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ombap &tottiib &tbool, Jllaf)im PRELIMINARY ASSESSMENT MATHEMATICS Grade : 80 Max. Marks : 10 s No. of Question No. of Printed-s ides 10 '\ 10 ; 07 .01.2025 oate . . 3 hours ourauon wers to thi.s Paper must be wri~en on the paper provided separately. ArtS You will not be allowed to wnte during first 15 minutes. This time is to be spent in reading the question paper. Tfre time given at the head of this Paper is the time allowed for writing answers. ~questions from Section A and anyfour questions from Section B. Atte:!,kfng, including rough work, must be clearly shown, and must be done on the same sheet as the rest of the answer. All otnfssfon of essential working will result in loss of marks. The intended marks for questions or parts of questions are gi.ven in brackets [ J. Mathem atical tables are provided. I Section A (Attempt all questions from this Section.) QUestion 1 Choose the correct answers to the questions from the given options. (Do not copy the question, write the correct answers only.) (i) (15) A man deposits f 2500 per month in a recurring deposit account for 2 years. If he gets f 6250 as interest at the time of maturity , the rate of interest is (a) 10% (b) 8% (c) 12% (d) 5% (ii) Assertion(A) : The ratio in which the join of A(-3,-1) and B(S, 7) divided by the line x = 2 is 5 : 3 Reason (R) : The point of intersection of line x = 2 with line segment AB is (2,0) (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true and R is the correct explanation of A. (d) Both A and R are true and R is not the correct explanation of A. 1 (iii) . 5 (-7,4) and (10,-2) The centroid of a triangle whose vertices are ( 3,- ) ' . 1S (a) (3, -1.5) (b) (2, -1) (c) (-1,2) (d) (0, -1) (iv) A company declares a dividend of 12% on ~100 shares. Am~ buys such shares and gets 15% on his investment. The price at which he bought the shares is: (a), 80 (b), 125 (c) , 85 - (d) ,100 (v) (vi) FABCDE is a regular hexagon, AB is parallel to x-axis. If the coordinates of the point B are (2,4) then the equation of BE is: (a) y = X + 2 (b) y + '13x = 4 + 2'13 (c) y - '13x = 4 - 2/3 (d) y + x = 6 If P and Q are the centres of two circles intersecting at B and C. ACD is a straight line and L APB = 130 , find x. D (a) 650 (b) 115 (c) 2300 (d) 1300 2 .., + -rs Assertion (A) : The value of sin A is the greatest for ~ PQA. p (vii) D B A Reason (R ) : The value of sin A does not depend on the side lengths but is a ratio of the side lengths. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and Rare true and R is the correct explanation of A. ld) Both A and Rare true and R is not the correct explanation of A. (viii) A fl ABC with LABC = 90 , AB= 15cm, AC= 17cm, circumscribes a circle. The radius of the circle is (a) 8.5cm (b) 4cm (c) 3cm (d) 7.5cm (ix) P(3,4) is a given point, P' is its image when reflected in the line y = 3. The equation of a line passing through P' parallel to x-axis is (a) y = 2 (b) x = 2 (c) y = -2 (d) x = -2 (x) If (x + y)th term of an A.Pis p and (x-y) th term is q then the xth term is equal to (a) pq (b) (p+q) 2 (c) (pq)2 (d) (p-q) 2 3 j (xi) uidistant from A and C is the . In rhombus ABCD, the locus of points eq bisector of LA and LC. (I) perpend icular bisector of AC. (II) (III) diagonal BD. Which of the above statement(s) is/are true? (a) Only {I) (b) Only (II) (c) (I) and (11) {4.) (11) and (III) (xii) If in triangle ABC, PQ II BC , AB II QR and PC intersec ts QR at 0, then ~ PBC is similar to A s (a) (b) (c) (d) C R llORC llPCA llOQC llABC If the probability of an event is p, then the probabili ty of its complem entary event is p-1. (II) Probability of an event can be 0. 7. (III} The probability that two friends will have same birthday in the 1 year 2025 is -365 . (xiii) (I) Which of the above statemen t( s) is / are correct? (a} Only II (b) Both I and II (c) Both II and III (d) Only III 4 C:, ftx:lP, 3 (xiV) If on dividing 2x -x:2- - ax+ 5 by 2x + 1, the remaind er is 6, then the value of a is : (a) -2 (b) 10 (c) -9 (d) 3 (XV) The value(s) of k for which the quadrati c equation (k-3)x2-2(k-3)x+2=0 has equal roots is 3 (I) 5 (II) Which of the above value(s) is/ are correct? (a) I (b) II (c) Both I and II (d) Neither I nor II Question 2 i) 3 If (x - 2) and (x + 1) are the factors of x + 3x2 +ax+ b, find the values of [4] a and b. ii) In the figure given below, XY is the diameter of the circle, PQ is a tangent [4] to the circle at Y, LAXB = 50 and L.ABX = 70 . Find a) LAYB X b) LYXB c) L.AYP d) LAPY (figure not drawn to scale) p y 5 Q n ven by ("51 , n e N iii) (a) Write the first four term s of the sequ ence gt 4 () (b) If the sum of its first 8 term s is k(S+./5 ) , find k. Question 3 th i) Points A and B have coordinates (7,-3) and (1,9) respective ly. Find e equa tion of perpendicular bisector of the line segm ent AB. (4) ii) A golf ball has diameter equa l to 4.1cm. Its surfa ce has 150 hemispherical dimples each of radiu s 2mm. Calc ulate the total surfa ce area of the ball whic h is exposed to the surro undi ngs. Give your answ er corre ct to the neare st squa re cm. (Take n =3.14) [4] iii) F?r the Annual Spor ts Meet of our school, stude nts parti cipat ed in the discu s throw competition. The dista nce throw n (in metre s) by the parti cipan ts is recor ded below: Dista nce in metr es 12-13 Num ber of stude nts 3 13-14 9 14-15 12 15-16 9 16-17 4 17-18 2 18-19 1 Use a graph pape r to draw an ogive for the ab 2cm = 1 metre on one axis and 2cm = 5 t d ove d1str1butio n. Take a scale of s u ents on the other a.xis Hence, using the graph estimate: a) the median. b) the uppe r quartile. c) the numb er of stude nts who thr ew a d'istan ce of 16.Sm and above. 6 (5] Section B (At t.m pt any four) Question 4 tion set and repr esen t it on Solve the following inequation, write the solu ~ i) ~rm~~~. 1 S 2x R xE -26-<2---3<2 ' by Sho rt Cut met hod . Give Find the mea n of the following dist ribu tion [3) you r answ er correct to the nea rest gram. ii) Weight (in gm) 80-8 5 85-9 0 90-9 5 95-1 00 Frequency 5 10 12 12 iii) 100 -105 105 -110 110 -115 8 2 the circle, tang ent AB In the figure given below, O is the cen tre of mee ts diam eter CD prod uced at A. a) Prove MDB ~ MBC. = 6cm, find AD b) If the radi us of the circle is 4.5cm and AB 1 [4) Question 5 i) ii) pap er num bere d 1 to 50. There were 50 que stio ns in an examination of question cho sen will Write down the probability that the num ber a) con tain atle ast one figure 3. b) be a composite num ber between 20 and 30. (3) c) not be divisible by eith er 2 or 3. 0 per mon th at 10% per A man has a recu rrin g deposit acco unt of ,100 time of mat urit y, find the tota l annum. If he gets f 5550 as inte rest at the [3] . time in year s for which the acco unt was held 7 iii) 5 5cm AC 5cm. Construc t a M.BC with BC 6.5 cm, AB record the radius Construc t the incircle of the trtangle. Measure (4] of the incircle. and Queatlon 6 i) Use graph sheet for this question. Take 2cm'" 1 unit on both tbe axes. a) Plot A(O,4), B(l,1), C(4,O), D(l,-1) and E:( o,-4 ) W 't down the b) Reflect B through the origin and name it as F. n e coordinat es of F. c) Reflect B and C along the y-axis and name them as H and G respectively. Write down the coordinat es of H and G . d) Join the points A,B,C,D,E,F,G,H and A in order and wnte the geometrical name of the figure formed. e) Find the area of the figure. [5] ii) A 1.4 m tall girl spots a balloon moving with the wind in a horizonta l line at a height of 91.4 m from the ground. The angle of elevation of the balloon from the eyes of the girl at that instant is 60 . After 6 seconds, the angle of elevation changes to 320. Find the speed of the balloon during that interval. Give your answer correct to 3 significan t figures. [5] Question 7 i) Find x and y if (3) ii) iii) How many terms of the A.P 24, 21, 18, ... must be taken so that their sum is 78? [3] A man sold x shares of, 40 paying 8% divid~~d at a discount of 1'0% and invested the proceeds in , 20 shares at a premium of 50% and paying 12% dividend. If the change in income is , 192, find the value of x. [4] 8 ,,/ Que stio n 8 i) Solve the fallo wing equa tion and give your answ er corr ect to 3 sign ifica nt figu res. 2x ii) 2 - lOx + S = o (3) A shop keep er bou ght a dish was her at a disc ount of 20% from a who lesa ler, the prin ted pric e of the dish was her bein g ,450 00. The shop keep er sells it to a cons ume r at a disc oun t of 10 % on the prin ted pric e. If the sale s are intra state and the rate of GST is 12 % , find: a) the pric e inclu sive of tax at whic h the shop keep er boug ht the dish was her. b) the tax (und er GST) paid by the shop keep er to the Stat e Gov ernm ent. (3) Dra w a line segm ent AB of leng th 12 cm. Loca te the mid -poi nt M of AB Dra w and desc ribe the locu s of a poin t whic h is a) at a dist ance of 3 cm from AB. b) at a dist ance of 5 cm from M. c) Mar k poin ts P, Q, R, S whic h satis fy both the cond ition s in (a) and (b). Nam e the quad rilat eral form ed. [4] Que stio n 9 iii) i) A mat hem atic s apti tude test of 50 stud ents was reco rded as follows: Mar ks No of stud ents 50-6 0 4 60-7 0 8 70-8 0 14 80-9 0 19 90-1 00 5 Usin g a grap h pap er, draw a histogram. for the abov e data and estim at~ ] the mod e. 3 ii) (ili) A map has a scal e of 1 : 2S0 ,000 . . km? the map 1s a Jour ney of 4 0 a) How man y cm on . 3cm 2 wha t is the actu al area of b) If the area of a lake on the map 18 ' (a] 1an2 ? ak the 1 em [1 4 Prove the iden tity: 3 B+cos39 sm 1-2c os28 9 sec9 -sin 6 ----tan8 -1 _J------ --------- Question 10 i) The thre e sides of a right triangle form thre e consecutive eve n num ber s. Find the lengths of the three sides, meAsured in cm. [3] ii) Show that point A(3,-2) is a poin t of trisectio n of the line seg men t join ing the poin ts (2, 1) and (5,-8). Also, find the coordin ates of the oth er poi nt of trisection. (3] iii) Usin g properties of proportion, find x 16 (a-x )3 a+x [4] = a+x a-x 10 j
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