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ICSE Class X Board Exam 2023 : Mathematics

20 pages, 85 questions, 6 questions with responses, 6 total responses,

Apurv Soni
Carmel Convent Senior Secondary School, Raigarh

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MATHEMATICS Maximum Marks: 80 Time allowed: Two and hulfhours Answers to this Paper must be writlen on the paper provided separalely. You will not be allowed to write during 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. SectionB. Attempt all questions from Section A and any four questions from 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 and graph papers are provided. SECTION A (40 Marks) (Attempt all questions from this Section.) Question 1 Choose the correct answers to the questions from the given options. [15] (Do not copy the questions, write the correct answers only.) ) ,the value of x and y respectively are: (a) 1,-2 (b)-2.1 (c) 1,2 (d)-2,-1 This paper consists of 11 printed pages and 1 blank page. T23 511 Copyright reserved. Turn Over ii) Ifr-2 is a factor of r (a) 3 (b) 2 - kx - 12, then the value of k is: (c)-2 -3 (d) (iii) In the given diagram RT is a tangent touching the circle at S. If LPST = 30 and LSPQ= 60 then 2PsQ is equal to: (a) 40 30 (6) 60P 60 R (d) 90 (iv) A letter is chosen at random from all the letters of the English alphabets. The probability that the letter chosen is a vowel, is: 26 5 b) 26 (c) 26 21 24 (v) T23 511 If3 is a root of the quadrtic equation x*-px +3 =0 then p is equal to: (a) 4 b) 3 (c) 5 (d) 2 2 (vi) In the given figure <BAP = 2DCP = 70, PC = 6 cm and CA =4 cm, then PD: DB is: (vii) B (a) 5:3 (b) 3:5 (c) 3:2 (d) 2:3 A 70 6 cm 4 cm The printed price of an article is P 3080. If the rate of GST is 10% then the GST charged is: 154 (a) (b) 308 (c) 30.80 d)15.40 (viii) (ix) (1 + sinA) (1 - (a) cosecA (b) sin?A (c) sec A (d) cosA sinA) is equal to: AABC The coordinates of the vertices of are respectively (4,-2), (6, 2) and (4, 6). The centroid G of AABC is: T23 511 (a) (2.2) (b) (2, 3) (c) (3,3) (d) (0, -1) 3 Turn Over (x) (xi) (xii) The nh term (a) 7 (b) 15 (c) 25 (d) 45 The mean (a) 4 (b) 6 (c) 9 (d) 36 of an Arithmetic Progression (A.P.) is 2n +5. The 10th term is: proportional between 4 and 9 is: Which of the distribution? (a) Median (b) Mode following cannot be determined graphically for a grouped frequency (c) Quartiles (d) (xii) (xiv) Mean Volume of a cylinder of height 3 cm is 48n. Radius of the cylinder is: (a) 48 cm (b) 16 cm (c) 4 cm (d) 24 cm Naveen deposits he receives (a) 84 (b) 42 (c) F24 (d) 284 T23 511 800 every month in a recurring deposit account for 6 months. If 4884 at the time of maturity, then the interest he earns is: (xv) Thesolution set for the incquation 2 + 414, re W is: (a) {1.2, 3,4. 5 (b) {0. 1. 2, 3, 4, 5) ()1.2.3,4} (d) {0, 1. 2, 3. 4 Question 2 14 i) Find the value of ' a ' ifr - a is a factor of the polynomial 3 (ii) Salman depositsF 1000 every month in a recurring deposit account for 2 years. Ifhe receives (ii) 141 26000 on maturity, find: (a) the total interest Salman earns. (b) the rate of interest. In the + r - a x -81 given figure 0, is the centre of the circle. CE is a tangent to the circle at A. 14 If LABD= 26 , then find: (a) BDA (b) BAD (c) LCAD (d) LODB C Dk Question 3 ) 41 Solve the following quadratic equation: r+4x-8 0 Give your answer correct to one decimal (Use mathematical T23 511 tables place. if necessary.) 5 Turn Over (i1) Prove the following identity: (sin 6 4 1(tan*0 +1)+I =0 Use graph sheet to answer this question. Take 2 em= I unit along both the axes. (iii) (a) Plot A. B, C where A(0, 4). B(1, 1) and C(4, 0) (b) Reflect A and B (c) Reflect B through the origin and name it F. Write down the coordinates of F. (d) Reflect B and C (e) Join points A, B, C, D, E, F, G, H and A in order and name the closed figure on on the x-axis and name them as E and D respectively. the y-axis and name them as H andG respectively. formed. SECTIONB (40 Marks) (Atempt anw four questions from this Section.) Question 4 () (31 I fA = Find A(B + (ii) ABC is C) - 14 atriangle whose vertices are A(1,-1), B(0, 4) and C(-6, 4). D is the midpoint of BC. Find the: (a) coordinates of D. (b) equation of the median AD. (ii) In the given figure, O is the centre of the circle. PQ is a tangent to the cir 4 Chord AB produced meets the tangent at P. AB 9 cm, BP = 16 cm, LPTB = 50 L0BA 45 Q Find: (a) length of PT (b) BAT 50 (c) BOT (d) r23 511 2ABT 45 A 9 Cn 6 B 16 cm P Question 5 () Mrs. Arora bought tlhe lollowing articles rom a departmental store: S. No. Item Ilair oil 2. 131 Price Rate of GST Discount 1200 18% R 100 600 12% Cashew nuts Find the: (i) (a) Total GST paid. (b) Total bill amount including GST. Solve the following inequation. Write down the solution set and represent it on the 3 real number line. -5(x -9)217-9x>x+2,x R (ii) In the given figure, AC/ DE// BF. 4 IfAC 24 cm, EG-8 cm, GB=16 cm, BF=30 cm. cm 24 c / | 30 C D (a) Prove AGED AGBF (b) Find DE (c) DB: AB 13 Question 6 131 The tollowing distribution gives the daily wages of 60 workers of a factory. Daily income in Use Number of workers () 200 300 6 300-400 10 400 500 14 500-600 16 600 700 10 700-8000 4 graph paper to answer this question. Take 2 cm =7 100 along one axis and 2 cm = 2 workers along the other axis. Draw a histogram and hence find the mode of the given distribution. (i) The 5h term and the 9 term of an Arithmetic Progression are 4 and-12 respectively Find: iii) (a) the first term (b) common difference (c) sum of 16 terms of the AP. A and B are two points on the r-axis and y-axis respectively. 4 4B X' 54 -3 2 - 2 Y' T23 511 8 3 X 4 (a) Write down the coondiates of A and (6) P is a pont on AB such that AP : PR B. 31 Using section formula find the coondinates of point P (c)Find the equation of a line passing through P and perpendicular to AB. (c) Question 7 A bag contains 25 cards, numbered through I to 25. A card is drawn at random. What (31 is the probability that the number on the card drawn is: (i) (a) multiple of5 (b) a perfect square (c) a prime number? A man covers a distance of 100 km, travelling with a uniform speed of r km/hr. Had 3 the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed. (ii) A solid is in the shape of a hemisphere of radius 7 em, surmounted by a cone of height 4 to cm. a The solid is immersed certain height. level. completely in a cylindrical container filled with water find the rise in the water If the radius of the cylinder is 14 cm, (41 Question 8 G) The following table gives the marks scored by a set of students in an examination. Calculate the mean of the distribution by using the short cut method. Marks Number of Students 0-10 3 10-20 8 20-30 14 30-40 9 40-50 50-60 i) 2 What number must be added to each ofthe numbers 4, 6, 8,11 in order to get the four (3 numbers in proportion? ii) Using ruler and compass construct a triangle ABC in which AB= 6 cm, 2BAC=120 and AC cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle. Question 9 ) Using Componendo and Dividendo solve for x: 2x +2+2x-13 2x +2- V2x -1 (i) Which term ofthe Arithmetic Progression (A.P.) 15, 30, 45, 60... is 3002 Hence find the T23 511 sum of all the terms of the Arithmetic 10 Progression (A.P.) 41 (i) From the top ships ot a tower 100 m hieh observes the angles of depression a man A and B, on ot the tovwer and or wo 41 opposite sides of the tower as 45" and 38" respectively. IT ine the ships are in the same horizontal line find the distance between the two ships A and B to the nearest metre. (se Mathematical Tables for this question., 38" 100 m A B C Question 10 41 Factorize completely using factor theorem: 2--13x -6 i) [6 Use graph paper to answer this question. During a medical checkup of 60 students in a school, weights were recorded as follows: Weight (in kg) | Number of Students 28-30 30-32 32-34 10 34-36 13 36-38 15 38-40 9 40-42 2 42-44 Taking 2 an ogive. cm = 2 kg along Use your graph (a) median (b) upper Quartile (c) number one axis and 2 cm= 10 students to f nd the: is above 37 of students whose weight kg along the other axis draw oUTIO OF TCsE AnEMATI CS PaPERBoand) Ushen i ()a ,-2 2+0 2 2 C J-2 5/4 8-12:2k - 4 :2k vi CY K-2 3:2 Vii) -3b+3 =o b s 4 309 b (asA 2, 2 CX) 4 25 C 4 . a 4 A-4 x2 -480 Mean (Xu) 16 bo,1,2,,4,S3 Queshon 2 3a Ca) = o ( iy Tneaest 26ooo - [ccox2 11) 3a31 -a-81 =o 2 c0o a A CL et emieirl 64' C)ZCAD -16' d ZODB 26 CL at alt. Seqmeat) Queshun 3 X y%1x-) - 4+ 2 2 - 46.128 -4+6.92P -y-6.92 2 2 2 -10 123 =1464 1S,-S.S -Leso x eeo t + t= 0 PHs H.P. - S.4644 27 a-3 s A (o,4) G (o,-4) () BU,) P H- Ry C4 h (4) y U,) eocagm 4 0) 4 l-4,9 SeCTon B ACD+C)-144 ]+ J)o 301 14 30 22 42 Uy Dot, ACI,-1) 28 4) D3,4 M D3,) 4)= +t-S+S S+4y+1-S=o ua PTPAtPB PT PT (b) pAed. intekehna herd Sx! SxY A1 wents faed) 0uA. alt. eqmeut) CLat Cauve t i c a CL a S )LhT - 45+ 46 A 8S Q5 &hlu aajua 2oo - Uu: l|oo S.P Hur b 4ST |le 198 a otk GST L5) otal bill LOBT 80-luo 198+42 = 270 Io0t6oD+ 27* : z9F0 40 Lun - 5+45 11-9 7+2 -S7, 11-45 17-27 t 7 4x-2 4S*<l.S,1.S, eR -8 ) m (a) -3 2 - 1 O 2 A GeD &BGBF Z4ED= LGB (4nt alty 30 LEGD= LsGF (veat . y AGeF A GED (b) DE o sConesp Se BP D 8ml Bs a 9a) DE= IS 30 c)nDAL 2 ADAE LiM= 2BDE (oresp y) oA 6 AA ADeE a 4a4 4d 4 Aq t8d,12 F DB F 8 DB AB S:8 S-x 2 0 C) 4+|6 8x2)= -16o. 20 ay A 4,0) Dlo,4 X 41+0x3 43 Yeaure -3 +3 :3 1 (n-I --1+3F0 PCI M +2 0 &lae lie t+ s MY MABM I ISJ 8y0-60J d-4 a DE DE be m 7o S {,y3. .. 25 xy 45 PCE) Ss,10,1s, 2s , +,,14, 25) = S PCE) 43,5,+, ", 13,12,2, 23 - 9 t o m. E ce) Ci +2Sn lo-e Ys Pe -20r a+r)- - SUosu 2o(X*s) >D +Snu +S Vs -2oD = So 20 - + S -SUa so (heaa Cauno ome nd 20 k . l e ujen m lndu Vdum 7 C)h27 : Vat. ] &e tmmad inkost + 474) s h 3 A 25 n-A leAss meuto O-10 S 0 - 20 IS 30-4 3 40 SD 45 sD-60 SS 10 Mean: 2S+12 80 27.2S 60 2 2+ 48 60 O 15x-14x= 43-4 4+a n+a) Rta1'64 44 tIS7 2.2 - 4 20 3 0 (i) 4+ 1-S. 14 moule dur A mak tr 2Lblkahy MCuk r tad1u. qng (ampunaueo d edyldendlsb 2t2 -JMt JaH 224 27t2 2 2 1 t 2 8ny 2+2=Y 6 6x 2- 2 0 +nA 20 () DLD P or Ac1 u0 au0-sa) 129.99 luo1.2791 lUt127.99 A 27.9= 228 m. 10 ()(7)= 2-7-1374 -2 1 ) : 2-2)---13-2)-6 6 - 9 +26--6 %-2% 70 n+2)A qhr 2-Sn-3 t2 2A-a-13a-6 J) M)= (+1)(2 -Sn-3) =n*2) 27-6at-31 = (n*) ( 2a(n -s) t1(n-J)7 -Sx-13 S-lox 3 Mtn)(n-3)(2nH (T7? Lderct 2 28 30 4 30-32 322-34 13 36 38 IS 53 40- 42 S 42- 44 60 vO.2 Me 36.2 guah ke 2k 3 45 h 38.20 Mod hudeus cabuM se= 60-37= 23 (lo De lstoned lo tla nwer booklot/) Index Number Subject aNo Signature of Candidate (Rtuled in 2 mm squars) F Co4) 1.C.S.E. 2021 (To be fastened to the answer booklet/s) Index Number Unique lD- Subject Q No (Ruled in 2 mm squares) Signature of Candidate 6'UD modeS2 1.C.S.E. 2021 .CS.E 2021 lo be faslened to the auwer booklet/s) Unique ID- Index Number Subject tO) O No (Ruled in 2 mm squaros) Sgnaturo of Canddate G w 32 Lea 36 4 41

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