PEPERIKSAAN PERCUBAAN SPM TAHUN 2007 ADDITIONAL MATHEMATICS. Form Five. Paper 2. Two hours and thirty minutes

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SULIT 347/ 347/ Form Five Additiol Mthemtics Pper September 007 ½ hours PEPERIKSAAN PERCUBAAN SPM TAHUN 007 ADDITIONAL MATHEMATICS Form Five Pper Two hours d

1 SULIT 347/ 347/ Form Five Additiol Mthemtics Pper September 007 ½ hours PEPERIKSAAN PERCUBAAN SPM TAHUN 007 ADDITIONAL MATHEMATICS Form Five Pper Two hours d thirty miutes DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE INSTRUCTED TO DO SO. Plese red the iformtio give o pge crefully. This questio pper cosists of 3 prited pges

2 SULIT 347/ INFORMATION FOR CANDIDATES This questio pper cosists of three sectios : Sectio A, Sectio B d Sectio C. Aswer ll questios i Sectio A, four questios from Sectio B d two questios from Sectio C. 3 Give oly oe swer/solutio to ech questio. 4 Show your workig. It my help you to get mrks. 5 The digrms i the questios provided re ot drw to scle uless stted. 6 The mrks llocted for ech questio d sub-prt of questio re show i brckets. 7 A list of formule is provided o pges d 3. 8 You my use four-figure mthemticl tble. 9 You my use o-progrmmble scietific clcultor. The followig formule my be helpful i swerig the questios. The symbols give re the oes commoly used. ALGEBRA b b 4 c x 8 log b log log c c b m x = m + 9 T ( ) d 3 m = m 0. S ( ) d 4 ( m ) = m T r r r 5 log m log mlog S, r r r m 6 log log mlog 3 S, r r 7 log m = log m

3 SULIT 3 347/ CALCULUS y = uv, dy dv du u v 4 Are uder curve = dx dx dx b y dx or b x dy 3 du dv v u u dy y, dx dx 5 Volume geerted = v dx v dy dx dy du du dx b b y dx or x dy STATISTICS x x N 7 I W ii W i i fx x f 8 P r! ( r)! 3 x x x x 9 N N C r! ( r)! r! 4 x x fx f f f x 0 P( A B) P ( A) P ( B) P ( A B ) N F 5 m L C f m ( ) r P X r C p q r, p q Me, r p 6 I Q Q pq 4 Z x [See overlef

4 SULIT 4 347/ GEOMETRY 4 Are of trigle = Distce = x x y y x y x y 3 x 3 y Mid poit x x y y x, y, 5 r x y ~ x y x y x y A poit dividig segmet of lie x mx y my x, y, m m 6 ^ r ~ x iy j x ~ ~ y TRIGONOMETRY Arc legth, s =r si A B si A cos Bcos Asi B 8 Are of sector, A r 9 cos A B si A cos B cos Asi B t A t B 3 si A cos A 0 ta B t A tb 4 5 t A sec A t A t A t A cosec A cot A b c si A si B si C 6 si A = si A cos A 3 b c bc cos A 7 cos A = cos A si A = cos A = si A 4 Are of trigle = si b C

5 SULIT 5 347/ Sectio A [40 mrks] Aswer ll questios. Solve the simulteous equtios correct to three deciml plces. 3m 3m m 6 7. Give your swer [6 mrks] () Express qudrtic fuctio f x x 4x 3 x p q. i the form of Hece, stte the mximum or miimum vlue of the fuctio. [3 mrks] (b) Fid the rge vlues of x for which xx 4. [3 mrks] 3 () Prove tht si x cot x cos x. [3 mrks] (b) Give cos, p p i. prove tht t. p ii. hece, fid si, whe p. [5 mrks] 4 () Fid the equtio of the orml to the curve 3 y x x t the poit (, -). [3 mrks] (b) Give y, fid the pproximte chge i y whe x decreses from 4 to 3.9. x [3 mrks] [See overlef

6 SULIT 6 347/ 5 () A curve hs grdiet fuctio of 3x x. Give tht the curve psses through the poit (,-3), fid the equtio of the curve. [3 mrks] y 4 4 y x 0 x DIAGRAM 4 (b) Digrm shows prt of the curve of y. Clculte the volume geerted x whe the shded regio is revolved through 360 bout the y-xis. [4 mrks]

7 SULIT 7 347/ 6 Digrm shows rrgemet of these right-gled trigles for the ifiite series of similr trigles. y cm x cm DIAGRAM The bse d the height of the first right-gled trigle is x cm d y cm respectively. The bse d the height of the subsequet trigle re qurter of the bse d hlf of the height of the previous trigle. () Show tht the res of the trigles form geometric progressio. Stte the commo rtio of the progressio. [3 mrks] (b) Give x = 60 cm d y = 30. (i) Determie which trigle hs re of 6 4 cm². (ii) Fid the sum to ifiity for the re, i cm², of ll the trigles. [4 mrks] [See overlef

8 SULIT 8 347/ Sectio B [40 mrks] Aswer four questios. 7 Use the grph pper provided to swer this questio. Tble shows experimet vlues of two vribles x d y. Vribles x d y re relted by the equtio y, where d b re costts. x b x y TABLE () Plot xy gist y by usig scle of cm to 0.5 uit o the y-xis d cm to uit to the xy-xis. Hece, drw the lie of best fit. (b) Use your grph from () to fid the vlues of d b. (c) Fid the vlue of the grdiet of the stright lie obtied whe y gist x. is plotted [0 mrks] 8 The coordites of poit A, B d C re (, ), (7, 8) d (-3, k) respectively. Give tht the re of ABC is 4 uit². () Fid i. the possible vlues of k. ii. the equtio of perpediculr bisector of AB. [6 mrks] (b) A poit P moves such tht its distce from poit A is lwys 0 uits. i. Fid the equtio of the locus of P. ii. Determie whether or ot this locus psses through the poit (4, ).

9 SULIT 9 347/ [4 mrks] 9 Tble shows the mrks scored by 00 studets i the Additiol Mthemtics Mrch Mothly test. () Bsed o the dt i Tble d without usig the grphicl method, clculte (i) the medi, (ii) the me, d (iii) the stdrd devitio. Mrks Number of scored studets TABLE [6 mrks] (b) Use the grph pper provided for this prt of the questio. Bsed o Tble, drw histogrm. Use your histogrm to estimte the mode for the mrks. [4 mrks] 0 () I exmitio, 65% of its cdidtes pssed with full certifictio. For smple of 0 cdidtes tke rdomly, fid the probbility of t lest 3 cdidtes will pss with full certifictio. [4 mrks] (b) Give tht the weight, i kg, of the studets i school hve orml distributio with me of 55 kg d vrice of 00 kg, fid (i) the z-score for the weight 66 kg, (ii) the weight of the studet tht correspod with the z-score of -.03, (iii) the probbility tht the weight of studet picked rdomly will be betwee 4 kg d 66 kg. [6 mrks] [See overlef

10 SULIT 0 347/ Digrm 3 shows squre ABCD with sides 5 cm i legth. BAPC is sector with its cetre t B d ABC is semicircle. D P A C R Q θ B Digrm DIAGRAM 3 [Use π= 3.4] () Clculte (i) the re of the segmet APC, [ mrks] (ii) the perimeter of the shded regios, [ mrks] (iii) the re of the shded regios, [ mrks] (b) Give tht BQR is sector with gle θt its cetre, B d the legth of the rc AP is 6 cm, fid (i) the gle θi rdis, [ mrk] (ii) the legth of the rc QR if the re of APQR is.6 cm. [3 mrks]

11 SULIT 347/ Sectio C [0 mrks] Aswer two questios. Digrm 4 shows the br chrt for the mothly sles of five essetil items sold t sudry shop. Tble 3 shows their price i the yer 000 d 006, d the correspodig price idex for the yer 006 tkig 000 s the bse yer. Cookig Oil Rice Slt Sugr Flour uits Digrm DIAGRAM 4 Items Price i the yer 000 Price i the yer 006 Price Idex for the yer 006 bsed o the yer 000 Cookig Oil x RM.50 5 Rice RM.60 RM.00 5 Slt RM0.40 RM0.55 y Sugr RM0.80 RM.0 50 Flour RM.00 z 0 TABLE 3 () (b) Fid the vlues of (i) x, (ii) y, (iii) z. [3 mrks] Fid the composite price idex for cookig oil, rice, slt, sugr d flour i the yer 006 bsed o the yer 000. [ mrks] [See overlef

12 SULIT 347/ (c) The totl mothly sle for cookig oil, rice, slt, sugr d flour i the yer 000 is RM 500. Clculte the correspodig mothly sle for the sme items i the yer 006. [ mrks] (d) From the yer 006 to the yer 007, the price of the cookig oil, rice d sugr icresed by %, while the price of both slt d flour icresed by 5 se. Fid the composite price idex for ll the five items i the yer 007 tkig 006 s the bse yer. [3 mrks] 3 Digrm 5 shows two trigles ABE d CDE. Give tht AB = 0 cm, DE = 0 cm, BAE = 30 o, AE = BE d AED is stright lie. B A 0 cm C 0 cm 30 o E Digrm DIAGRAM 3 5 D () Fid the legth, i cm, of AE. [ mrks] (b) If the re of trigle ABE is twice the re of trigle CDE, fid the legth of CE. [3 mrks] (c) Fid the legth of CD. [ mrks] (d) (i) Clculte the gle CDE. (ii) Sketch d lbel the trigle CDF iside the trigle CDE, such tht CF = CE d gle CDF = gle CDE. [3 mrks]

13 SULIT 3 347/ 4 Two prticles A d B re trvellig i the sme directio log stright lie. The velocity of prticle A, V A ms -, is give by V A = 0-0t d the velocity of prticle B, VB ms -, is give by VB = 3t - 8t + 4 where t is the time, i secods, fter pssig poit O. Fid () the ccelertio of prticle B t the momet of pssig poit O, [ mrks] (b) the time itervl whe prticles A d B move i the sme directio gi, [ mrks] (c) the distce trvelled by prticle A durig the itervl of two secods fter it hs mometrily stop, [3 mrks] (d) the time whe prticle A will meet with prticle B gi. [3 mrks] 5 For this questio, use the grph pper provided. x d y re two positive itegers tht coform with the followig costrits: I: The miimum vlue of x + 3y is 90. II: The mximum vlue of 3x + y is twice the miimum vlue of x + 3y. III: The vlue of x exceeds tht of y by t lest 40. () Write dow iequlity for ech of the costrit stted bove. [3 mrks] (b) Usig scle of cm to 0 uit o both xes, costruct, shde d lbel the regio R which stisfies ll the bove costrits. [3 mrks] (c) Give tht x is the umber of slippers d y is the umber of shoes sold by Syrikt Best Footwer. By usig your grph, fid (i) the mximum vlue for k whe x = 40 if y is k times the vlue of x. (ii) the mximum totl profit gied by the compy if it ers RM 3 for pir of slippers d RM for pir of shoes. [4 mrks] END OF THE QUESTION PAPER [See overlef

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time allowed Two hours (Plus 5 minutes reading time)

HIGHER SCHOOL CERTIFICATE EXAMINATION 999 MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/ UNIT (COMMON) Time llowed Two hours (Plus 5 miutes redig time) DIRECTIONS TO CANDIDATES Attempt ALL questios. ALL questios