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ICSE Class X Prelims 2021 : Mathematics (Manovikas English Medium School, South Goa) : Prelim paper for the year 2019-2020

6 pages, 32 questions, 0 questions with responses, 0 total responses,

Fahad Imran
Manovikas English Medium School, South Goa
1st to 10th

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MAN OVU(AS ENGLISH MEDIUM SCHOOL Prclimin::111' Examination 2019 - 2020 , d) \ MATHEMATICS MAX. MARKS: 80 __ f "\. T: ~ ! -t - Ol - 20.tO DURATION: 2.: hours 2 -~--- --- -- ----~- ---------------..:.... ol A nswcrs l o Lhis Paper must be written on the paper provided separately. You }Viii not be allowed to write during the first 15 minutes. Sc ho This time is Lo be spent in reading the question paper. f he time given at the head of this Paper is the time allowed for writing the answers. Attempt all questionsfrom Section A and any/our questions.fr om 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 [ J. Mathematical tables are provided. as - ov QU ESTI ON 1 ik SECTION -A {40 Marks) (Attempt all question from this section) (a ) So lve the following ineq uation and write down the solution set. x+l -3(x-7)> 15-7x >-3 , xEZ r3 J an Represent the solution set on the number line. [3] M (b) I11 the figure given below AP and BP are tangents to the circle with centre O. If L CS P = 25 and L CAP= 40 , find (i) L ADB (ii) L AOB (iii) L ACB (iv ) L APB . p This paper consists of 6 printed pages Page I (c) If M =[~ cos sin 3 oo 0 (i) (ii) cos oo ], and ~ 4 sin 30 Write the order of matrix X, Find the matrix X = [4s] such th:u MX ==N , 141 QUESTION 2 (b) Find the equation of the line passing through the intersection of + Sy - 4 = O with X-axis and parallel to the line (c) In the given figure, EB ..L + 8 = o. Sc ho 2x 3x - 7y 13j ol (a) Mrs. David deposits ~JOO per month in a bank for 2 years in a recurring deposit account. If she gets ~7725 at the time of maturity, what is the rate of interest per annum? IJ I AC , BG 1. AE and CF J_ AE. BC Prove that : ( i) fl ABC~ fl DCB (ii) BD BE' AB 14] 0 A ik as E. QUESTION 3 C ov B I~l M an (a) A shopkeeper buys an article whose marked price is ~8000 at some rate of discount from a wholesaler. He sells the article to a consumer at the marked price. If the shopkeeper pays a tax of ~72 to the Central Governm ent: find the rate of discount at which he bought the article from the wholesaler. The sales are intrastate and the rate of GST is 18%. (b) Use ruler and compass only . Take points P and Q at a distance of 9 cm from each other. At point P draw a circle of radius 1.5 cm and at point Q draw a circle of radius 2.5 cm. Locate point X on PQ such that PX = 3 cm. Through X draw tangents to the circles with centre p and Q. Measure the length of tangents. 13] (c) A box contains balls numbered from 11 to 40. A ball is drawn at random. Find the probability that the ball drawn bears: (iii) A prime number (i) A perfect square, (ii) A number less than 21 (iv) A multipl e of 5 -------------------- ----Page 2 i t I QUESTION 4 /31 (a)___S::alculate the median and mode for the following distribution : Age (in yrs) 23 21 26 18 16 Nwnber of students 5 4 3 7 29 3 6 ---- (b) Wat~r flows through a cy Iindrical pipe of internal diameter 7 cm at 36 km/hr. Calculate the time in minutes it would take to fill cylindri cal tank the radius or whose base is 35 cm and height is 1 m. (c) A line whose equation is x + y = 7 is the perpendicular bisector of line AB where co- ordinates of Bare ( 2 , I ). Find the co- ordinates of A. Also find the equation of AB . ol IJ J Sc ho - l4.1 SECTION - B (40 Marks) (Attempt any four questions from this section) QUESTION 5 as (a) The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream. ik /3] liI ov (b) Arlok saved every year half as much as he saved _the previ ous yea r. If he total l:-1 saved <93750 in 4 years, how much did he save in the first year? an (c) Using ruler and compass only construct tJ.ABC such that Al3 = 5 cm , L!\ BC and radius of circumcircle of tJ.ABC is 3.5 cm. On the sa me di agram construct a circle touching AB at its midpoint and also touchin g side AC . - 7~ 11 [--1/ M QUESTION 6 /JI (a) An aeroplane is 30 m long and its model is 15 cm long. If the total outer 2 surface area of the model is 150 cm , find the cost of painting the outer surface area of the aeroplane at the rate of RS. 120 per m2 if 50 m 2 is lett out for windo ws. (b) Manoj sold a certain number of <20 shares paying 8% di vidend at< 18. and invested the proceeds in <10 shares, paying 12% di vidend at 50% premium. If the difference in his annual income is < 120, find the number or shares sold by Manoj. \, (c) If ax 3 + 3x 2 + bx - 2 has a factor (x + 1) and leaves re1rn1indt'1 divided by (x + 2) , find the values of a and h. Page J 7 \ \ 'ht.' ll I :: ii I t) l lESTIO N 7 (a) So lve the equation ( 4x - 7)x + 2 = 0 and write your answer conect rJ two deci mal places. 11pln 1 (b) I ise grnph paper fo r thi s question. Take sca le of 1 cm = 1 unit on both axes. 1 0A 8 1. , 1w tri angle 0 1\B is rellccted in the ori gin O to th e triangle l 1,1h' ll1c co-ordin utcs ( - J . _ 4) and ( 0 , -.5 ) respecti ve ly. r4l A ' ancl r3t Sc ho ol (i) Write the co-ordinates of A and B . ( ii) Represent the given information on the graph paper. (iii ) Write the geo~1etrical name of the figure ABA B, . Find its perimeter. (iv) Write the co-ordinate of AH , the reflection of A in the origin followed by re nection in Y axis (v) Write the coco rdinate or B11 , the refl ection of Bin the X-axi s followed by reflection in origin. \.C) ln the given figure PQRS is a cycli c quadrilateral .PQ and SR produced 0 [3] an ov ik as meet at T (i) Prove that tJ. TPS ~ /J. TRQ. (ii ) Find SP and PQ, ifTP = 18 cm , RQ = 4 cm , ST= 30 cm and TR = 6 cm. (iii) Find area of quadrilateral PQRS if area of /J.PTS = 27 cm 2 . M p QU ESTION 8 (a) Find the value of k for which the equation has equal roots. Also, find 3x(3x - 8) +k =0 (b) Prove that: cotA -1 _ 2- sec 2 A - l+tanA the roots. (c) cotA [3] If the mean of the following di stribution is 98.04 and the sum of l'l'equcncies is 50; find the values of a and b : i ss interva l 84 - 90 90 - 96 I 02 - I 08 96 - 102 requency 8 {I b ~r [3] IA] - 15 l 08 - 114 5 Page 4 - - ,.,.,,. ," . . .., ~ QUESTION 9 (;:i ) T \1\1() r ir r ]p c:: i ntPr<:Pr1' ,, ,, r l, 0 t l,~ - ~ " 4 n , ... . 1n . ' _ ' P and Q. The tangents at p and Q intersect at po int T . Prove that P BQT is a eye1i c quadrilateral. 131 ~ (b)IfA=[} ~] , B=[~ i] andC=[! 1 2 ~] ; finc!A - 6 B+BC 131 as 1 Sc ho ol p QUESTION 10 ov ik (c) A solid toy is in the form of a hemisphere sunnounted by a ri ght circular cone. 14] Height of the cone is 2 cm and the diameter of the base is 4 cm . I f a right circular cylinder circumscribes the solid, find how much more space it v,1 ill cover. I' M (I an (a) In the given figure XY is a diameter of the circle and PQ is a tangent to the circl e at Y. If L.. AXB = 50 and L ABX= 70 , calcul ate L BAY and L APY . ,:-- ? ~ ::::::::,,- '"'L--C::::::::::: - ~ Page 5 - -=:::_;, ~ , rJ l f 1 ,, l,1 thv t1-in-11 lit'-urL' 1\BCI> is :1 parnlklograrn and /\P : Pl3 == 3: 5. Calculate l3J (6 PRN) : rU" ( trapezium APND) tii) PN: BC and ar(!:,PMN): ar(6BMC) (iii) BM : DM and BM : BD. (i) Cl'r D ____ C A 2,[6 . = {33+ /2 , then find the value of 2 x+J3 ---;;; x-v3 x+/2 + -x-v2 r:, as (c l II' X P Sc ho ol )';;: QUESTION 11 ik (n) The monthly income of a group of 320 employees in a company is given below: [4] [6] an ov Monthly 600070008000- 900010000- I 1000120008000 9000 incomes (~) 7000 10000 11000 12000 13000 45 20 65 95 60 30 5 Number of employees I Tak ing 2 cm = ~ 1000 on one axis and 2 cm = 50 vvorkers on the other axis, Draw an ugivc for the above distribut ion. Use the graph to calculate: Median ,:vuge, Upper quartile wage, Ir the salary or a senior employee is above ~ 11500, find the number of senior employees in the company. M (i) (ii) (iii ) 1 h) 1:rnrn the tnp /\ ol'a ta ll house AB o!'height 50 111 the angle of depression of the [4] point P midway between the house and a pole on the opposite side across a hroad street is found to he 45 . Also the angle of depression of the top of the pole as observed from A is 20 . Find the breadth of the street and the height of the pole. Page 6

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