gce-o-level-2008-amaths-4038-paper-2-solutions

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Unformatted text preview: GCE Add Unau Please AD Pap 1. T ( ( ( ‘O’ Level October itional Mathem thorized copying, e call 93805290 or e DITIONAL MA er 2 Suggeste Topic: Exponentia (i) Given: V =100 When the man ∴ value of mo (ii) When t = 12, v 4000 = 1 0.4 = e ln 0.4 = − p = ୪୬ ି ≈ V = 1 Sub t = 18 into (iii) Sub v = 1000 in 1000 = 10 0.1 = e-0 ln 0.1 = -0. t = ୪ ି଴. ≈ 30 ≈ 30 ∴ age of moto by ex r/November 2008 atics (4038/0 resale or distribut mail [email protected] ATHEMATIC d Solutions al Functions 00e- pt bought the motorcy torcycle when boug = 4000: 0000e- p (12)-12 p 12 p ln e ଴.ସ ଵଶ .076358 0000e-0.076358 t …… (1): Value after 18 nto (1): 000e-0.076358 t 0.076358 t 076358 t ln e ୪୬ ଴.ଵ .଴଻଺ଷହ଼ .2 months months (nearest m rcycle when expec ampaper.com.sg 8 Suggested Solut 2) ion prohibited. paper.com.sg for ex S Oct ycle, t = 0. ht = 10000e = \$10000 …. (1) months = 10000e ≈ 2529.8 ൎ \$2530 onth) cted value is \$1000 Note: V < \$ since the e − depreciatio V ions xam papers and tuitio 4038 ober/November e -0.076358 (18) (3 s.f.) is 30 months. 1000 when t = 31 mo pt curve describes the n of value over time. t n matters. /02 2008 2. onths, Topic: Quadratic 2 x 2 – 4 x + 3 = 0 ⇒ Sum of roots: Product of roots: New sum of roots: ሺߙ ଶ ൅ 2ሻ ൅ ሺߚ ଶ ൅ New product of roo ሺߙ ଶ ൅ 2ሻሺߚ ଶ ൅ 2ሻ ∴ equation with ro x 2 – 5 x + ଷଷ ସ = 0 ⇒ 4 x 2 – 20 x + Equations (Sum & a = 2, b = − 4, c = 3 ߙ ൅ ߚ ൌ െ ௕ ௔ ൌ ߙߚ ൌ ௖ ௔ ൌ ଷ ଶ 2ሻ = ߙ ଶ ൅ ߚ ଶ ൅ 4 = ሾሺߙ ൅ ߚሻ ଶ െ 2 = (2) 2 െ 2 ቀ ଷ ଶ ቁ + 4 = 5 ts: = ߙ ଶ ߚ ଶ ൅ 2ߙ ଶ ൅ 2 = ሺߙߚሻ ଶ ൅ 2ሺߙ ଶ ൅ = ሺߙߚሻ ଶ ൅ 2ሾሺߙ ൅ = ଽ ସ + 2 [4 − 2 ቀ ଷ ଶ ቁ ] + = ଽ ସ + 2 + 4 = 8 ଵ ସ = ଷଷ ସ ots α 2 + 2, β 2 + 2: 0 33 = 0 x 2 © 2008 exampape Product of Roots െ ିସ ଶ ൌ 2 ߙߚሿ ൅ 4 ߚ ଶ ൅ 4 ߚ ଶ ሻ + 4 ߚሻ ଶ െ 2ߙߚሿ + 4 + 4 : Sub ߙ ߙ ଶ ൅ ߚ ଶ Useful e Sub ߙ 2 – (Sum of roots) x + Page 1 o r.com.sg. All rights res s) ൅ ߚ ൌ 2, ߙߚ ൌ ଷ ଶ ൌ ሺߙ ൅ ߚሻ ଶ െ 2ߙ xpression: ൅ ߚ ൌ 2, ߙߚ ൌ ଷ ଶ (Product of roots) = 0 of 8 served. ߚ 0 GCE Add Unau Please 3. T ( ( ‘O’ Level October itional Mathem thorized copying, e call 93805290 or e Topic: Trigonome (i) tan A + cot A = L.H.S.: ୱ୧୬ ஺ ୡ୭ୱ ஺ ൅ (ii) tan A + cot A = From (i): 2 co ⇒ Basic a 2 A ≈ 41.81 ° , 360 ° + 4 ≈ 41.81 ° , ∴ A = 20.9 ° , by ex r/November 2008 atics (4038/0 resale or distribut mail [email protected] try (Trigonometri 2 cosec 2 A ୡ୭ୱ ஺ ୱ୧୬ ஺ = ୱ୧୬ మ ஺ାୡ୭ୱ మ ୡ୭ୱ ஺ ୱ୧୬ ஺ = ଵ ୱ୧୬ ஺ ୡ୭ୱ ஺ = ଵ మ ౩౟౤ ಲ ౙ౥౩ ಲ మ = ଶ ୱ୧୬ ଶ஺ = 2 cosec 2 = R.H.S. (P 3 sec 2 A = 3 ଶ ୱ୧୬ ଶ஺ = 3 sin 2 A = ଶ ଷ ngle α = sin ିଵ ቀ ଶ ଷ ቁ ≈ 41.81 ° 180 ° − 41.81 °...
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