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KAPOL VIDYANIDHI INTERNATIONAL SCHOOL(ICSE) TEMPLE OF KNOWLEDGE STD IX 5.03.21 THIRD TERMINAL EXAMINATION SUBJECT : MATHEMATICS DUR:2hrs 30mins MARKS:80 Answer 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 the time allowed for writing the answers. Attempt 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 (Answer all questions) (40 MARKS) Q 1. a. Rationalise the denominator of 7 - 5 7 + 5 [3] b. If a + b = 10, ab = 21, find the value of 3 ( 2 + 2 ) c. Q2 a. [3] 5000 amounts to 5600 in 1 year compounded annually. Find the rate of interest per annum . Find the compound interest for the year . [4] Factorise the given expression: 3x2 8x + 4 [3] b.S Solve the following pair of equations: [3] 3 3x 5y = - 1 , 2x = y - 3 c. Q3 a. Solve for x and y if 3 x -y = 27 , 3 x+ y = 243 [4] In a circle of radius 10 cm , a chord AB is of length 12cm . Find the perpendicular distance of the chord from the centre . [3] b. Find the value of if ( tan - 1 ) ( cosec 3 - 1) = 0 [3] c. Find the area of a ring shaped region enclosed between two concentric circles of radii 20cm and 15 cm . [4] Page 1 of 5 Q4 a. From the given figure, find the value of x. b. Solve : cos 75 o + sin 12 o - cos 18 o sin 15o cos 78 o sin 72o c. The marks obtained by 30 students is given below: [3] [3] [4] 08 , 17 , 33, 41 , 47 , 23 , 20, 34 09 , 18, 42, 14, 30, 19, 29, 11 36, 48, 40 , 24, 22, 02, 16 , 21, 15, 32, 47 , 44, 33, 01 Prepare a grouped frequency distribution table from given data taking class interval 1 - 10, 11 20 , 21 - 30 . 41 50. Section B (Answer any 4 questions) (40 MARKS) Q5. a. If the distance between the points (4, k ) and (1, 0) is 5 units , find k. b. The cost of fencing a circular field at 9.50 per metre is 2926. Find the cost of ploughing the field at 2.50 per sq metre . c. Plot A (-2 ,0) , B (5,0), C (5, 6) and D (-2 ,6 ). What is the name of the figure formed ? Page 2 of 5 [3] [3] [4] Q6. a. Find the value of (Cos 0 + Cos 45 + Sin 30 ) (Sin 90 - Sin 45 + Cos 60 ) [3] b. The sum of the ages of two brothers is 25 years and their difference is 3 years . Find their ages . [3] c. The area of an isosceles triangle is 12cm2 and its base is 8 cm in length. Find the perimeter of the triangle . [4] In the given figure , ABC is an equilateral triangle . Find the measures of the angles marked x, y, z . [3] b. The mean of eight variables is 10 . Seven of them are 6 ,6, 8 ,10 ,10 ,8 ,7. Find the 8th variable . [3] c. The sides of a triangle are in ratio 4 : 5 : 7. If the perimeter of the triangle is 32cm . Find the area of the triangle . [4] Given 13 sin A = 5, evaluate 4 sin A - 3 cos A tan A [3] Rationalize the denominator of : [3] Q7. a. Q8. a. b. 1 5 3 - 3 5 c. Solve the following equations by cross multiplication : x - 3 y = 7 , 3 x - 3 y = 15 Page 3 of 5 [4] Q9. a. b. On a certain sum of money , the compound interest for 2 years is 2172. If the rates of interest for successive years are 6% and 8% per year ,then find the sum of money invested . [4] Solve graphically the given equations : [6] x 2y = 0 x+y=9 Q10 a. b. 70 Evaluate 20 + 59 31 - 8 sin2 30o [3] Find the co-ordinates of points on the x - axis which are at a distance of 5 units from the point ( 6, - 3) . c. From the given figure , find the length of sides PR and SR . Hence find the area of SRP . [3] [4] P 24cm S 20cm R 15cm Q11 a. c. [3] Solve the following simultaneous equations : 2 b. Q + 5 = 1 4 1 , + 1 1 = 12 [3] Factorise : 9a2 + 3a - 8b - 64 b2 [4] Draw a frequency polygon to represent the following data : Class interval Frequency 10 - 20 10 20 - 30 25 30 - 40 12 40 - 50 08 Page 4 of 5 50 - 60 05 Page 5 of 5
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