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HlJTCffl NGS HIGH SCHOO~ ~ HALF D JUNIO}:J COlJtMF! YEAJ.U.y EXAMINATION i o.J_2- ?,020 MhTHBMATlCS CLABSX Total number of printed sides : 4 Attempt ull questions from Section A and any four from Se-ct ton B. AU woi -king, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential ~ork.ing will result in loss of marks. The in.te nded marks for questions or parts of C{J;estions are given in brackets/]. Mathematical tabr . ~ d- I I T l41 Question 2 (a) Solve the followir.g inequation and write the solution set and represent it on the number line . -X 3 X 1 1 2 3 6 s - --1- < - , x c R P.T.O t d the foll owing dis tributj<m . (b) Calc ulate Ll1c m od inn a nd th c mo c .or - ----Mnrks obtain ed " ---.- - - 2 0 4 3 6 T 7 I _ ,.-- __ 19 I _ _ _ ---J,..- (out o{ 10) 1 Nu mb~.c:;ySlltdcnts _ -- 18 12 .r 3 ) 21 8 12 (c) Mr.Raj inve s ted Rs .9600 on Rs . 100 nhares at Rs. 20 p remium IJ3:ying: th dividend. He sold che ~hares when t_he price rose to Rs. 160 . H~ mves proceeds (excluding dividend) i.n 10% Rs.SO shares at Rs.40. Pm<l ilie e 1) mig:nal number of' shares . 2) sale proceeds. 3) new nurnber of shares . i4l 4) change in the two dividends . t uestion 3 accouni ~~~ . f.a)Mr. Ra .ri has a re.:urring deposit He depo~i.res Rs.2500 per month for 2 y rs . If he gets Rs.6625 t the tirire.,of matunty, find: ~ ' . . ~~ r3 J 1} the mteres t paid by the bank.,;) thef ~te of mterest . l . ~(.-w@"'l.F' ::~~:;_,_., ~u,,,, _, _.. ,;,: z: ?'M;c ~ -- ,,-: ..zd.ff. ~ . (b) Show th~~t (x -2) 1s a factor _9M~ polynormal completely. . I :i~2 - 4x W.~i,[f?~;-~ -~~ -, ~ .. .JO ,.~ the --~;;~ ~: ~ ~-(c) A pole 6 m high is JJffi_cn the top ~ __ 13, -~ wer. Tbe_,angie of e~ / ~ tion of the top of ~e pole ~P15e~~f{l~m a pom}T~t-fe gr01~~~~}?jf a the ~gle ~: . depress10n ~=~_JJ:ie pomt_ J(~f.1 th:~ p of~J_gwer 1s 4:~J?md me height o:r -~::=::?;:.b.-~zy,, A - -Y.' <', ._ Titl th e t ower .,#.,,.-1 ,h., '<W,,i;;;-/)?. o;.:-;;:_-;:, 1 ..;, ~-:r-~%~ ~ W/2:'l"'_.,; ~4.,. :::~ . ... ~ -;,?fE:;-> ';;:-7.~t,;. -!j_~1f???" - uesti0l7~ ~4~&,;< -;;i"' ~ 1h., ~,...,_ $,-JJA, '-Mm ~ (a): f '~~}lm of ll:_e fi~ - g terms -4 and the fifth term i.s 4 times the tE~,t erm, t~,J;'ffi.~~~~ "lffo.!' [3 } ' i(~. /.:;J.'.:"'' '(i . && _ :-. , !#' ~Z~-o,~, ,74> ,7..> . , . ~_,.,,., , ~ ~ -. ,,, 'I - ... - --~r o ,_.t~~- . > ,:?;:? ta 8 {b) Prov e m l @~f:_ n ~ zl:::, 1-co: e '<{. -'/ + ,,-; ; -wd 1 + sec 8 cosecf} ' - ~-'?-?.- . ..,,'l"...:~, [3 1 1 ,:: Av - :?"...,.. ?;; {c)Use graph papert~.r._ this ques.tion ( take 2cm = 1 unit along both axes} (1) Plot_the point~Qffi+::,-9): , A (-4, 4), B(-3,0) and C(0 ,-3) (2) Reflect A and B 1tfih'.e Y axis and name them A' and B ' respec tiYe!y . W rite" down their coorcili1ates. (3~ Name the figure OABCB'A' and find its area . [4 ] Section B &9 lvr'i! an y four q uestions fro m this section> Question 5 (a) Solve the quadratic equation 3x 2 -x- 7 =0 arid give your ans\\ er corre<:I to two significant figures . [3) (b) If 6 is mean proportion betwe en the numbers X and Y and 48 is the third proportional to X and Y, find the numbers. [3 1 (c) A {1, -5}, B (2, 2) and C (-2, 4) are the vertices of D. ABC.. Find the equation of: (1) The ffif.!dian of the triangle through A (2) The altitude of the triangle through B 1_3) The line through C and parallel to AB. {4 ] on~ . . CBQ=48 and a=2b, ln the give:n figure . ABCD is a cyclic quadrilateral, L (3~ Cak ulat e the numerical value of a and b. D p Q I I Marks obtained i~WJO students in an examination are given below : 0> Marks . . ~~lt ~i -t " 20- 30- 40- 50- 60- 70- 80lC1 :~; ~ o 30 40 50 60 70 80 90 90100 ,,;,V Number of 5 ~:- 10 14 21 25 34 27 36 16 12 '1 ::.tudents Draw an ogive for the following distribution. From the graph, find : (1) the median (2) upper quartile Pl the number of students scoring above 65 marks (4) if 10 students qualify for merit schlorship, find the minimum marks required to qualify. l6} I . Ouestlc,n 8 (a) ~alcul:3-te the ratio in which the line joining A(-4, 2) and 8(3, 6) is divided by tne pomt P{x, 3). Also find x. J'p,,. ~ {31 . . :tJ'lb) :he total_ s1.1rfa~e of a circular cylinder is 462cm2. If its curved surface area W is one thi.rd of its total surface area, find the volume of the cylinder. P.T.O / [31 ~ of 50_~~ ~~_s ~ e n~corded as given below 0 85 ) \ ---- 85-90 90-95 - 10 8 95-100 12 --- 190105 105110 110- 8 4 3 llS.. \ Calculnte the mean weight to the nearest gram by Step -Deviation method. [4] Question 9 (a) In t he adjoining figure, chords AB and diameter CD of a circle with centre 0 meet at P. PT is a tangent to the circle at T. If AP= 16 cm, AB= 12 cm and DP = 2 cm, find the radius of the circle. Also find the length of PT. [3] A (a) If A I I =l~ -z11 and B l!1 il ,find matrix X if X- 3B = = 2A. [31 (b) 1\vo dice are thrown .at the same time. Find the probability of getting: 1) a doublet 2) a sum of atmost 8 3) sum of atleast 11. [31 / ( c) In the figure gjven below, ABC is a triangle with LEDB = LACB. If BE ::. 6cm, EC = 4cm, BD = 5cm and area of ~BED = 9 cm2 , calculate 1) the length of AB 2) the area of MBC l4\
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