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JSS INTERNATIONAL SCHOOL, DUBAI , Mock II Examination 2020-21 MATHEMATICS Grade: X Duration: 2Hr.30Min Max Marks: 80 Date: 17/01/2021 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 [ ]. -----------------------------------------------------------------------------------------------------------------------------------------SECTION A (40 Marks) Attempt all questions from this Section. Question 1 (a) If b is the mean proportion between a and c prove that 4 + 2 2 + 4 4 + 2 2 + 4 = 2 2 (b) Solve the equation 4 2 5x 3 = 0 and give your answer to two decimal places. (3) (3) (c) AB and CD are two parallel chords of a circle such that AB = 24cm and CD = 10cm.If the radius of the circle is 13cm, find the distance between the two chords. (4) Question 2 (a) Using remainder theorem find the value of k if on dividing 2 3 + 3 2 kx + 5 by (x-2) leaves a remainder 7. (3) (b) Given A = [ 2 0 1 ] and I = [ 1 7 0 0 ] and 2 = 9A + m.I , find m. 1 (3) (c) The mean of the following numbers 45,52,60, x,69,70,26,81,94 is 68. Find the value of x. Hence estimate the median. (4) Question 3 (a) Solve the following inequation and write the solution set of 13x 5 < 15x + 4 < 7x + 12 ,x R and represent the solution set on a number line. (3) (b) Three vertices of a parallelogram ABCD taken in order are A(3,6), B(5,10),C(3,2). Find (i) the coordinates of the fourth vertex D (ii) length of diagonal BD (iii) equation of side AB of the parallelogram ABCD (3) (c) The volume of a Conical tent is 1232 cu.mts and the area of the bare floor is 154 sq.mts, Calculate the (i) radius of the floor (ii) height of the tent (iii) length of the canvas required to cover this conical tent, if its width is 2m. Question 4 (a) A die has 6 faces marked by the given numbers as shown below (4) The dice is thrown once. What is the probability of getting? (3) (i) a positive integer (ii) an integer greater than -3 (iii) the smallest integer (b) Shahrukh opened a recurring deposit account in a bank and deposited 800 per month for 18months.If he received 15084 at the time of maturity, find the rate of interest per annum. (3) (c) Use graph paper to answer the following questions. (i) Plot the points A (-4,2) and B (2,4) (ii) is the image of B when reflected in the y -axis. Plot it on the graph paper and write the coordinates of . (iii) is the image of B when reflected in the line A . Write the co-ordinates of . (iv) Write the geometrical name of the figure AB (4) SECTION B (40 Marks) Attempt any four questions from this Section Question 5 (a) In the given figure, the line segment AB meets x-axis at A and y-axis at B. The point P (-3,4) on AB divides it in the ratio 2:3. Find the co-ordinates of A and B. (3) (b) Using the properties of proportion solve for x 4 +1 17 = 2 2 8 (3) (c) A shopkeeper purchases a certain number of books for 960. If the cost per book was 8 less, the number of books that could be purchased for 960 would be 4 more. Write an equation, taking the original cost of each book to be .x, and solve it to find the original cost of the books. (4) Question 6 (a) Without solving the following quadratic equation, find the value of m for which the given equation has real and equal roots. 2 + 2(m 1) x +(m+5) = 0 (3) (b) As observed from the top of a 80m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse in horizontal line with its base are 300 and 400 respectively. Find the distance between the two ships. Give your answer to the nearest meter. (3) 2 1+ (c) Prove that ( 1)2 = 1 (4) Question 7 (a) Using Step Deviation method calculate the mean marks of the following distribution. CI 50-55 55-60 Frequency 5 20 Also state the modal class. 60-65 10 65-70 10 70-75 9 75-80 6 80-85 12 85-90 8 (5) (b) Marks obtained by 200 students in an examination are given below Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No. of 5 11 10 20 28 37 40 Students Draw an Ogive for the given distribution, Using the graph determine 70-80 29 80-90 14 90-100 6 (i) the median marks (ii) the number of students who failed if minimum marks required to pass is 40. (iii) If scoring 85 and more marks is considered as grade one, find the number of students who secured grade one in the examination. (5) Question 8 (a) In the figure, O is the center of the circle and AB is a tangent to it at point B. If BDC =650 find BAO. (3) ( + )2 (b) If x,y,z are in continued proportion, prove that ( + )2 = (3) (c) A shopkeeper sells an article at the listed price of 1500. The rate of GST on the article is 18%. If the sales are intra state and the shopkeeper pays a tax (under GST) of 27 to the Central Government, find the amount inclusive of tax at which the shopkeeper purchased the article from the wholesaler. (4) Question 9 (a) Sixteen cards are labelled as a,b,c,d, m,n,o,p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is (i) a vowel (ii) a consonant (iii) none of the letters of the word MEDIAN (3) (b) A conical tent is to accommodate 77 persons. Each person must have 16m2 of air to breathe. Given the radius of the tent as 7m, find the height of the tent and also its curved surface area. (3) (c) The sum of the first five terms and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms. (4) Question 10 (a) Mrs. Goswami deposits 1000 every month in a recurring deposit account for 3 years at 8% interest pe annum. Find the matured value. (3) (b) Find the equation of a line with x intercept 5 and passing through the point (4 , - 7) . (3) (c)In a school the weekly pocket money of 50 students is as follows. (4) Weekly Pocket Money(in ) 40-50 50-60 60-70 70-80 80-90 90-100 No:of Students 2 8 12 14 8 6 Draw a histogram and a frequency polygon on the same graph also find the mode using the graph. Question 11 (a) The speed of an express train is x km/hr and the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train. (3) (b) Find a if the two polynomials a 3 + 3 2 9 and 2 3 +4x+a leaves the same remainder when divided by (x+3). (3) (c) In the given figure AE and BC intersect each other at point D. If CDE = 900 , AB = 5cm, BD = 4cm and CD = 9cm, find DE. (4)
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