1 1.1 1 1.2 1 3 2.1 3 2.2 5 2.3 6 2.4 24 51 3.1 51 3.2 52 3.3 56 57 4.1 57 4.2 57 4.3 58 4.4 58 4.5 59 4.6 60 i
4.7 60 4.8 61 4.9 61 63 5.1 63 5.2 65 5.3 66 71 6.1 71 6.2 71 6.3 71 6.4 72 73 77 86 ii
iii 405 3426 9265 ccdoma@emb.gov.hk
iv
1.1 1.2 21 1
2
2.1 ( ) (1) ( ) 3
(2) ( + ) (3) ( + ) 15% 405 ( ) 10% ~ 12.5% 270 ~ 338 15% 405 2.1.1 (a) 4
(b) (c) (d) (e) 2.1.2 (a) (b) (c) (d) (e) 2.2 5
2.3 2.3.1 6
2.3.2 7
2.3.3 2.3.4 10% 12.5% 270 338 2.3.5 8
1. 1.1 18 1.2 9 1.3 y = ax 2 + bx + c ax 2 + bx + c = 0 y = ax 1.4 a ± bi 2 ± 48 1.5 1.8 < 0
1.6 600 600 + = 49 x x 1 5.3 10 1.7 1.8 (a) (b) 2. 2.1 12
2.2 1 2 2.3 11 2.4 3. 3.1 15 3.2 3.3
3.4 3.5 y = 2 x y = log 2 x y = x 12 3.6 3.7
4. 4.1 13 4.2 4.3 13 4.4 H.C.F. gcd 4.5 5. 5.1 10 0 360 5.2
5.3 6. 6.1 9 6.2 6.3 14 7. 7.1 16 (a) T( n ) = ½ [T(n 1 ) + T( n +1)], (b) { T(n) } { T(n) + a } 7.2 7.3 7.4
7.5 7.6 7.7 15 8. 8.1 14 8.2 8.3 8.4 8.5 8.6
9. 9.1 11 9.2 y = f (x) f (x) = k 9.3 y = f (x) f (x) > k f (x) < k f (x) k f (x) k 16 9.4 f (x) f (x) + k f (x + k) k f (x) f (kx) 10. 10.1 24 10.2 10.3 10.4 10.5
10.6 10.1 10.5 11. 11.1 8 11.2 17 11.3 y = ax 2 + bx + c 12. 12.1 x = h y = k 14 12.2 12.3
12.4 12.5 12.6 18 13. 13.1 20 13.2 θ 90 ± θ 13.3 a sin θ = b a cos θ = b a tan θ = b 0 360 0 360 13.4 ab sin C 180 ± θ 13.5
13.6 13.7 13.4 13.6 19 1999 23 14. 14.1 12 14.2 P n r n P r n P r 14.3
14.4 C n r n C r n n C r r 14.5 15. 15.1 11 20 15.2 P(A B) = P(A) + P(B) P(A B) 15.3 15.4 P(A B) = P(A) P (B A) 15.5 16. 16.1 13 16.2
16.3 16.4 16.5 21 16.6 (i) (ii) (iii) (iv) 17. 17.1 9 17.2
17.3 22 18. 21 (a) (b) y = kx n
23 19. 20 (1) 270 (2) (2) 338
2.4 2.4.1 24
2.4.2 7 2.4.3 15% 405 2.4.4 25
1. 1.1. 1.1.1. (a + b) n n 5 26 1.1.2. (1 + x) n n x < 1 2 3 1.2. x x 1.2.1. e x = 1+ x + + +... e 6 2! 3! 1.2.2. 11
2. 2.1. 2.1.1. 6 2.1.2. 2.1.3. d y y' f '(x) d x 27 2.1.4. y = f (x) x = x 0 d y f '(x 0 ) d x x= x 0 2.2. 2.2.1. 12 : (C)' = 0 (x n )' = n x n -1 (e x )' = e x (ln x)' = (log a x)' = 1 x (a x )' = a x lna 1 x ln a
2.2.2. x n n e x ln x a x log a x a a 1 2.3. 2.3.1. y" f "(x) 2 2 d y d x 2 28 2.3.2. 2.4. 2.4.1. 8 28 3. 3.1. 3.1.1. 1
3.2. 3.2.1. u dx 8 : k dx = kx + C n+ 1 n x x d x = + C n + 1 n 1 1 x x d = ln x + C 29 e x dx = e x + C 3.2.2. 3.2.3. 3.3. 3.3.1. 12 3.3.2. : a f ( x)d x = f ( x) d x b a f ( x)d x = 0 a b a
30 b f ( x) d x = f ( x)d x + f ( x) d x a b a < c < b a c k f ( x) d x = k f ( x) d x k a b ( f ( x) ± g( x)) d x a b = f ( x) d x ± b a b a b a g( x) d x f ( x) d x = f ( t) d t a b pb+ q f px + q)d x = a pa+ q b a ( 1 p f ( x) d x, p 0 b c 3.3.3. x n ( n ) 3.3.4.
3.4. 3.4.1. 4 25 4. 31 4.1. 4.1.1. 5 4.1.2. P(A B) = P(A) P(B A) P(D C) = P(D) C D 4.2. 4.2.1. 4 5. 9 5.1 5.1.1 1
5.2 5.2.1 8 5.2.2 E(X) Var(X) 5.2.3 E(aX + b) = a E(X) + b Var(aX + b) = a 2 Var(X) 32 5.3 5.3.1 6 ( ) 5.3.2 5.4 5.4.1 4 ( 5.4.2 )
5.5 5.5.1 4 ( ) 5.5.2 5.6 5.6.1 4 33 27 6. 6.1 6.1.1 3 6.1.2 N(µ, σ 2 ) σ 1
6.2 6.2.1 2 6.3 6.3.1 x 1 x 2 P(X > x 1 ) 8 P(X < x 2 ) P(x 1 < X < x 2 ) 6.3.2 34 13 7. 7.1 7.1.1 3 7.1.2 n µ µ 2 σ n σ 2
7.1.3 7.1.4 7.2 7.2.1 7 7.2.2 n (a). 35 (b). n 7.3 7.3.1 2 n 12 p q (= 1 p)
8. 8.1. 10 10 135 36
2.4.5 2.4.6 2.4.7 15% ( 405 ) 2.4.8 37
1. 1.1 k 1.1.1 2 a ± b 2.2.1 1.2 1.2.1 6 1.3 1.3.1 4 x r (a + bx) n a b n 38
1.4 1.4.1 12 1.4.2 1.4.3 1 + tan 2 θ = sec 2 θ 1 + cot 2 θ = cosec 2 θ sin 2 θ + cos 2 θ = 1 1.4.4 sin(a ± B) = sin A cos B ± cos A sin B cos(a ± B) = cos A cos B m sin A sin B tan(a ± B) = tan A ± tan B 1 m tan A tanb sin 2A = 2 sin A cos A cos 2A = cos 2 A sin 2 A tan 2A = = 1 2 sin 2 A = 2 cos 2 A 1 2 tan A 1 tan 2 A sin 2 A = 2 1 (1 cos 2A) 39
cos 2 A = 2 1 (1 + cos 2A) 2 sin A cos B = sin(a + B) + sin(a B) 2 cos A cos B = cos(a + B) + cos(a B) 2 sin A sin B = cos(a B) cos(a + B) A + B A B sin A + sin B = 2 sin cos 2 2 A + B A B sin A sin B = 2 cos sin 2 2 A + B A B cos A + cos B = 2 cos cos 2 2 A + B A B cos A cos B = 2 sin sin 2 2 1 sin 2 A = (1 cos 2A) 2 1 cos 2 A = (1 + cos2a) 2 40
1.5 e 1.5.1 e 2 1 n e e lim (1 + ) n e x e n 26 2. 2.1 2.1.1 6 x sgn(x) x x 41
sin θ lim θ 0 θ = 1 e x 1 lim x 0 x = 1 2.2 2.2.1 16 C x n n x sin x cos x e x ln x 42
2.2.2 (C)' = 0 (x n )' = n x n 1 n (sin x)' = cos x (cos x)' = sin x (tan x)' = sec 2 x (cot x)' = cosec 2 x (sec x)' = sec x tan x (cosec x)' = cosec x cot x (e x )' = e x (ln x)' = 1 x 2.2.3 2.2.3 2.2.4 2.2.5 43
2.3 2.3.1 14 2.3.2 2.3.3 2.3.4 36 3. 3.1 3.1.1 16 3.1.2 k dx = kx + C n+ 1 n x x d x = + C n 1 n + 1 1 x x d = ln x + C 44
e x dx = e x + C sin x dx = cos x + C cos x dx = sin x + C sec 2 x dx = tan x + C cosec 2 x dx = cot x + C sec x tan x dx = sec x + C cosec x cot x dx = cosec x + C 3.1.4 3.1.6 3.1.3 3.1.4 du = u' dx u x 3.1.5 2 3.1.6 a 2 x 2 2 2, x a 2 2 a + x sin 1 x tan 1 x 45
3.2 3.2.1 13 3.2.2 a f ( x)d x = b a a f ( x)d x = 0 b a f ( x) d x b c b f ( x)d x = f ( x)d x + f ( x) d x a a < c < b a b b k f ( x)d x = k f ( x) d x k a b ( f ( x) ± g( x)) d x = a b f ( x)d x ± a b a a g( x) d x b f ( x)d x = b f ( t) d t a a c 46
3.2.3 b a f ( x) d x = F(b) F(a) d F(x) = f (x) d x 3.2.4 3.2.5 3.2.6 aa f ( x)d x = 0 f a a f ( x)d x = 2 f ( x)d x f a 0 nt T f ( x)d x = n f ( x)d x 0 0 f (x + T ) = f (x) f 47
3.3 3.3.1 9 3.3.2 38 4. 4.1 4.1.1 4 A 1 1 = adj A A 4.2 4.2.1 12 4.2.2 A (A 1 ) 1 = A (λa ) 1 = λ 1 A 1 (A n ) 1 = (A 1 ) n 48
(A t ) 1 = (A 1 ) t A 1 = A 1 (AB) 1 = B 1 A 1 A B λ 4.3 4.3.1 9 4.3.2 4.3.3 25 49
5. 5.1 10 10 : 135 50
3.1 (a) (b) (c) (d) (a) (b) (c) (d) (e) (f) 51
(a) (b) (c) (d) (e) (f) 3.2 52
53
54
55
3.3 270 338 10% 12.5% 405 15% 56
4.1 4.2 21 57
58 4.3 4.4
4.5 59
4.6 4.7 60
4.8 4.9 61
62
5.1 63
64 - : - - - - Shirley Clarke 64
5.2 5.2.1 65
5.2.2 5.3 5.3.1 66
5.3.2 85 % 15 % 67
68
69
70
6.1 6.2 6.3 71
6.4 Java QuickMath Ask Dr Math Ask NRICH 72
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(31) 2002 (32) 2004 (33) 1981 1 4 (34) 1995 (35) 1997 (36) 1998 (37) Dunham, William 1995 (38) 1997 (39) 1980 (40) Bolt, Brain ( 1995 (41) Bolt, Brain ( 1995 (42) Bolt, Brain ( ) 1996 (43) Bolt, Brain, & Hobbs, David ( ) 1996 (44) Bolt, Brain ( ) 1996 (45) 1999 (46) 1999 (47) 2003 (48) 2003 : (49) 2003 : (50) 2003 : 79
(51) 1993 (52) 2004 (53) ( ) 1967 (54) 2004 (55) 1985 (56) 1956 : (57) 1963 : (58) 1963 : (59) 2003 : (60) 2000 : (61) 2000 : (62) 2000 : (63) 1996 (64) ( ) 2003 (65) ( ) 1992 1984 (66) ( ) 1998 (67) Sobel, Max A., & Maletsky, Evan M. ( ) 1996 (68) 1998 (69) 2002 80
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(14) Fun Mathematics Lessons http://math.rice.edu/~lanius/lessons/ (15) Java Applets on Mathematics http://www.walter-fendt.de/m14e/index.html (16) Manipula Math with Java http://www.ies.co.jp/math/java/ (17) Math in Daily Life http://www.learner.org/exhibits/dailymath/ (18) Maths On-line http://www.univie.ac.at/future.media/moe/galerie.html (19) Math Forum T2T Elementary Thoughts http://mathforum.org/t2t/faq/gail/index.html (20) Mathematical Association of America Online http://www.maa.org/ (21) Mathematics LIVE on the Web http://www.aamt.edu.au/archives/livemath/mathview/home.htm (22) MathNet http://mathsnet.net/index.html (23) MSTE Online Resources http://www.mste.uiuc.edu/resources.php (24) National Council of Teachers of Mathematics http://www.nctm.org/ (25) Numeracy Teaching Ideas http://www.teachingideas.co.uk/maths/contents.htm (26) Open-ended Assessment in Mathematics http://www.heinemann.com/math/register.cfm (27) Project Interactivate http://www.shodor.org/interactivate/ (28) Schools of California Online Resources for Education (SCORE) Mathematics http://score.kings.k12.ca.us/ 87
(29) Secondary Mathematics Assessment and Resource Database (SMARD) http://smard.cqu.edu.au/ (30) Shapescape http://www.shapescape.com/ (31) http://menet.math.ecnu.edu.cn/index.php (32) http://www.czsx.com.cn/ (33) http://www.pep.com.cn/gzsx/ (34) GSP, Flash, LOGO http://www.math.ntnu.edu.tw/~cyc/_private/m14.htm (35) http://www.math.ntnu.edu.tw/index-c.html. (36) Mathematical Excalibur http://www. math.ust.hk/mathematical_excalibur/ (37) http://www.plklht.edu.hk/funmaths/fmaths.html (38) http://www.math.ied.edu.hk/spkwan/paperfolding/index.htm (39) Cartoon of the Week http://www.carolina.com/math/cartoons/mcarch.asp (40) Cut-the-knot Interactive Games http://www.cut-the-knot.com/games.html (41) Curve Fitting Expert http://curveexpert.webhop.biz/ (42) The Integrator 88
http://integrals.wolfram.com/ (43) Living Mathematics http://sunsite.ubc.ca/livingmathematics/ (44) Mathematical Stamp Collecting http://www.math.wfu.edu/~kuz/stamps/stamppage.htm (45) Mathpuzzle http://mathpuzzle.com/ (46) Mega Mathematics http://www.cs.uidaho.edu/~casey931/mega-math/index.html (47) The National Math Trail http://www.nationalmathtrail.org/ (48) NRICH Mathematics Enrichment Club http://nrich.maths.org/ (49) Origami and Mathematics http://www.paperfolding.com/math/ (50) Probability Games http://www.betweenwaters.com/probab/probab.html. (51) Census & Statistics Department http://www.info.gov.hk/censtatd/chinese/hkstat/index.html (52) Agriculture, Fisheries and Conservation Department Country and Marine Parks Authority http://parks.afcd.gov.hk/newparks/chi/statistics/index.htm (53) Narcotics Division, Security Bureau http://www.nd.gov.hk/c_statistics_list.htm (54) Environmental Protection Department http://www.epd.gov.hk/epd/tc_chi/environmentinhk/waste/data/waste_data.ht ml (55) The Land Registry 89
http://www.landreg.gov.hk/ch/monthly/monthly.htm (56) Hong Kong Statistical Society http:/www.hkss.org.hk/ (57) Business-Stat Online http://stat.tdctrade.com/index_c.html (58) Hong Kong International Airport-International Air Traffic Statistics at HKIA http://www.hongkongairport.com/chi/aboutus/statistics.html (59) Singapore Department of Statistics http://www.singstat.gov.sg/keystats/mqstats/indicators.html (60) Macau - Statistics and Census Service http://www.dsec.gov.mo/c_index.html (61) Statistical Glossary http://www.statsoft.com/textbook/glosfra.html (62) U.S. Census Bureau http://www.census.gov/main/www/access.html (63) Economic and Social Commission for Asia and the Pacific (ESCAP) -- Statistics Division http://www.unescap.org/stat/data/index.asp (64) Economic Commission for Europe (ECE) -- Statistical Division http://www.unece.org/stats/data.htm (65) European Union: Eurostat http://europa.eu.int/comm/eurostat/ (66) Food and Agriculture Organization of the United Nations (FAO) http://www.fao.org/waicent/portal/statistics_en.asp (67) Organization for Economic Co-operation and Development (OECD) http://www.oecd.org/statsportal/0,2639,en_2825_293564_1_1_1_1_1,00.htm l (68) United Nations Development Programme (UNDP) http://hdr.undp.org/statistics/data/ (69) United Nations Educational, Scientific and Cultural Organization (UNESCO) http://stats.uis.unesco.org/reportfolders/reportfolders.aspx 90
(70) United Nations Headquarters -- Statistics Division (UNSD) http://unstats.un.org/unsd/databases.htm (71) The World Bank Group http://devdata.worldbank.org/data-query/ (72) World Health Organization (WHO) http://www3.who.int/whosis/mort/text/download.cfm?path=whosis,mort,mor t_download&language=english. (73) http://www.cmi.hku.hk/ref/glossary/mat/k.htm (74) Eric Weisstein's World of Mathematics http://mathworld.wolfram.com/ (75) Interactive Mathematics Dictionary http://www.intermath-uga.gatech.edu/dictnary/homepg.asp (76) Wikipedia - Mathematics http://www.wikipedia.org/wiki/mathematics (77) Math Dictionary http://users.adelphia.net/~mathhomeworkhelp/index.html (78) Glossary of Mathematical Terms http://www.cut-the-knot.com/glossary/atop.shtml (79) The Internet Glossary of Statistical Terms http://www.animatedsoftware.com/statglos/statglos.htm (80) Eurostat ISI Glossary of Statistics http://europa.eu.int/en/comm/eurostat/research/isi/alpha/en/en_list.htm (81) Xah Visual Dictionary of Special Plane Curves http://www.xahlee.org/specialplanecurves_dir/specialplanecurves.html (82) The Encyclopedia of Polyhedra http://www.georgehart.com/virtual-polyhedra/vp.html (83) Mathematical Quotation Server 91
http://math.furman.edu/mqs.html (84) A Dictionary of Measures, Units and Conversions http://www.ex.ac.uk/cimt/dictunit/dictunit.htm - SI. (85) MacTutor History of Mathematics http://www-gap.dcs.st-and.ac.uk/~history/ (86) Chronological List of Mathematicians http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html - 1725 (87) Mathematicians who were born or died today http://www-history.mcs.st-and.ac.uk/~history/day_files/now.html (88) http://www.chiculture.net/0803/html/index.html. (89) Cabri Geometry http://www.ti.com/calc/docs/cabri.htm (90) QuickMath http://www.quickmath.com/ (91) Geometer's Sketchpad http://www.keypress.com/pages/prod_sketchpad.html (92) Peanut Software (Winplot, Wingeom, Winstats,..) http://math.exeter.edu/rparris/winplot.html (93) Poly http://www.peda.com/poly/ (94) GAMS Guide to Available Mathematical Software http://gams.nist.gov/ (95) Math WWW Virtual Library Mathematics Software 92
http://www.math.fsu.edu/science/software.html (96) University of Haifa - Mathematical Software Resources http://math.haifa.ac.il/msoftware.html (97) NCTM Illuminations - Tools http://illuminations.nctm.org/tools/index.aspx. (98) Hong Kong Mathematics Olympiad (HKMO) http://www.ied.edu.hk/math/main.htm (99) Mathematics Project Competition For Secondary Schools http://cd1.emb.hkedcity.net/cd/maths/en/ref_res/proj_learn/index.html (100) Hang Lung Mathematics Award http://www.hkedcity.net/article/special/hanglung/news.phtml (101) International Mathematics Olympiad Hong Kong Preliminary Selection Contest http://gifted.hkedcity.net (102) International Mathematical Olympiad http://www.camel.math.ca/imo/ (103) Mathematics Challenge for Young Australians http://www.amt.canberra.edu.au/wwwroot/mcya.htmll (104) World Class Tests http://www.worldclassarena.org/ondemand/default.asp?bhcp=1 (105) Web Sites with information about Mathematics Competitions http://www.mathpropress.com/competitions.html. (106) Mathematical Database http://eng.mathdb.org/ 93
(107) The Math Forum http://mathforum.org/ (108) Mathematics Virtual Library http://www.math.fsu.edu/science/math.html (109) American Mathematical Society http://e-math.ams.org/ (110) Lodon Mathematical Society http://www.lms.ac.uk/ (111) http://www.math.tku.edu.tw/c_index.htm (112) http://www.math.ntu.edu.tw/home_c.htm (113) http://www.mathland.idv.tw/ (114) http://www.mikekong.net/maths/maths-frame.php (115) http://www.edp.ust.hk/math/ 94