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SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE Class Subject Exam Date Marks Time Total No. of Printed sides 10 Mathematics Reprelim 09.01.2017 80 2 hrs. 3 General Instructions: 1. Attempt all questions from section-A. 2. Attempt any 4 complete questions from section B 3. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. 4. Omission of essential working will result in loss of marks. 5. Mathematical tables are provided. SECTION A (40 Marks) Attempt all questions from this section Question 1 A) If AB = BA find the values of x and y where A = [ ] 5 2 7 3 and B = [ ] 3 x y 5 . [3] B) Solve the following quadratic equation using the formula and give your answer correct to two significant figures: 3 x2 10 x + 4=0 [3] C) Show that the progression 4 , 5/2 , 1 , 1 /2 , 2 , is an A.P. Find its ii) common difference iii) 25th term. i) first term [4] Question 2 A) Priya deposits a certain sum of money each month in a recurring deposit account of a bank. If the rate of interest is 9% per annum and Priya gets Rs. 23139 from the bank after 1 years , find the value of his monthly instalment. [3] B) A hemisphere is surmounted by a cone of slant height 16cm. The surface area of the solid is 660 cm2. Find the radius of the base of the cone. [3] C) Use the factor theorem to factorise completely the polynomial 6x 3 + 11x2 3x 2 [4] Question 3 A) A manufacturer produces an article for Rs. 5000 and sells it to a wholesaler. The wholesaler sells it to a retailer. VAT charged is 10% and profit made at each stage is Rs 1000. Calculate i) the total VAT collected by the Government on the sale of the article. ii) The price at which the article can be bought by the customer. [3] B) Solve the following inequality and represent the solution set on the number line: 2 x 1 2 1 , x N . 3 2 6 [3] C) In the adjoining figure O is the centre of the circle, in which ORS = 58 and Reflex QOR = 250 . Find QSR , OQR and QPS . [4] Question 4 A) The mean of 8, 10, x+1, x+3, x+4 and 19 is 13. Find i) the value of x ii) the median. 3 B) Prove that : sin A 2 sin A 2 cos 3 A cos A = tan A. [3] 1 [3] C) In ABC , ABC = DAC , AB = 8 cm, AC = 4 cm and AD = 5 cm. i) Prove that : ACD BCA [4] ii) find BC and CD iii) find area( ACD) : area ( ABC). SECTION B ( Attempt any four complete questions from this section ) Question 5 A) A card is drawn at random from a pack of well shuffled playing cards. Find the probability that the card drawn is i) a multiple of 3 ii) a black face card iii) neither a club nor a king. [3] B) If A = [ 1 4 3 2 ] find the value of A2 2I where I is the unit matrix of order 2. C) Use graph paper to answer this question. Plot A (2 , 3) and B (6 , 3 ). i) Reflect A in origin to get the image D, and write its coordinates. ii) Reflect A in the x-axis to get the image C, and write its coordinates. iii) Give a geometrical name for the figure ABCD. iv) Find the area of the figure ABCD. [3] [4] Question 6 1 1 1 A) How many terms of the G.P 1, , , . must be taken to make the sum equal to 2 4 8 85 . 128 [3] B) Twenty-one glass spheres each od radius 2 cm are packed in to a rectangular box of internal dimensions 16 cm X 8 cm X 8 cm and then the box is completely filled with water. Find the volume of water filled in the box. [3] C) In what ratio the line y = 3 divide the line joining the points A (2 , 6) and B (- 12, - 1)? Find the coordinates of the point of intersection. [4] Question 7 A) A rectangular tank has length 4m , width 3m and capacity 30 m 3. A small model of the tank is made with capacity 240 cm3. Find i) the scale factor ii) the length of the model. [3] B) Chords AB and CD intersect at a point P. AP = 3cm, CD = 10cm and PB = 8cm.Find the length of CP. [3] C) Calculate the mean of the distribution given below, using step deviation method. [4] Marks No. of students 11 20 2 21 30 6 31 40 10 41 50 12 Question 8 2 51 60 9 61 70 7 71 - 80 4 A) A man buys 400, twenty rupee shares at a premium of Rs. 8 each and receives a dividend of 12% Find : i) the amount invested by him ii) his total income from the shares iii) the percentage of return on his money. [3] B) In the adjoining figure, ABC is a triangle. PQ BC. Prove that the [3] median AD bisects PQ. C) Two men are standing on the either side of the tower. They measure the angles of elevation of the top of the tower as 27 and 34 respectively. If the height of the tower is 50m, find the distance between the two men. [4] Question 9 A) ABCD is a kite. B ( 7 , - 1) and D ( 9 , - 5) are the end points of the shorter diagonal. Find the equation of the longer diagonal. [3] B) The weight of 60 boys are given in the following distribution table. Weight(kg) 39 37 No. of boys 11 10 Find i) the median ii) the lower quartile. 41 11 [3] 38 9 40 19 C) A wire of length 60 cm is bent to for a right angled triangle and its hypotenuse is 26 cm. Find the other two sides of the triangle. [4] Question 10. ABC A) Using ruler and compasses only, construct ABC with BC = 6 cm, = 120 and AB = 3.5 cm. Draw a circle with BC as diameter. Find the point(s) on the circumference which is equidistant from AB and AC . [4] B) Age of 200 students from a school who participated in a drawing competition is tabulated as follows: [6] Age in 4 6 6 8 8 10 10 12 12 14 14 16 16 18 years No. of 8 10 20 46 56 38 22 students Draw an ogive for the given distribution on a graph sheet and use it to find : i) the median ii) the number of students older than 15 years iii) the upper quartile. Question 11. A) Using properties of proportion solve for x, x 0 . x 2 + x 3 x 3 = 4 x 2+ 3 x 2 . 3 x 2 [3] B) In the adjoining figure , O is the centre of the circle . AT and BT are the tangents. If ATB = 70 . Find AOB and AQB . [3] C) Using ruler and compasses only, construct a ABC, given that AB = 6cm, BC = 8cm and median AM = 5cm. Draw an incircle to the triangle. 3 [4] ******************************** 4
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