempt any four questions from this section. Question 5. (a) An article is available for Rs 2750 inclusive of sales tax at the rate of 10%. Find its list price. What will be its new selling price, if the rate of sales tax to 12%? [3] x y z x3 y3 z3 3 xyz (b) If a = b = c ,then prove that 3 + 3 + 3 = abc . [3] a b c (c) In the given figure, AB is a chord of the circle with center O and BT in tangent to the circle. If OAB=35 , find the value of x and y. Question 6. (a) A (3, 5) and B (-2, 3) are two points. Find (i) The gradient of AB (ii) Equation of AB [3] (iii) The coordinates of the point, where AB intersects the x-axis. (b) A man buys 350 hundred-rupee shares of a company at a premium of 20% from the market. The company pays 12% dividend annually. Find [3] (i) His total investment made by man (ii) His annual income from the shares, and (iii) The rate of interest on his investment. (c) A solid cylinder of diameter 12cm and height 15cm is melted and recast into 12 toys in the shape of a right circular cone mounted on a hemisphere. Find (i) the radius of the hemisphere and (ii) the total height of the toy, if the height of the cone is three times the radius. [4] (iv) Question 7. (a) Find the mean by step-deviation method. (v) Marks (vii) 0-80 (viii) 80-160 (ix) 160-240 (x) 240-320 (xi) 320-400 [4] (vi) Number of students (xii) 22 (xiii) 35 (xiv) 44 (xv) 25 (xvi) 24 (xvii) (b) In this figure, chords AB and CD intersect at P. if AB=5 cm, BP=3cm and PD=4cm, find the length of CD. If PT is tangent to the circle, find its length correct to 1 d.p. (xviii) (c) Find the value of x and y, when (xix) [ ][ ] [ ] [ ] 4 3 x +2 4 = 2 2 1 2 5 4y (xx) Question 8. (a) A sum of money is lent at compound interest payable annually. If the interest for the second year and third year are Rs. 660 and Rs. 726 respectively, find the rate and the sum. [4] (b) Use ruler and compass only for this question. (xxi) Construct PQR, where PQ=4.5 cm and QR=6cm and PQR=60 and construct a circle of radius 2cm to touch AB and AC. [3] cot cot 1 . (c) Prove that, 1+tan = 2 sec 2 [3] (xxii) Question 9. (a) If (x+2) and (x-3) are factors of x 3+ ax+ b , find the value of a and b. with these values of a and b, factorize the given expression. [3] 2 (b) Solve: 5(3 x+ 1) +6 ( 3 x+ 1 ) 8=0 . [3] (c) A page from Vikrant s Saving Bank Account is given below (xxiii) Date (xxiv) Partic (xxv) Withd (xxvi) Depo (xxvii) Ba ulars rawal sits lance s (xxviii) 01. (xxxiv) B/ (xl) ----(xlvi) ---(lii) 3400. 01.20 F (xli) --(xlvii)2100. 00 04 (xxxv) By (xlii) 3500.0 00 (liii) 5500. (xxix) 08.01. cash 0 (xlviii) --00 2004 (xxxvi) To (xliii) --(liv) 2000. (xxx) 18.02. chequ (xliv) 500.00 (xlix) 1600. 00 2004 e (xlv) ----00 (lv) 3600. (xxxi) 19.05. (xxxvii) By (l) ---00 2004 cash (li) 1100. (lvi) 3100. (xxxii) 15. (xxxviii) To 00 00 07.20 self (lvii) 4200. 04 (xxxix) By 00 (xxxiii) 07. cash 10.20 04 (lviii) On 30.10.2004 he closed the account. Find the interest he received on closing the account when the rate of interest was 5% per annum. (lix) Question 10. (a) A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost him Rs. 1 less. How many books did he buy? [4] (b) Marks obtained by 200 students in a test were recorded as given below [6] (lx) M (lxi) (lxii) (lxiii) (lxiv) (lxv) (lxvi) (lxvii) (lxviii) a 1 2 3 4 5 6 7 9 r k s (lxix) N (lxx) (lxxi) (lxxii) (lxxiii) (lxxiv) (lxxv) (lxxvi) (lxxvii) u 7 1 2 4 5 3 1 7 m b e r o f s t u d e n t s (lxxviii) (lxxix) Draw the cumulative frequency table. From the graph, find (i) The median (ii) The number of students scoring more than 35% marks. (lxxx)

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