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Mathematics (3 hours) Prelim -1 2024-25 GRADE: X Max. Marks: 80 Answers to this Paper must be written on the paper provided 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 I and any four questions from Section II. The intended marks for questions or parts of questions, are given in brackets [ ]. _______________________________________________________________________ SECTION I (40 Marks) Attempt all questions from this Section Question 1 (a) [15] If ( 3), (2 + 1) (4 + 3) are three consecutive terms of an A.P., find the value of k (i) 2 (ii) -2 ICSE This Paper consists of 12 printed pages Turn over (iii) 0 (iv) 4 Sunil Kumar invests Rs 36,000 in buying Rs 100 shares at Rs 20 premium. The dividend is 15% per annum, the percentage return on his investment. (b) (i) 50/3% (ii) 20% (iii) 12.5 % (iv) 15 % (c) If = ( (i) ( 0 0 0 ) 0 (ii) ( 1 3 2 ) 4 (iii) ( 1 3 (iv) ( 2 6 1 3 2 1 ) and = ( 4 0 0 ) , what is ? 1 2 ) 4 4 ) 8 The solution of the quadratic equation 3( + 3) = 0 (d) correct to two significant figures (i) 4.9, 1.9 (ii) 4.854, 1.854 (iii) 4.85, 1.854 (iv) ICSE2 4.85, 1.85 In the adjoining figure, AC is a diameter of the circle. (e) AP= 3 cm and PB = 4 cm and QP AB. If the area of APQ is 18 2 , then the area of shaded portion QPBC is (i) 49 2 (ii) 32 2 (iii) 80 2 (iv) 98 2 In a GP, if the first term is 5 and the common ratio is r , the ratio of the 6th term to the 3rd term is 27. What is the value of r ? (f) (i) 2 (ii) 3 (iii) 1.5 (iv) 4 On a number line, which inequality does a shaded circle at 7 with a line extending to the left represent? (g) (h) (i) < 7 , (ii) 7 , (iii) 7 , (iv) 7 , A point (4, 7) is reflected first across the and then across the axis. What are the coordinates of the final image? ICSE3Turn over (i) ( 4, 7) (ii) (4, 7) (iii) ( 4,7) (iv) (4,7) Offices in Bangalore are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. The probability that they remain absent on consecutive days on: (i) (i) 2 5 (ii) 4 25 (iii) 1 5 (iv) 8 25 The angle of elevation from a point 30 feet from the base of a pole, of height h, as level ground to the top of the pole is 45 . Which equation can be used to find the height of the pole. (j) (i) 45 = /30 (ii) 45 = 30/ (iii) 45 = /30 (iv) 45 = /30 A dealer in Patna (Bihar) sold a TV to a consumer in Gaya (Bihar). The marked price of the TV was 25,000 and the dealer offered a discount of 20%. The rate of GST is 28%. Discount received by the consumer (k) (i) ICSE4 2000 (ii) 5000 (iii) 7000 (iv) 3500 The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas in the two cases is (l) (i) 2:3 (ii) 3:2 (iii) 8:27 (iv) 4:9 Assertion (A): The point dividing the line joining A(2,3) and B(8,7) in the ratio 1:1 is (6,5). (m) Reason (R): The section formula is used to find the coordinates of a point dividing a line segment in a given ratio. (i) Both A and R are true, and R is the correct explanation of A. (ii) Both A and R are true, but R is not the correct explanation of A. (iii) A is true, but R is false. (iv) A is false, but R is true. If two triangles are similar and the ratio of the areas of the triangles is 9:16 ,what is the ratio of their corresponding sides? (n) (i) 3:4 (ii) 4:5 (iii) 9:16 (iv) 16:9 ICSE5Turn over The value of cos 0 . cos 1 . cos 2 . cos 3 cos 89 cos 90 is (o) (i) 1 (ii) -1 (iii) 0 (iv) 1 2 Q2 (a) In the adjoining diagram and are the tangents to the circle with centre 4 and radius 7 cm. Given , = 25 . Find: a) Length of PR b) Value of , i.e. c) , in the nearest degree. (use mathematical tables) (b) The vertices of a triangle ABC are A(0,5), B(-1,-2) and C(11,7). Write down the 4 equation of BC. Find, i) The equation of line through A and perpendicular to BC. ii) The co-ordinates of the point P, where the perpendicular through A , as obtained in (i) meets BC. (c) The sequence 2,9,16, is given. (a) Identify if the given sequence is an AP or a GP. Give reasons to support your answer. (b) Find the 20th term of the sequence. (c) Find the difference between the sum of its first 22 and 25 terms. (d)If k is added to each of the above terms, will the new sequence be in A.P. or G.P.? ICSE6 4 Q3 (a) Given 9 2 4 is a factor of 9 3 2 + 8. 4 a) Find the value of and using the remainder and factor theorem. b) Factorise the given polynomial completely. (b) A hemispherical tank full of water is emptied by a pipe at the rate of 25 7 liters per 4 second. How much time will it take to empty half the tank, if it is 3 m in diameter? Also find the cost of painting the closed tank if cost of painting is Rs. 26 per 2 . (c) Plot the points A(2,2), and B (6, -2) in the graph and answer the following: (a) 5 Reflect points A in origin to point D and write the co-ordinates of point D. (b) Reflect points A in line y = - 2 to point C and write the co-ordinates of points C. (c) Find a point P on CD which is invariant under reflection in x = 0, write its coordinates. (d) Write the geometrical name of the closed figure ABCD. (e) Write the co-ordinates of the point of intersection of the diagonals of ABCD. Section B Attempt any four questions Q4 (a) 3 Prove that: sec +tan 1 cos = tan sec +1 1 (b) A man invested 45,000 in 15% 100 shares quoted at 125. When the market value of these share rose to 140. He sold same shares, just enough to raise 8,400 calculate. (i) The number of shares he still holds. (ii) The dividend due to him on these remaining shares. ICSE7Turn over 3 (c) Use ruler and compass only for answering this question. Draw a circle of radius 4 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P. Measure and write down the length of any one tangent Q5 (a) Using properties of proportion, solve for . Given that is positive. 2 + 4 2 1 2 4 2 1 (b) 3 =4 Amit deposited 600 per month in a recurring deposit account. The bank pays a 3 simple interest of 12% p.a. Calculate the: (a) number of monthly instalments Amit deposits to get a maturity amount of 11826? (b) total interest paid by the bank. (c) total amount deposited by him. (c) In the given figure, an isosceles is inscribed in a circle with centre O. PQ 4 is tangent to the circle at C. OM is perpendicular to chord AC and = 65 . Find: i) ii) iii) Q6 (a) The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is 1/5. The probability of selecting a black marble at random from the same jar is 1/4. If the jar contains 11 green marbles, find the total number of marbles in the jar. ICSE8 3 (b) The marked price of a toy is same as the percentage of GST that is charged. The 3 price of the toy is 24 including GST. Taking the marked price as , form an equation and solve it to find . (c) If , , are in A.P. and , , are in G.P., whereas , , are also in G.P. Show 4 that: 2 , 2 , 2 are in A.P. Q7 (a) (b) AB is a diameter of a circle with centre ( 2,5) and (3, 7). Find: i) The length of the radius ii) The coordinate of point . The following table gives the petrol prices per litre for a period of 50 days. Price 85-90 No of days 12 90-95 95-100 100-105 105-110 10 8 15 5 3 3 Find the mean price of petrol per litre to the nearest rupee using step-deviation method. (c) In the given figure (not drawn to scale), BC is parallel to EF, CD is parallel to FG, AE: EB = 2:3, BAD= 70 , ACB = 105 , ADC = 40 and AC is bisector of BAD. (a) Prove AEF ~ AGF (b) Find: i. AG: AD ii. area of ACB: area ACD iii. area of quadrilateral EFCB: area of AEF Q8 ICSE9Turn over 4 (a) 3 A drone camera is used to shoot an object P from two different positions R and S along the same vertical line QRS. The angle of depression of the object P from these two positions are 35 and 60 respectively as shown in the diagram. If the distance of the objects P from point Q is 50 metres, then find the distance between R and S correct to the nearest metres. (b) Solve the following linear inequation and represent the solution set on the number 3 line. 4 19 < (c) 3 2 2 + , 2 5 4 There is a rectangular field whose length is 48 m and width is 40 m. A flower bed is prepared in its center leaving a path al l around the flower bed. The total cost 40 of laying the flower bed and gravelling the path at 20 and 15 per square meter, respectively is 37540. Find the width of 48 the gravel path. Q9 (a) Construct a triangle ABC such that AB = 7cm, BC = 6cm and CA = 5cm. (use ruler and compass to do so). (a) Draw the locus of the points such that (i) it is equidistant from BC and BA. (ii) it is equidistant from points A and B. (b) Mark P where the loci (i) and (ii) meet , measure and write length of PA. ICSE10 3 (b) 3 The model of a building is constructed with the scale factor 1:30. a) If the height of the model is 80 cm , find the actual height of the building in metres. b) If the actual volume of a tank at the top of the building is 27 3 , find the volume of the tank on the top of the model. (c) Use graph paper for this question. The marks obtained by 120 students in an 4 English test are given below: Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90100 No of 5 9 16 22 26 18 11 6 4 3 students Draw the ogive and hence, estimate: (i) the median marks. (ii) the number of students who did not pass the test if the pass percentage was 50. Q10 (a) If A= [ 3 4 ] , B= [ 3 8 4 1 ] , C= [ 0 3 4 ] and 3 2 = 6 , find the values 3 of , and . (b) Solve the following Quadratic Equation: 2 7 + 3 = 0 .Give your answer correct to two decimal places ICSE11Turn over 3 (c) In the given figure, the centre O of the small circle lies on the circumference of the bigger circle. If = 75 and = 40 . Find ICSE12 i) ii) iii) iv) 4
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