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ICSE Class X Prelims 2024 : Mathematics (St. Francis School (SFS), Borivali, Mumbai)

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A ST. FRANCISSCHOOL, MT. POINSUR, BORIVALI(W), MUMBAI Sub: MATHEMATICS 1" ASSESSMENT 2023-24 Time: 02%brs Class<X) Marks: 80 Date: 30/08/2023. 10 Attempt all questions from Section Aand Section B. All working, including rough work, must be clearly showh and must be done on the same the rest of the answer. sheet as Omission of essential working will result in the 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. Questionl Choose the correct answers to the questions from the given options. (Donot copy the question, write the correct answers only) () The discriminant of the equation: 5x - 2x - 3 = 0 is: (a) 7 b) 64 (c) 49 (d) 8 (i) For a transaction of 80000, if the GST rate is 18%, then CGST is: fa) 7,200 (b) 14,400 (c) 6,400 (d) 0 (iii) Chetan deposits 600 per month forlyear and8 months in a Recurring Deposit Scheme. If he receives 13050 as the maturity amount, the interest earned is: (a) 150 (b) 2250 (c) 5010 (3050500120 3os0- 2000 1050 (iv) In which of the following cases, the sum of twomatrices Aand B can be obtained, a) A=[1 2]; B= 9) A = : - ) e)A-B9 - 7 8 (9A-:B-[) 1 (v) x,y, zare in continued proportion, then= * (c) x y? g2 (vi) Iffor an A.P, T, =3 (a)-36 (d) y2 4n then 6" term of the A.P. is: (b) 27 (c) -27 (d) -21 (vii) The reflection of the point P (-2,3) in the x -axis is: (a) (2, 3) (vii) (b) (2, -3) 1 tan A+cot A (a) sin A (b (d) (-2, 3) tanft is equal to: cos A (9) (-2, -3) sin A cos A V) sin A cos A (d) 1 CosA A1 Std10 Mathermatics 2023 -24 (os? Page 1 of 4 (ix) The solution set for the given real number line is: (d) x>-1 (c)x>-1 (b) xs-1 (a) x<-1 terms are: two (d)1,0 (x) The first two terms of an A.P. are -3, 2. The next ()7,12 (a) 7,9 (c) 0, 2 (xi) The face value of ashare if 300 shares of give an 7% dividend annual dividend 2100 - 2100is: of 7 FV (o (a) 110 (b) *120 (c) R105 aj100 (xi) In the given diagram, the value of x is: 50 m 25 (a) V3 m (of 25 m (b) 100 m (a) 25V3 m (xiii) The distance between A and B by road is 240 km and by train it is 300 km. A car starts from station A witha speed x km/h whereas a train starts from station B with a speed 20 km/h more than the speed of the car. The time taken by the car to reach the station B is: (d) 300 x+20 (xiv) Which of the following statement is not true. Pood (a) All identity matrices are square matrix (b} All null matrices are square matrix (C) For a square matrix, number of rows= number of columns (d) A square matrix which has all its elements zero each except those on the leading diagonal is called a diagonal matrix (xv) The value of tan ( <90 ) (a) decreases o) increases as increases. (c) remains the same (d) zero Question2 (a) Rekha opened a recurring deposit account in a bank and deposited 1000 per month for 2 years. If she received 25500 at the time of maturity, find: i) total money deposited, i ) interest earned in 2 years, [4] ii) the rate of interest. A1Std10 Mathematics 2023 -24 Page 2 of 4 (b) Solve the inequation and graph the solution on the number line. -3 +xs+2< +2x,xE 1 41 (c) Find: )(1+) (4] i)(1+ 1 1 Using the above results, prove that: (1+a)1 +;cot20) sin29-sin 0 Question 3 B-c-Jand D-[ [4] (b) In the following diagram, AB is a floor-board; PQRS is a cubical box with each edge = 1m and B = 60. Calculate the length of the board AB. Give your [4] () Given AFind: AB+2C-4D. answer corect to the nearest whole number. A A P -| both axes. (c) Attempt this question on graph paper, Take 2 cm = 1 unit on [5] (1) Plot the points A (-4,2) and B (2, 4) on the graph paper. (i) A' is the image of A when reflected in the y- axis. Plot it on the graph paper and write the co-ordinates of A'. (ii)B' is the image of Bwhen reflected in the line AA'. Plot it on the graph paper. (iv) Write the geometrical name of the figure ABA'B. l6oo SECTION B(40 Marks) Atempt all questions from this Section Question 4 (a) A shopkeeper buys an article at a discount of 20% on the marked price of 2000. The shopkeeper offers a discount of 12% on the M.P to his customer. If GST charged [3] is 5%, find: (i)) the GST collected from the shopkeeper by the Government. g(848 (ii) the amount paid by the customer for the article. (b) Solve the following equation. Give yo answer correct to 2 decimal places. 5x2 -3x - 4 = 0 [3] (.24 (c) Show that (x - 3) is a factor of (2x -3x2- 11x + 6) [4] Hence factorize the given expression completely. ( ar3 sl(e) A1 Std10 Mathematics 2023 -24 Page 3 of 4 [3] [10 -] 15 Question 5 (a) Find the value of x [3] and y if: on the number graph the solution set and inequation (b) Solve the x*+1 R -1 <3 +4x < 23, x E if the value of x and dividendo to find (c) Use componendo Question 6 [4] price. acertain (3] rate Ifthe at declared on 20 shares selling (a) Adividend of 9% is 16300 calculate: of return is 7%, 71260. 2 dividend of the market value of the share, obtain an annual () to invested given the amount to be (ii) for whichthe p, of value equation, findthe (b) Without solvingthe following equation has equal roots. 4,3 9x + (p + 3)x +1= 0 playgroundandthe inthe son find: her alady is watching fromthe base ofthe building, (c) From the window of abuilding, child is 50 maway angle of depression is 35 . Ifthe i) the height of the window. i) give your answer correct to [3] [4] nearest meter. Question 7 4x- 10) by (x + (a) On dividing (ax' + 9x' + [31 3), we get S5 as the remainder. Find the value of a. - 2 1,-5,-11,.. (b) Find the nth term of the A.P. 13, 7, Using it, find its 9th term. [3] -35, (4] remaining, kept one for his use and then sold the (c) A man bought x chairs for 6000. He for. Thereby he made a profit of 1200 on the each for 60 more than what he had paid buy? whole transaction. How many chairs did he 60004 60 6o0 booo 60-60 6 212 ?13 - 2007 + 200 - G01 A1 Std1O Mathematics 2023-24 Page 4 of4

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Additional Info : ICSE Class X Mid-term 2024 : Mathematics (St. Francis School (SFS), Borivali, Mumbai)
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