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ICSE Class X Prelims 2019 : Mathematics (The Future Foundation School (TFFS), Kolkata)

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Khushi Shrivastav
The Future Foundation School (TFFS), Kolkata

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THE FUTURE FOUNDATION SCHOOL PRE BOARD EXAMINATION SESSION 2019 2020 MATHEMATICS (Two hours and a half) (Maximum Marks : 80) CLASS X DATE 9.12.2019 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) Solve the following inequation and write down the solution set : 2x + 1 x 1 x +2 1 , x R 3 Represent the solution set on a number line. [3] (b) A man buys 100 shares in a company at Rs 150 each. The company issues one bonus share for every two shares held by him. When the price of the shares fell to Rs 120 he sold the shares. Find the percentage gain. [3] (c) Find the Mode and Median of the following set of numbers : 32, 20, 40, 21, 32, 21, 20, 32, 25, 23, 25, 25, 30, 23, 25, 29, 25, 40. [4] Question 2. (a) Using factor Theorem show that g(x)=3x + 2a -y is a factor of f(x)= 9x2 4a2 + 4ay y 2 [3] (b) 2 Prove that 1 1cos = sin + sin [3] (c) Which terms of the A.P. 121, 117, 113 is the first negative term? [4] This paper consists of 5 printed pages and 1 blank page. 2019 Turn over Question 3. (a) Evaluate without using Tables: [3] (b) Write down the equation of the line which passes through P, where P divides the line segment joining A(-2,6) and B(3,-4) in the ratio 2:3 and it is perpendicular to AB. [3] (c) A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into the water and it s size is such that when it touches the sides then it is just immersed. What fraction of the water overflows? [4] Question 4. (a) Five numbers are in continued proportion. The product of the first and fifth is 256 and the sum of the second and fourth is 40. Find the numbers. [3] (b) Solve 2x2 6x + 3 = 0 (give answer correct to two decimal places.) [3] (c) A shopkeeper buys an article whose printed price is Rs 5000 from a wholesaler at a discount of 20% and sells it to a consumer at the printed price. If the sales are intra-state and the rate of GST is 18%, find: (i) The price of the article inclusive of GST at which the shopkeeper bought it. (ii) The amount of SGST paid by the shopkeeper. (iii) The amount of GST received by Central Government. (iv) The amount which the consumer pays for the article. [4] SECTION B (40 Marks ) ( Attempt any four questions from this section) Question 5. (a) A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) Not red? (ii) Red or white? (iii) Neither white nor green? [3] (b) A lady opened a Recurring Deposit Account of Rs 4000/- per month in a Bank. What will she get at the time of maturity at the end of 2 years. The rate of interest is 10% p.a. [3] (c) A(3,2) , B(0,3) and C(0,-4) are the vertices of a triangle. (i) A 1 and A 2 are the reflections of A in the x-axis and the origin respectively. Write down the co-ordinates of A 1 and A 2 . (ii) Write down the co-ordinates of B 1 , the reflection of B in the x-axis. (iii) Which three points are invariant on reflection in y-axis? [4] 2 2019 Turn over (iv) Reflect ABC in the y-axis. What type of figure is formed by ABC and its image. Question 6. (a) 1 If AP= x , BQ= z , RC= y then prove that x [3] + 1 y = 1 z (b) If the third and sixth terms of a GP are 6 and 48 respectively, find the first term and common ratio of the GP. [3] (c) The barrel of a fountain pen, cylindrical in shape, is 7cm long and 0.5cm in diameter. A full barrel of ink in the pen will be used up when writing 310 words. How many words would use up a bottle of ink containing one-fifth of a litre? (give answer to the nearest whole no.) [4] Question 7. (a) [3] O In the figure O is the centre, AE is the diameter. CDE = 140 and AB=BC. Calculate the angles ABC and BEC. Prove that BO CE. (b) On a map down to a scale of 1:125000 a triangular plot of land has the following measurements PQ=10cm, QR=8cm, P RQ = 90 . Calculate (i) The actual length of PQ in km. (ii) The area of the plot in square kilometre. [3] 3 2019 Turn over (c) Find x and y if [4] Question 8. (a) Find the sum of this A.P: 1, 4, 7, 10,......... to 14 terms. [3] (b) P(2,-4), Q(3,3) and R(-1,5) are the vertices of triangle PQR. Find the equation of the median of the triangle through P. [3] (c) Construct a triangle ABC such that AB=5cm, BC=8cm and AC=10cm. Find a point D such that BD=DC and ABCD is a cyclic quadrilateral. [4] Question 9. (a) The angles of elevation of the top of a tower from two points at distance x and y from the base and on the same straight line with it are complementary. Prove that the height of the tower is xy x+7 + x x+7 x (b) Solve (c) The daily expenditure of 100 families is given below: [3] [3] =7 [4] Expenditure in Rs No. of families 40-60 5 60-80 25 80-100 a 100-120 b 120-140 5 The mean daily expenditure per family is Rs 88. Calculate the missing frequencies a and b. Question 10. (a) Construct a hexagon of side 5cm. Inscribe the polygon with a circle. [4] 4 2019 Turn over (b) The income of the parents of 100 students in a class in a certain university is tabulated below Income in Rs No. of students 0-8000 8 8000-16000 35 16000-24000 35 24000-32000 14 32000-40000 8 [6] (i) Draw an ogive to estimate the median income and interquartile range. (ii) If 15% of the students are given freeships on the basis of the income of their parents, find the annual income of parents, below which the freeships will be awarded. Question 11. (a) Find the value of a if ax3 x2 15x + 18 leaves a remainder 4 when divided by (x-1). Hence factorize completely if (x-2) is a factor. [3] (b) Two cars leave the same place at the same time. The first car travels due west and the second car due north. The first car travels 5km/hr faster than second car. If after 2 hours, they are 50km apart, find the average speed of the car due west. [3] (c) Estimate the mode for the ages of 400 patients in a hospital on a day with the help of a Histogram. [4] Age in years No. of patients 10-20 30 20-30 50 30-40 80 40-50 90 50-60 50 60-70 40 70-80 60 5 2019 Turn over

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