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ICSE Class X Mid-term 2019 : Mathematics

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Khushi Shrivastav
The Future Foundation School (TFFS), Kolkata

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THE FUTURE FOUNDATION SCHOOL HALF YEARLY EXAMINATION SESSION 2019 2020 MATHEMATICS (Two hours and a half) (Maximum Marks : 80) CLASS X DATE 16.09.19 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 a ny 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) [3] 3 + x 8x + 2 14 + 2x, x I 3 3 b) A man invested Rs.36,000 in buying Rs.100 shares at Rs.20 premium. The dividend is 15% per annum. Find i)the number of shares he buys. ii)his yearly dividend. iii)the percentage return on his investment. Give your answer correct to the nearest whole no. [3] c) Find the mean,median and mode of the following distribution 8,10,7,6,10,11,6,13,10 [4] Question 2. a) Given that (x+2) and (x+3) are factors of 2x3 + ax2 + 7x b . Determine the values of a and b. b) c) Prove that tan2 (Sec 1) 2 = 1 + Cos 1 Cos The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference. [3] [3] [4] This paper consists of 5 printed pages and 1 blank page. 2019 Turn over Question 3. a) b) [3] Given a line segment AB joining the points A(-4, 6) and B(8 ,-3). Find i)the ratio in which AB is divided by the y-axis. ii)the co-ordinates of the point of intersection of AB with the y-axis. c) [3] [4] The given figure represents a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6cm each and the slant height of the cone is 5cm. Calculate i)the height of the cone. ii)the volume of the solid. Question 4. a) What least number must be added to each of the numbers 5,11,19 and 37 so that they are in proportion? [3] b) Solve the following quadratic equation and give the answer correct to two significant figures. 4x 2 7x + 2 = 0 [3] c) Use ruler and compass only for answering this question. Construct a regular Hexagon of side 4cm. Circumscribe the polygon with a circle. [4] SECTION B (40 Marks ) ( Attempt any four questions from this section) Question 5. a) A dice is thrown once. What is the probability that the i)number is even. ii)number is greater than 2 ? b) A lady deposits Rs.1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value. 2 2019 [3] [3] c) (Use graph paper for this question) A(0,3) , B(3,-2) and O(0,0) are the vertices of triangle ABO. i)Plot the triangle on a graph sheet taking 2cm=1 unit on both the axes. ii)Plot D the reflection of B in the Y-axis and write its co-ordinates. iii)Give the geometrical name of the figure ABOD. Question 6. a) A town covers an area of 160 hectares. What area does it represent on a map of scale 1:200000 ? Answer in cm 2 . (1 hectare = 10,000 m 2 ) [4] [3] b) The n Th term of a G.P is 128 and the sum of its n terms is 255. If its common ratio is 2, then find its first term. [3] c) A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone. [4] Question 7. a) Use ruler compass only for this question. i)Construct a ABC, where AB=3.5cm, BC=6cm and ABC = 60 . ii)Construct the locus of points inside the triangle which are equidistant from BA and BC. iii)Construct the locus of points inside the triangle which are equidistant from B and C. b) The monthly pocket money of Ravi and Sanjeev are in the ratio 5:7. Their expenditures are in the ratio 3:5. If each saves Rs.80 every month, find their monthly pocket money. c) [3] [3] [4] Question 8. a) Find the sum of first 22 terms of an AP in which d=7 and a 22 is 149. [3] b) Find the equation of a line with x intercept equal to 5 and passing through the point (4, -7). [3] c) Using ruler and compass, construct a triangle ABC in which AB=5.5cm, BC=3.4cm and CA=4.9cm. Construct a circle inscribing the triangle. [4] 3 2019 Question 9. a) The following table gives the wages of workers in a factory : Wages in Rs. No. of workers 45-50 5 50-55 8 55-60 30 60-65 25 65-70 14 70-75 12 75-80 6 [3] Calculate the mean by step deviation method. b) a 2 + b2 + a 2 b2 Given x= a2 + b2 a2 b2 2 2a2 x that b = 2 x +1 c) A shopkeeper buys an article whose list price is RS.8000/- at some rate of discount from a wholesaler. He sells the article to a consumer at the list price.The sales are intra-state and the rate of GST is 18%. If the shopkeeper pays a tax (under GST) of Rs72 to the State Government, find the rate of discount at which he bought the article from the wholesaler. , Use componendo and dividendo to prove Question 10. a) The monthly income of a group of 320 employees in a company is given below : Monthly Income No. of Employees 6000-7000 20 7000-8000 45 8000-9000 65 9000-10000 95 10000-11000 60 11000-12000 30 12000-13000 5 Draw an Ogive of the given distribution on a graph sheet taking 2cm=Rs.1000 4 2019 [3] [4] [6] on one axis and 2cm=50 employees on the other axis. From the graph determine i)the median wage. ii)the number of employees whose income is below Rs.8500. iii)if the salary of a senior employee is above Rs.11,500 then find the number of senior employees in the company. iv)the upper quartile. b) From two points A and B on the same side of a building, the angle of elevation of the top of the building are 30 and 60 respectively. If the height of the building is 10m, find the distance between A and B correct to two decimal places. Question 11. a) Find the value of k if (x-2) is a factor of x3 + 2x2 k x + 10 . Hence factorise the polynomial completely. [4] [3] b) A positive number is divided into two parts such that the sum of the squares of the two parts is 208. The square of the large part is 18 times the smaller part. Taking x as the smaller part of the two parts, find the number. [3] c) A Mathematics Aptitude Test of 50 students was recorded as follows: [4] Marks Number of students 50-60 4 60-70 8 70-80 14 80-90 19 90-100 5 Draw a histogram for the above data using a graph paper and locate the Mode. 5 2019

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