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ARYA VIDYA MANDIR GROUP OF SCHOOLS TERMINAL REVIEW- SEPTEMBER 2022 Marks: 80 MATHEMATICS Std: X Time: 2 % hr Date: 12/09/2022 *********** Answers to this paper must be written on the paper provided separately You will not be allowed to write during the first 15 mimutes This time is to be spent in reading the question paper The time given at the head of the paper is the time allotted for writing the answers. Attempt all questions from Section A and any four questions from Section B All essential working should be clearly shown whenever needed on the same sheet The omission of the essential working will result in the loss of marks. Do the rough working at the bottom of the paper. The intended marks for questions or parts of questions are given in the brackets [ This paper comprises 8 printed pages. Section A (40 marks) (Attempt all the questions from this Section) Question1 Choose the correct answers to the questions from the given options: (i) a bank for 2 years, which The interest earned on a recurring deposit account with annum on a monthly installment of F1000 is: pays 6% rate of interest per (a) (b) (c) (d) Gi) [15) T1000 1500 10000 15000 In an intrastate transaction, goods GST is 18%, find the CGST. (a) (b) c) (d) 4500 2250 2750 3750 worth 25000 are sold. If the applicable rate of 2 Contd.. (1) Std X Mathematics Terminal Review The solution set for the given number -76-5 (a) 2 3 4 5 -2 xS 1, x cR} When the discriminant of the real and equal (a) (b) real and unequal (c) not real (d) zero of the factors of x2 - quadratic equation 4x 5 X+ 5 (a) X- 1 (b) +4 (c) (d)x5 (vi) 1 (-3,-2, -1,0, 1,2} (d) One 0 2,-1,0, 1) (c) (V) -1 line is: -2<x< 1, xe R} () (iv) -3 -2 -4 September 2022 If (x* + y*): 2xy 1:1 (a) = 5 :3, then one b? 4ac> 0 then the roots - are: is: of the possible values of x: y is. (b) (c) (d) (vii) Given :2 3:1 X= The order of matrix Xis: 2 x 2 (a) (b) 1x2 2x1 (c) (d) (vii) 1 x 1 The point A(5, 0) is invariant when reflected about (a) (b) (c) (d) x axis y axis origin a line parallel to x axis 5 units above it ... -3 Contd (ix) The class mark for the class interval 10 20 is 10 (a) 15 (b) (c) (d) (x) Std X Mathematics Terminal Review September 2022 17.5 20 TWo dice are thrown. Find the probability of getting the same number on both. (a) (b) (c) (d) 1/4 1/2 3/4 1/6 xi) Shiny has a recurring deposit account in a post office for 1 year at 10% p.a. simple interest. If her monthly installment is R4000, calculate the interest at the time of maturity. 3000 (a) 2000 (b) 2500 (c) 2600 (d) (xii) A consumer buys a refrigerator at R36000 from a dealer. What GST does she have to pay to the State Government if the rate of GST is 18%? (a) (b) (c) (d) (xii) (xiv) T6000 T6480 T6840 T8000 The solution set of the inequation 3 (a) x:xER, x<3} (b) x: xER, xs3} c) x: xER, x>3} (d) x: xER, x23) The solution of the equation 3 x - (a) x= 1 or x = 2 (b) X=-1 or x = - 2 (c) X= 1 orX =0 (d) X = 0 or x = 2 2x 2 3x - 2 = 12, given that x R is: x is: .4 A Std X Contd (xv) If a polynomial f(x) by (x a), in f(x). is divided substituling (a) (b) xa (c) x-a (d) xa = 0 - then the remainder fla) 2022 is obtained by X0 Question 2 (a) Terminal Review Septemtber Mathematics Find the total amount to be paid for the given 4 bill. Rate of GST Market Price Discount (Rs.) (Rs.) Stent Rs. 24500.00 Rs. 2000 28% Oxygen cylinder Rs. 33000.00 Rs. 1500 18 % Articles (b) Find the values of a, b, (c Saksham has a month for two x and y, if 41 34+7 b-gI=L0 He deposits F1000 per recurring deposit account in a bank. time of maturity, find years. If he gets 26,050 at the [4) the interest paid by the bank (ii) the rate of interest Question 3 (a) Factorise the given polynomial completely, using 41 Factor Theorem: 6x-17x2 + 4x+ 7 (b) Two coins are tossed at the same time. Find the probability of getting () a head on the first coin and tail on the second (Gi) a head and a tail (ii) at least one head .5 .. 5 Contd... (c) Std X Mathematics Terminal Review Use a graph sheet for this question. Take 2 cm Plot the points, A(0. 4) and B(-3, 2). () Reflect point B through the line x 0 and 1 unit = September 2022 along name it as = the 5) axes B () (ui) Reflect point B through the orig1n and name it as B. Reflect point A through the line y 0 and name it as A'. (iv) Join the = points AB'B"ABA and give the geometrical name of the closed figure so formed. Section B (40 marks) (Attempt any four questions from this Secton) Question 4 (a) Find the discriminant of the following quadratic equation: 3x*- 7x 0, and + hence find the nature of the roots. (b) Solve the following inequation and represent the solution x- (C) The 11< 2x - on the number line.: 1, x eR 7 3 following table gives the price range of 50 items in a shop. 10-20 20-30 30-40 40-50 Price () No. of items 11 Find the mean price 7 15 4 50- 60 8 of all the items to the nearest rupee using step deviation - method. Question5 (a) (D) A point P is reflected in the origin. Coordinates 0) (i) the coordinates of P. the coordinates of the image ofP in the (i) the coordinates of the image in Evaluate AB ofP of its x - image are (5, 4). Find 3 axis. the line x = -2. 5C A28- and C ...6 6- Std X Mathematics Terminal Review September 2022 Contd... c) Solve for x, 141 using the properties of proportion. 5x+2x-6- 4 Sx-/2x-6 Question 6 (a) lf 6is the mean proportion between two numbers x and y and 162 Is the third proportional to x and y, find the numbers. (b) [3 When x + 4x- kx - 6 is divided by x - 3, the remainder is k. Find the value of the constant k. (c 3 Use a graph sheet for this question. Draw a histogram for the monthly salary of 50 workers in the following table and hence estimate the mode for the following distribution. Take 2 cm = 500 along the x-axis and 2 cm =5 members along the y-axis. 4 Monthly salary () No. of workers 3500 000- 45500- 5000 5500- 4000 4500 5000 5500 6000 10 12 18 Question 7 (a) Show that (b) Solve the following inequation and write the solution set: (3x 4) and (2x 1) are factors of 6x- 11x + 4 - 3x-4< 15x +8 13] - 12x +20, x E VW. Represent the solution on a real number line. 31 . -7- Contd. Std X Mathematics Terminal Review September 2022 Manufacturer Asells a sewing machine to a dealer B for 5000. The dealer B Sells it to a customer at a profit of 7500. If the sales are intra-state and the rate of GST is 12%, find () the amount of GST paid by dealer B to the Central Government. () the amount of GST received by the State Government. (iil) the amount that the customer pays for the machine. 4 Question 8 (a) Rajesh deposits R1500 every month in a recurring deposit account for 1 % years. If the rate of interest is 6% per annum, find the interest and maturity value he will receive on maturity. (a-b) (b) Ifa, b, c, d are in continued proportion, prove that: (c) Solve the quadratic equation and give your answer correct to two significant 3 (b-c) figures. 5x+3x-4 0 Question9 (a) A bag contains some red, blue and green pens. The probability of selecting a red pen is and blue pen is.Ifthe bag contains 20 green pens, then find: () (i) (b) total number of pens in the bag. probabilty of selecting a green pen. P is the solution set of 7x + 3 < 3x -4, where x E R. Find the solution set and graph the solution set on the number line. (c) 13] If A=-1 4 3 find the value of A2 - 61, where I is the unit matrix of order 2. [4 ..8 -8Std X Mathematics Terminal Review Contd September 2022 Question 10 (a) Sheeba has a cumulative deposit account of 7500 per month at 8% per annun time for {36100 at the time of maturity, find the total Simple interest. lf she gets 4 wh.ch the account was held. (b Use a admitted graph sheet for this question. The weights of 120 patients 16) hospital are given below: Weights (kg) 40-50 10 No. of 50 60 60 13 in a 70 70 80 80 90 90 100 20 15 25 30 100110 patients Use 2 cm = 10 kg and 2 cm = 20 patienis along x-axis and y-axis respectively to draw an ogive and hence estimate: (0) (i) the median weight (ii) percentage of patients whose weight is below 60 kg. the inter quartile range of weights
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