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ICSE Class X Prelims 2022 : Mathematics (Greenwood High International School, Bengaluru)

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GREENWOOD HIGH TERM EXAMINATION - 1 SEPT OCT 2021 MATHEMATICS 1 Grade: 9 Time: 2 hours 2 Date: 20/09/2021 Max. Mark: 80 Answers to this paper must be written on A4 paper separately. You will not be allowed to write during the 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 loss of marks. This paper consists of 5 printed sides. SECTION A (40 Marks) Attempt all questions from this Section Question 1 (a) If x = 1 2, find the value of x2 + 1 [3] 2 (b) If tan x + cot x = 2, find tan2 x + cot2 x [3] (c) In the given figure D, E and F are the mid-points of the sides BC, CA and AB respectively of ABC. If AB = 6 cm, BC = 4.8 cm and CA = 5.6 cm, find the perimeter of : A (i) the trapezium FBCE E F (ii) the triangle DEF B D C [4] Page 1 of 5 Question 2 (a) Find the length of AB, given A ( 2, 4) and B (7, 8) [3] (b) Factorise: a2 + b2 2(ab ac + bc) [3] (c) If the sum of two numbers is 7 and sum of their cubes is 133, find the sum of their squares. [4] Question 3 2 (a) Given: (80 + ) = (0.6)2 3x 3 , find x. [3] A (b) In the given triangle AB = PQ BR = QC AB BC and PQ RQ Prove that: AC = PR P B R C (c) Draw a frequency polygon with respect to the following data Class interval Frequency 120-130 12 130-140 16 140-150 30 150-160 20 160-170 14 Q [3] [4] 170-180 8 Question 4 (a) Calculate the mean and the median of the following distribution: 96, 111, 108, 99, 115, 89, 82, 101, 96 and 77 [3] (b) If (a2 + b2 + c2) = 74 and ab + bc + ac = 61, find (a + b + c). (c) Solve for x and y: 20 + + 3 = 7, 8 15 + =5 [3] [4] Page 2 of 5 SECTION B (40 Marks) Attempt any four questions from this Section Question 5 (a) If a = 2 1 2 2 (b) Given: ,b= 2+ 1 2 2 +1 and a b = 0, find the value of x. 1 1 2 3 = 2 , find x3 (c) If 8cot x = 15, find [3] [3] (2 + 2 sin )(1 sin ) [4] (1 + cos )(2 2 cos ) Question 6 (a) Prove that the medians of an equilateral triangle are of the same length. [3] (b) Without using trigonometric tables, find the value of: cos2 45 + sin2 60 + sin2 30 [3] (c) Using a graph paper find the solution of the simultaneous equations: 2x + 3y = 8 and 4x y = 2 Question 7 [4] P (a) In the given figure, PSR = 90 If PQ = 13 cm, PS = 12 cm, RQ = 4 cm, calculate the length of PR. [3] 2 1 1 9 (b) Simplify: ( ) 2 3(8)3 (4)0 + ( ) 2 4 16 S Q R [3] (c) A two-digit number is seven times the sum of the digits. The number formed by reversing the digits is 18 less than the original number. Find the number. [4] Page 3 of 5 Question 8 (a) If 5 1 5 + 1 + 5 + 1 = a + b 5 , Find the values of a and b. 5 1 [3] (b) Factorise: x6 26x3 27 [3] (c) Find the mean of the following data (Express your answer correct to two places of decimal) [4] x f 25 5 35 10 45 19 55 24 65 18 75 6 Question 9 (a) Factorise: 9x2 4a2 + 4ay y2 [3] (b) Ten percent of the red balls were added to twenty percent of blue balls and the total was 24. Three times the number of red balls exceeds the number of blue balls by 20. How many red balls and how many blue balls are there? [3] (c) Prove that the quadrilateral formed by joining the mid points of the adjacent sides of a rhombus is a rectangle. [4] Question 10 (a) From the following table given the marks of 37 students of a class find the median marks obtained. [3] Marks obtained Frequency 20 9 22 4 17 5 15 3 25 6 30 10 (b) If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5), find the value of p. [3] (c) A man sees the top of a building 12 m high by focusing his binoculars at an angle of 600 to the horizontal. Find the distance of the man from the building. (Take 3 = 1.73) [4] Page 4 of 5 Question 11 (a) Simplify: 6 2 + 3 + 3 2 6 + 3 4 3 [3] 6 + 2 (b) Without using trigonometric tables evaluate: tan 50 tan 350 tan 600 tan 550 tan 850 [3] R (c) In the adjoining figure, RP = RQ and M and N are points on the sides RQ and RP respectively of triangle PQR such that QM = PN. Prove that OP = OQ where O is the point of intersection of PM and QN. N M O P Q [4] Page 5 of 5

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