SULT 347/ Rumus-umus eikut oleh memtu d mejw sol. Simol-simol yg diei dlh yg is diguk. LGER. 4c x 5. log m log m log 9. T d. m m m 6. log = log m log 0. S d m m 3. 7. log m log m. S, m m logc 4. 8. log. T log c 3. S, KLKULUS (CLCULUS) dy dv du. y uv, u v 4. Lus di wh legkug (e ude cuve) dx dx dx = ydx tu (o) du dv v u u dy. y, dx dx 5. sipdu j (Volume geeted) v dx v dy dy du 3. = y dx tu (o) x dy dx du dx STTSTK (STTSTCS) x Q. x 6. 00. P() X C, p q p q N Q fx. x 7. f o x x x! 3. x 8. P 3. N N! x! 4. x 9. C 4. 5. W i W i i xdy. Mi (Me), p f x fx X Z f f!! N F m L C 0. P()()() P P P fm pq
x x y y GEMETR (GEMETRY). Jk (Distce) 4. Lus segitig (e of tigle). Titik tegh (Midpoit) x x y y x, y, 5. x y 3. Titik yg memhgi sutu temeeg gis 6. ˆ ( poit dividig segmet of lie) x, y, x y x y x y x y x y x y 3 3 3 3 xi yj x y x mx y my m m TRGNMETR (TRGNMETRY). Pjg legkok, s j 8. si si kos kossi c legth, s si si cos cossi. Lus sekto, L 9. kos koskos si si j e of secto, cos cos cos si si 3. si kos si cos 4. sek t sec t 0. t t t t t t. t t c. si si si C 5. kosek 3. kot c c kos cosec cot c c cos 6. si si kos 4. Lus segitig (e of tigle) si si cos = sic 7. kos si kos kos si cos cos si cos si
Sectio [40 mks] swe ll questios. Solve the followig simulteous equtios: x y xy 7 x y 5 [5 mks]. ) The qudtic equtio x 6x 7 mx 3 of m. hs two equl oots. Fid the possile vlues ) Hece, detemie the sttioy poit d detemie the xis of symmety fo the ove equtio. 3. closed ectgul ox is mde of vey thi sheet metl, d its legth is thee times its width. f the volume of the ox is 88 cm 3, show tht its sufce e is equl to the width of the ox. Fid y diffeetitio the dimesio of the ox of lest sufce e. 768 6x x cm, whee x cm is 4. set of dt which cosists of 5 umes hs me of d stdd devitio of 3. ) Fo the set of dt, fid i) the sum of the umes, ii) the sum of sques of the umes ) othe set of dt which cosists of 5 umes with me of d vice of 8 is dded to the oigil set of dt. Fo the comied set of dt, fid i) the ew me ii) the ew stdd devitio [5 mks] 5. Digm shows tigle XY. The stight lie Y itesects the stight lie X t C. t is give tht X x, Y y, X d Y Y 3 ) Expess ech of the followig vectos i tems of x d y i) ii) X iii) Y [5 mks] C ) Give tht C hx d C k Y, fid the X vlue of h d of k. [4 mks] 6. The histogm elow shows the mks otied y Fom 5 clss of studets i dditiol Mthemtics test. Digm 5 7 9 ) Without dwig ogive, clculte the medi mk ) Clculte the stdd devitio of the mks distiutio. 3
Sectio [40 mks] swe y fou questios fom this sectio. 7. Use the gph ppe to swe this questio Tle shows the vlues of two viles, x d y, otied fom expeimet px The viles x d y e elted y the equtio y, whee p d q e costts. qx x 3 4 5 6 y.60 0.55 0.94 0.089 0.040 0.07 Tle ) sed o tle, costuct suitle tle fo the vlues of x y [ mk] ) Plot x y gist x, usig scle of cm to uit o the x-xis d cm to 0.5 uit o the x y - xis Hece, dw the lie of est fit. c) Use the gph dw to give the est estimted vlue of i) y whe x =.5 ii) p iii) q [6 mks] 8. Digm shows equtio y x( x 4), the x-xis, the stight lie y = 5 d the stight lie y 5 y x( x 4) Digm Fid ) The tuig poit of the cuve y x( x 4) [ mks] ) Detemie the xis of symmety of the cuve. [ mk] c) The equtios of oml t poit d poit d) Hece o othewise, detemie the poit of itesectio, D of the oml t poit d oml t the poit e) Wht c you sy out the positio of poit D, the midpoit of d the tuig poit of the cuve y x( x 4)? [ mk] 9. Digm 3 shows two cs, PQ d RS, of two cocetic cicles, with the sme cete. RQ is pepedicul to S. R Give tht P = Q = 5 cm d PQ di, Digm 3 fid ) the peimete of the shded egio, P [7 mks] ) the e of the shded egio. d Q S 4
0. Solutios y scle dwig will ot e ccepted fo this questio. Digm 4 shows tht the stight lies d C e pepedicul to ech othe. The equtio of the stight lie C is x y 6 ) Fid y i) the equtio of the stight lie givig you swe i the geel fom, ii) the coodites of poit. C [4 mks] ) The stight lie is exteded to poit D such x tht : D = : 3. Clculte the e of tigle ( 9, 4) D. x y 6 c) poit M moves such tht the gle M is lwys Digm 4 ight-gle. Fid the equtio of the locus of M.. ) Digm 5 shows shded egio ouded y the cuve y x k, the y-xis d the stight lies y 3 d y 3. f the e of the shded egio is 30 uits, fid the vlue of k. y [4 mks] y x k 3 x Digm 5 3 ) Fid the tio of the volumes if the shded egio is otted out the y-xis fo 80 o to tht of the shded egio if it is otted out the x-xis fo 80 o. [6 mks] Sectio C [0 mks] swe y two questios fom this sectio.. The cost to poduce ti of pit depeds o the cost of the w mteils, the poductio cost d the pckgig cost. The tle shows the pice idices d weightges of those costs. 00 (sed o Cost the ye 999) 005 (sed o the ye 999) 005 (sed o the ye 00) Weightges, w Rw mteils 75 8 04 x Poductio h 00 5 5 Pckgig 45 k 0 ) Give tht the composite idex of the cost to poduce ti of pit fo the ye 005 sed o the ye 00 is 7.7, fid the vlue of x. ) Give tht the pice of ti of pit i the ye 00 ws RM 30, clculte its coespodig pice i the ye 005. [ mk] c) Fid the vlues of i) h, ii) k. [6 mks] 5
3. ) f m log6 3 d log6 5, expess log 45 i tems of m d. [5 mks] ) Give log x 6, log x 8 d log x 3, fid the vlue of log c x [5 mks] c 4. Digm 6 shows, EC d ED e stight lies d E = ED. t is give tht = 9 cm, o o D = 4 cm, CD = 5 cm, ED 5 d CD 35. Digm 6 Clculte ) the legth of D, [4 mks] ) D, [ mks] c) the e of the whole digm. [4 mks] 5. Digm 7 shows cicul cylide of height h d dius sumouted y hemisphee of the sme dius. h Digm 7 Expess the totl sufce e S of the oject d the totl volume V i tems of h d. [ mks] 3 5 f the totl sufce e S is 0, expess h i tems of d hece show tht V 0. 6 [ mks] Fid the vlue of which mkes V mximum d clculte the mximum vlue of V, givig you swe i tems of [6 mks] Ed of Questios 6