Trial Mat T 954/2
9
SEKOLAH MENENGAH DATUK PETER MOJUNTIN, SABAH PEPERIKSAAN PERCUBAAN PENGGAL 2, 2014 MATEMATIK T Section A [45 marks] Answer all questions 1. The equation of a curve is (a) Show that [4m] (b) Find the equation of normal to the curve at the point P(1,2), giving your answer in the form . [3m] 2. The variables and are related by the differential equation . It is given that when . Find the expression for in terms of . [6m] 3. By using the substitution show that = . [8m] 4. By using an integrating factor, find the solution of the differential equation given that when [8m] 5. Water is leaking from a hole at the bottom of a large tank. The volume of the water in the tank at time t hours is V m 3 . The rate of decrease of V is directly proportional to V 3 . (a) Write down a differential equation satisfied by V. [1m]
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Transcript of Trial Mat T 954/2
SEKOLAH MENENGAH DATUK PETER MOJUNTIN, SABAHPEPERIKSAAN PERCUBAAN PENGGAL 2, 2014MATEMATIK TSection A 4! "#$%&'An&(e$ #)) *+e&tion&1, T-e e*+#tion o. # c+$/e i&0#1S-o( t-#t 4"'0213in4 t-e e*+#tion o. no$"#) to t-e c+$/e #t t-e 5oint P01,21, 6i/in6 7o+$ #n&(e$ in t-e .o$", 8"'2, T-e /#$i#2)e& #n4 #$e $e)#te4 27 t-e 4i9e$enti#) e*+#tion , It i& 6i/en t-#t (-en,3in4 t-e e:5$e&&ion .o$ in te$"& o., ;"'8, B7 +&in6 t-e &+2&tit+tion &-o( t-#t/e o$4in#te& to >n4 #n #55$o:i"#te /#)+e .o$ t-e inte6$#),3in4 t-e e:#ct /#)+e o., 6i/in6 7o+$ #n&(e$ in 4 &i6ni>c#nt >6+$e&,3in4 t-e 5e$cent#6e o. e$$o$ in t-e #2o/e #55$o:i"#tion, A"'Section B 01! "#$%&'An&(e$ one *+e&tion on)7A, 0#1T-e .+nction . i& 4e>ne4 27 U&e M#c)#+$inC& t-eo$e" to &-o( t-#t (-en i& e:5#n4e4 in #&cen4in6 5o(e$& o. D0i1 t-e >$&t t-$ee te$"& #$e ;"'0ii1 t-e coeEcient o.i& Be$o, 8"'021Hence ($ite 4o(n t-e >$&t t(o nonFBe$o te$"& in t-e e:5#n&ion, in #&cen4in6 5o(e$& o. o.,1"'0c1U&e t-e &e$ie& e:5#n&ion V2 3600at+1at 2tcos2xdx03cos2xdx03f x( ) ln 1+ex( )f x( )xln2 + 12 x+ 18x2x3xln1+ex2
_, to ($ite 4o(n t-e >$&t t-$ee te$"& in t-e e:5#n&ion, in #&cen4in6 5o(e$& o. o.,
1"'041U&e 7o+$ #n&(e$& in 5#$t& 021 #n4 0c1 to >n4
4"'=, S%etc- on t-e "e coo$4in#te #:e&, t-e 6$#5-& o.#n4,S-o( t-#t t-e e*+#tion e2x x 5 0 -#& # $oot in t-e inte$/#),U&e t-e Ne(tonFR#5-&on "et-o4 (it- t-e initi#) e&ti"#tex0 0.5to e&ti"#te t-e $oot co$$ect to t-$ee 4eci"#) 5)#ce&, 11"'3in4 t-e #$e# 2o+n4e4 27 t-e c+$/e&,F#:i& #n4F#:i& 6i/in6 7o+$ #n&(e$& in 2 4eci"#) 5)#ce&, 4"'END O3 GUESTIONNo M#$% Sc-e"e S+2 M#$%&Co""ent&ln 1+ x( ) x 12 x2+ 13x3...xln 1 x2( )limx0ln1+ex2
_,+ ln 1 x2( )xsin x
1]1111y e2xy x+5[1, 0]x y10#1#& # 4e$i/#ti/e o. #& # 4e$i/#ti/e o.B1B1M1A1 c#o1021At P01,21, B1M1A12 M1M1M1A1M1A1 ;8 ?-en ?-en
