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MOCK EXAMINATION 2 - 2017 MATHEMATICS Grade: 10 Time: 2 hrs. Date: 9th Apr, 2017 Max. Marks: 80 [The time stated above is the time allowed for writing the examination. In addition, the first 15 minutes will be the time given for reading the question paper.] INSTRUCTIONS 1. Answer all questions from Section A and any FOUR questions from section B. 2. All working, including rough work, should be done on the same sheet and adjacent to answer. 3. The intended marks for questions or parts of questions are given in brackets [ ]. SECTION A [40 Marks] QUESTION 1 [3 + 3 + 4] a) A man invests 15000 at compound interest, payable annually. After one year his money amounts to 16800. Find i. The rate of interest ii. The interest for the second year iii. The interest for the third year. b) List the solution set of: 2x - 3 < x + 2 3x + 5, x I and graph these values of on a number line. c) A card is drawn from a well shuffled pack of 52 playing cards. Find the probability that the card drawn is i. A red face card. ii. Neither an ace nor a king of red colour. iii. Neither a card of diamonds nor a red queen. Page 1 of 6 QUESTION 2 a) If A = [3 + 3 + 4] 3 3 0 0 , find matrix B such that A2 + 3B = . 1 0 0 0 b) Aarti has a recurring deposit account in a bank for 5 years at 9% per annum simple interest. If she gets 51607.50 at the time of maturity, find the monthly instalment. c) If the line joining the points M (-2,3) and N (5,-4) is perpendicular to the line 2x + py 7 = 0, find the value of p. QUESTION 3 [3 + 3 + 4] a) Without using trigonometric tables, evaluate: Sec 41 sin 49 + cos 49 cosec 41 - (tan 20 tan 60 tan 70 ) b) Using Factor Theorem, factorize the following polynomial completely: 2x3 + 3x2 11x 6. c) In the adjoining figure, triangular piece OAD is removed from a piece of cardboard in the shape of a quadrant of a circle with centre O and radius 7 cm. If OA = 3cm and OD 4cm, find: i. The area of the remaining part ii. The perimeter of the remaining part QUESTION 4 [3 + 3 + 4] a) Points A and B have coordinates (3,2) and (7,6) respectively. Find : i. The slope of AB. ii. The equation of the right bisector of the segment AB. b) In the adjoining figure, DC is tangent to the circle at the point D and ABC is a straight line. i. Prove that ACD ~ DCB. ii. if AB = 10 cm and BC = 8 cm, find the length of DC. Page 2 of 6 c) Use a graph paper for this question, Take 1cm = 1unit on both axes. i. Plot the points A(2,4) and B(-3,-2). ii. Reflect the points A and B in the y-axis to get their images A and B respectively. Write down the coordinate of A and B . iii. Write down the geometrical name of the figure of AA BB iv. Name its line(s) of symmetry. Section B [40 Marks] (Answer any four questions) QUESTION 5 [3 + 3 + 4] a) A shopkeeper buys an article whose marked price is 4000 from a manufacturing company at a discount of 20%. The rate of sales tax (under VAT) on the article is 8%. If he sells the article to a consumer at a discount of 5%, find: i. The VAT paid by the manufacturing company. ii. The VAT paid by the shopkeeper. iii. The amount paid by the consumer. = , find the value of x using the properties of proportion. b) If c) In the figure, DEB = BCA. Prove that BED = BCA. If BD = 4 cm, DC = 6 cm, BE = 5 cm and area of ABC = 44 cm2, find: i. The length of AB ii. Area of BED. iii. Area of quad. AEDC : area of ABC. QUESTION 6 [3 + 3 + 4] a) Find the value of m for which the following equation has equal roots : (m 1) x2 + 2(m + 1)x + 9 = 0 b) The adjoining figure represents a hemisphere of radius 7cm surmounted by a right circular cone of same base radius. If the slant height of the cone is 25cm, find: i. The height of the cone. ii. The volume of the solid iii. The surface area of the solid. Take = Page 3 of 6 c) A man has 60 shares of nominal value 100 and sells them when these are at a premium of 60%. He invests the proceeds in in shares of nominal value 50, quoted at 4% discount, paying 18% dividend annually. Calculate: i. The number of shares he buys. ii. His annual dividend from these shares. QUESTION 7 [3 + 3 + 4] a) The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Find the values of p and q: Class Interval 0 - 20 20 40 40 60 60 80 80 100 100 120 Frequency b) Given A = 0 5 p 10 q 7 8 0 0 2 2 , B = , C = and BA = C2. find the value of p and q. 2 2 2 1 0 c) In the adjoining figure, O is the centre of the circumcircle of triangle ABC and tangents at to the circle at points A and B interest at P. If AOC = 140 and APB = 80 , find the measure of: (i) PAB (ii) ACB (iii) CAB (iv) ABC QUESTION 8 [5 + 5] a) The table given below shows the daily wages of the workers of a factory: Marks 250-255 255-260 260-265 265-270 No. of Students 6 8 7 14 270-275 21 275-280 280-285 285-290 12 9 3 Using a graph paper, draw an ogive for the above distribution. Use your ogive to estimate: i. ii. The median wages. The number of workers getting wages above 280. Page 4 of 6 b) Mrs Shukla has a saving bank account in state bank of India. A page from her passbook has the following entries: Date Particular Withdrawals (in ) Deposits ( in ) Balance (in ) Jan 1 B/F .. 1560.00 Jan - 7 By clearing .. 4000.00 5560.00 Feb - 14 To cheque 2000.00 3560.00 June - 13 By transfer . 5000.00 8560.00 July - 27 To cheque 2015.00 6545.00 Oct - 23 To self 5000.00 1545.00 Nov - 6 To self 500.00 1045.00 Dec - 3 By cash 470 1515 Year 2016 If the interest earned by Mrs Shukla at the end of the year 2016 is 196.25, find the rate of interest paid by the bank. QUESTION 9 a) Prove that: [3 + 3 + 4] = (sec A tan A)2. b) A spherical shell of copper whose external radius is 9 cm, is melted into a conical solid of 28 cm in diameter and of 4 cm height. Find the inner diameter of the shell.( = ) c) Using ruler and compass construct a triangle ABC in which base BC = 6.5 cm, AB = 5 cm and ABC = 120 . i. Construct a circle circumscribing the triangle ABC. ii. Draw a cyclic quadrilateral ABCD so that D is equidistant from A and B. QUESTION 10 [3 + 3 + 4] a) 480 is divided equally among x children. If the children were 20 more, then each would have got 12 less. Find x. b) Two coins are tossed simultaneously once. Find the probability of getting: i. Exactly one head ii. Atleast one head iii. Atmost one head Page 5 of 6 c) From the top of a tower, the angles of depression of the top and bottom of a building, are observed to be 30 and 60 respectively. If the height of the building is 45 metres, find the height of the tower. QUESTION 11 [3 + 3 + 4] a) The price of a TV set inclusive of sales tax at 8% is 23598. Find the amount of sales tax paid. b) In what ratio is the line joining the points (3,4) and (8,-6) divided by the x-axis? Also find the co-ordinates of the point of division. c) A man deposits 600 per month in a recurring deposit account for a period of 3 years. If she gets 23931 at the time of maturity, find the rate of interest *************************************************************************** Page 6 of 6
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