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KARNATAKA ICSE SCHOOLS ASSOCIATION _______________________________________________________________________________________ PREPARATORY EXAMINATION (FEBRUARY 2021) (Two hours and a half) 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 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. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. _______________________________________________________________________________________ SECTION A (40 Marks) Attempt all questions from this Section. QUESTION 1 = (a) If , prove that: = . (b) Solve the following inequation and graph the solution set on a number line. [3] [3] 2 3 < + 1 4 + 7, (c) Cards bearing number 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 are put in a box. A card is drawn at random from the box. Find the probability of getting a card which is: (i) An even number. (ii) A number divisible by 6. (iii) A number less than 30 and greater than 12. (iv) A perfect square. 1|Page [4] QUESTION 2 (a) Solve the following quadratic equation and correct to two decimal places. [3] 2 6 + 3 = 0 (b) The polynomials + 3 3 and 2 5 + when divided by ( 4) leaves the same remainder. Find the value of . [3] (c) Find the ratio in which the point ( , 1) divides the join of A( 5,4) and B(3, 2). Hence find a. [4] QUESTION 3 (a) If you were to start a recurring deposit account in a bank depositing 800 per month for 3 years at the rate of 6% per annum. Calculate the amount that you would receive at the time of maturity? (b) Find the value of x and y. 2 6 7 + 9 4 5 [3] [3] 7 10 7 = 5 17 15 (c) If (2 + 1), (4 + 3), (8 + 1) are 3 consecutive terms of an A.P., find the value of k and the 18th term of this sequence. [4] QUESTION 4 (a) In the given figure, AB is the diameter of the circle. DC is parallel to AB and CAB = 35 . [3] Find: (i) ADC (ii) DAC. D A QUESTION 6 3 35 [3] C matrix X. B (b) Prove that: + = 0 + . 2|Page [3] (c) The following table shows the age distribution of cases of certain diseases admitted during a year in a particular hospital. Find the mode from the following distribution. Age (in years) Frequency 10 20 20 30 30 40 40 50 60 70 6 12 20 14 4 SECTION B (40 Marks) Attempt any four questions from this Section. QUESTION 5 (a) The sum of first 6 terms of an A.P. is 63. The ratio of the 10th term to the 20th term is 1:2. Calculate the first and 15th terms. [3] (b) Using properties of proportion, solve for a. [3] = 3. (c) Show that ( 2) is a factor of 7 + 14 8. Hence factorise the expression completely. [4] QUESTION 6 (a) Given 8 2 12 = , find matrix X. 2 4 4 (b) Prove that: + = + . [3] [3] (c) A two-digit number is 5 times the sum of its digits and is also equal to 5 more than twice the product of the digits. Find the number. [4] QUESTION 7 (a) Rahul an engineering student prepared a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each conical part has a height of 2 cm, find: (i) The volume of air contained in Rahul s model. (ii) The cost of painting the outer surface of the model at 15 per cm2. 3|Page [4] (b) A survey height (in cm) of 60 boys belonging to class X of a school was conducted. The following data was recorded. Height (in cm) 135 140 140 145 145 150 150 155 155 160 160 165 165 170 No. of boys 4 8 20 14 7 6 1 (Take 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along another axis.) Draw the ogive of the above distribution and hence use the graph to estimate: (i) The median (ii) The lower quartile (iii) The upper quartile. (iv) If 10 boys are considered to be very tall, what is the minimum height required to be in the tall category. QUESTION 8 (a) From a point O on the ground, the angle of elevation of the top of a tower is 30 and the top of a flag staff, which is on the top of the tower is 60 . If the length of the flag staff is 5m, find the height of tower. (b) Find the missing frequency in the following table. The mean of the distribution is 56. Class Interval Frequency [3] [3] 0 20 20 40 40 60 60 80 80 100 100 120 16 11 f 16 12 10 (c) In the given figure, PQL and PRM are two tangents to the circle with centre O at points Q and R respectively. If S is a point on the circle such that SQL = 55 and SRM = 45 , find the reflex QOR. Q S 4|Page P O R QUESTION 9 (a) On a graph plot points A(4,6) and B(1,2). (i) [3] Plot A , the image of A when reflected in y-axis. (ii) Plot B , the image of B when reflected in the line AA . (iii) Write the equation of the line AA and name the figure ABA B . (b) In the figure ABC and CEF are two triangles where AB is parallel to CE and AF:AC is 5:8. [3] (i) Prove that ADF CEF. (ii) Find AD if CE = 6cm. (iii) If DF is parallel to BC, find the ratio of the area of ABC to the area of trapezium DFCB. (c) The catalogue price of a computer is 45,000. The shopkeeper gives a discount of 15% on the listed price. He further gives an off-season discount of 10% on the discounted price. However, GST at 8% is charged on the remaining price. Find: (i) The amount of CGST and SGST. (ii) The total price a costumer has to pay for the computer. [4] QUESTION 10 (a) A solid cylinder with base radius 8 cm is melted to form a cone of height 6 cm. Find the radius of the base of cone. (b) For what value of k are the roots of the quadratic equation 2 5 + 10 = 0 real and equal? [3] [3] (c) (i) Frame the equation of a line -intercept = 5 and passing through a point (4, 7). (ii) Find whether the point (6,7) lies on the above line. [4] QUESTION 11 (a) Find the sum of first 20 terms of an A.P. whose nth term is given by = 7 3 . [3] (b) Jeevan had a RD account in a bank for 2 years at 6% per annum simple interest. If he gets 1500 as interest at the time of maturity, find: (i) The monthly instalment. (ii) The amount of maturity. 5|Page [3] (c) Calculate the mean marks of the following distribution. Class [4] 50 55 55 60 60 65 65 70 70 75 75 80 80 85 9 20 12 11 9 10 9 interval Frequency *************************************************************************** 6|Page
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