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MOCK EXAMINATION 1 2017 MATHEMATICS Grade: 10 Time: 2 hrs. Date: 26th Feb, 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 laptop is marked at 17600 inclusive of the sales tax. If the rate of sales tax is 10%, calculate: i. The list price of the laptop ii. The amount of sales tax in . b) The simple interest on a sum of money for 2 years at 4% is 450. Find the compound interest on this sum of money at the same rate for 1 year if the interest is reckoned halfyearly. c) What number should be subtracted from 2x3 5x2 + 5x so that the resulting polynomial has a factor 2x 3? Question 2 3 a) Given A = 0 [3 + 3 + 4] 0 , B = 4 0 and AB = A + B, find the values of a, b and c. Page 1 of 6 b) Without using trigonometrical tables, evaluate: + + 2 tan15 . tan45 . tan75 c) A boy scored the following marks in various class test during a term, each test being marked out of 20. 15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16 i. ii. iii. iv. What are his modal marks? What are his median marks? What are his mean marks? What is the range of marks? Question 3 [3 + 3 + 4] a) Solve: 2x2 + 2x 3 = 0, giving your answer, correct to one decimal place. b) ABC and DBC are right-angled on hypotenuse BC. AC and DB intersect at P. Prove that: AP PC = BP PD. c) A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height. Question 4 [3 + 3 + 4] a) Find the points of trisection of the line segment joining the points (1, 2) and (11, 9). b) Factorize: x3 7x + 6, using factor theorem. c) Use graph paper for the question. A (0,3) and B (3 3, 2) and O(0,0) are the vertices of triangle ABO . (i) Plot the triangle on a graph sheet taking 2 cm = 1 unit on both axes. (ii) Plot D the reflection of B in the y-axis, and write its co-ordinates. (iii) Write down the geometric name of the figure ABOD. (iv) Write the equation of the line of symmetry of the figure ABOD. Page 2 of 6 Section B [40 Marks] (Answer any four Questions) Question 5 [3 + 3 + 4] a) A shopkeeper bought an article at a discount of 15% on the printed price. After charging a sales tax of 5% on the printed price, he sells the article at 630. Find his profit. b) Find the equation of the perpendicular dropped from the point ( 1,2) onto the line joining (1, 4) and (2, 3). c) In the figure given along-side AB = 24 cm and M is the midpoint of AB. Semicircles are drawn on AB, AM and MB as diameters. A circle with centre C touches all three semicircles. Find its radius. Question 6 [3 + 3 + 4] a) Two circles of radii 25 cm and 9 cm touch externally. Find the length off the direct common tangent. b) Prove that: = tan c) Following table shows the marks obtained by 40 students at a short assessment is given below, where a and b are two missing data. If the mean of the distribution is 7.2, find a and b. Marks Number of students 5 6 6 a 7 16 Question 7 8 13 9 b [3 + 3 + 4] a) By purchasing 25 shares of 10 each a man gets 4% profit on his investment. What rate percent is the company paying? What is his dividend if he buys 60 shares? b) In the given figure, APB is the tangent to the circle with centre O. If DPC = 20 and PDC = 42 . Find the values of x, y and z. Page 3 of 6 c) The angle of elevation of the top of a hill from the foot of the tower is 60 and the angle of elevation of the top of the tower from the foot of the hill is 30 . If the tower is 20 m high, find: i. The height of the hill ii. The distance between the hill and the tower. Question 8 [5 + 5] a) Using ruler and compasses only: i. Construct ABC in which BC = 6 cm and ABC = 120 and AB = 3.5 cm. ii. In the above figure, draw a circle with BC as diameter. Find a point P , on the circumference of the circle, which is equidistant from AB and BC. iii. Measure BCP. b) Mrs Anita has an account in the State Bank of India. The following entries are from her pass book: Date Particular Withdrawal( ) Deposit ( ) Balance ( ) 01 01 15 B/F ------- --------- 1276.00 07 01 15 By Cheque ------- 2307.00 3583.00 09 03 15 To self 2000.00 --------- 1583.00 26 03 15 By Cash ------- 6200.00 7783.00 10 06 15 To Cheque 4500.00 -------- 3283.00 15 07 15 By clearing ------- 2629.00 5912.00 18 10 15 To Cheque no. 227 525.00 --------- 5387.00 27 10 15 To self 2700.00 --------- 2687.00 03 11 15 By cash ------- 1500.00 4187.00 06 12 15 To Cheque no. 228 1000.00 --------- 3187.00 23 12 15 By transfer -------- 2928.00 6115.00 Calculate the interest due to her for the year 2015 at 4.5% per annum, if the interest is paid once in a year at the end of December. Also find the total amount she will receive on the 12th of January, by the bank in his saving bank if she closes the account on 12th January, 2016. Page 4 of 6 QUESTION 9 [3 + 3 + 4] a) Ankita and Nagma are friends. They were both born in 1990. What is the probability that they have: i. Same birthday? ii. Different birthdays? b) Two vertices of a triangle are ( 1, 4) and (5, 2). If the centroid is (0, 3), find the third vertex. c) A man has a recurring deposit account in a post office for 3 years at 8% p.a simple interest. If he gets 1998 as interest at the time of maturity, find: i. The monthly instalment, ii. The amount of maturity. QUESTION 10 [3 + 3 + 4] a) In the given figure, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively. Given that AB = 8 cm, calculate PQ. b) If three quantities are in continued proportion, prove that the first is to the third is the duplicate ratio of the first to the second. c) For the following frequency distribution, draw a histogram. Hence, calculate the Mode. Class Frequency 30 - 40 4 40 50 3 50 - 60 8 60 - 70 11 70 - 80 6 QUESTION 11 80 - 90 2 [3 + 3 + 4] a) A spherical ball of lead 6 cm in diameter is melted and recast into three spherical balls. The diameter of two of these are 5 cm and 4 cm respectively. Find the radius of the third ball. b) B takes 16 days less than A to do a piece of work. If both working together can do it in 15 days, in how many days will B alone complete the work? c) P is the solution set of 7x 2 > 4x + 1 and Q is the solution set of 9x 45 5(x 5 ); where x R. Write the solution set and represent the following on a number line. i. P Q, (ii) P Q, (iii) P Q ********************************************************************* Page 5 of 6 . Page 6 of 6
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