2012/02/19

銜接課程詞彙表 Word List in S1 Bridging Programme

0 回應
各位同工(或中一家長),有否擔心學生上中一後應付不了英文的要求?這裡要介紹名為 PuzzleMaker 的網站。我嘗試根據香港中一上學期的幾節課做了以下好些填字拼圖,大都是個人認為中一生宜盡早掌握。各位同工,偶爾放在工作紙裡面倒也不錯。

Commonly used terms in questions
according to..., base on, refer to, among, apart from

VERB or others
calculate, evaluate, find, solve, complete, obtain, search
express, explain, represent, describe, indicate, consider, determine, convert
estimate, judge, decide
construct, measure, produce, extend, present, join, draw, connect
combine, split, classify
expand, simplify,
change, increase, decrease, reduce, rise, raise, fall, upward, downward,
arrange, ascending order of magnitude, descending order of magnitude
include, exclude, internal, external

NOUN or others
solution, answer, result, value,
half, quarter
exact, accurate, approximate
corresponding, proportional
each, per, whole, entire, ratio
new, initial, original,
daily,  weekly, bi-weekly, monthly, quarterly, yearly, annual
respectively
whether, if

SYMBOLS
( ) , [ ], { } Parentheses, Square brackets, Braces
is equal to , is not equal to, is approximately equal to
is less than , is greater than / exceed,
is parallel to ,is perpendicular to
percentage
positive, negative
angle, triangle
because, since, therefore
...is congruent to..., ...is similar to...

Algaebra
Numbers
Whole number/ integer, natural number, decimal, digit
Factor, Multiple, prime factor
Prime number, Composite number
H.C.F. Highest Common Factor
L.C.M. Least Common Multiple

Arithmetic Operations
Addition – add.. to , plus, sum, total, summand, addend
Subtraction – subtract.. from, minus, difference, minuend, subtrahend
Multiplication – multiply.. by, times, product
Division – divide.. by, quotient, dividend, divisor, remainder

Fraction
Numerator, Denominator
Proper fraction, improper fraction, mixed number

Index
Index Notation, base, index, indices
a squared
a cubed
a to the power n,
the nth power of a

Geometry
Line
Side, height, high, base, longer base, shorter base, width, wide, breadth, length, long,
perimeter, hypotenuse, adjacent, opposite, curve, intersection, ray

Plane figure
polygon, triangle, square, rectangle, quadrilateral, trapezium, rhombus, kite, ellipse, circle
parallelogram, pentagon, hexagon, heptagon, octagon, figure, diagram, arrowhead,
diagonal, area, shaded region, dimension, regular, irregular

Triangle
scalene triangle, isosceles triangle, equilateral triangle
right-angled triangle, acute-angled triangle, obtuse-angled triangle

Solid
Prism, cube, cuboid, triangular prism, square prism, rectangular prism, trapezoidal prism,
cylinder, pyramid, cone, sphere, vertex, vertices, edge, volume, total surface area, face,
lateral faces, cross-section, curved surface

Angle
Degree, protractor, clockwise, anti-clockwise, vertex, vertices, arm, acute angle, right
angle, obtuse angle, reflex angle, straight angle, round angle, outer, inner, base angle,
interior angle, exterior angle, degree, minute, second,

Circle
radius, radii, diameter, arc, circumference, centre, compasses, protractor

Others
bar chart, broken-line graph, pie chart, scatter diagram
cost price, selling price, marked price, profit, loss, discount, gain, earn, suffer, sell, sold,
sale, buy, bought, purchase, dozen
principal, interest, interest rate, amount, deposit, withdraw, depreciate, account
reflection, rotation, translation, axis, image, enlarge, reduce
round off, round up, round down, decimal places

Useful Websites
Mathematics Games
http://www.math.ied.edu.hk/Links/game.htm
Arithmetic
http://mathworld.wolfram.com/topics/Arithmetic.html
Geometry
http://www.scienceu.com/geometry/facts/solids/handson.html
http://www.mathsnet.net/geometry/solid/index.html
Symmetry
http://www.mathsnet.net/transformations/index.html
http://mathworld.wolfram.com/Rotation.html
http://mathworld.wolfram.com/Reflection.html
http://mathworld.wolfram.com/Translation.html


KEYWORD: add, answer, bracket, difference, divide, equal, multiply, product, quotient, subtract, sum
KEYWORD: duration, height, length, price, speed, temperature, weight, width
KEYWORD: arithmetic, Fibonacci, formula, geometric, negative, positive, sequence, square,substitution, term, triangular
KEYWORD: acute, angle, circle,

KEYWORD: equation, root, setup, solution, solve, unknown


2012/02/12

三門問題 Monty Hall Problem 2012

0 回應
假設你參加這樣一個猜獎遊戲:眼前有三扇關上的門(且叫A、B、C啦),其中一扇門後面藏著大獎,另外兩扇門後面空空如也。玩法是,當你選好一扇門後(假設是A),主持人打開C門,裡面是空的。現在他給你一次換選B門的機會,那麼你是否「應該」換呢?(順帶一提,主持人是知道真正答案,倘若玩家最初選對了,主持人則隨意開一扇門,當然這點也不會讓玩家知道)


或者用比較數學的講法,在主持人提示了一個無獎的門之後,換門的得獎機率是否大於不換?
正向中三及中五教授「機率論」,我心想好否在堂上引入上述的「三門問題」,問題本身簡單、易懂,答案也很簡單、但卻有點反直覺。(答案在最下面,你可以自行核對。)不過今次想介紹一些網上相關的片。

如果學生想睇片的可考慮這個,適用於以英語作授課語言。


最近見到有補習社拍了一個全新版本,夠噱頭!(先旨聲明,本人及本網誌對有關機構並無瓜葛,個人頗欣賞明仔,但對有關導師甚無好感亦無惡意。)


喜歡看連續劇的我推薦「Numb3r」(中譯:數字搜查線,但我仲未找到 DVD >_<)

喜歡電影的我推薦這齣(中文片名:決勝21點),真人真事改編,故事描述任教於麻省理工學院的數學教授米基解開撲克牌21點的必勝程式後,決定延攬6位天才學生加入團隊並前往賭城大試手氣。幾個人憑著破解程式在賭城大賺一筆,不過,贏得的巨額賭金和偽造身分,卻讓他們成為賭場盯稍對象,引來重重危險殺機...


還有無什麼好例子?來個午間數學活動,從做中學,效果又如何?






答案:換門的得獎機率是 2/3,不換是 1/3,所以你應該要換。
我試用歸納法解釋一下,舉個例子:如果有十扇門,你選好後主持人打開八個無獎的門,那麼換門的得獎機率是 9/10,不換是 1/10。規則不變,轉換某些參數,事情就清楚得多,明白嗎?

2012/02/10

[問題] 給 S.5D 的 Assignment

0 回應
The following picture is just for fun only...


有關同學(尤其是未領取工作紙的同學),可先預留位置,題目詳見如下:

Q1
In a pond, the number of orange goldfish is 8 more than that of black goldfish. If a goldfish is selected from the pond randomly, the probability of selecting a black goldfish is seven over eighteen. How many black goldfish are there in the pond?

Q2
A four-digit number is formed by arranging 1, 2, 3 and 5 randomly without repetition. Find the probabilities of the following events.
(a) The thousand digit of the number is 1.
(b) The number is an odd number.

Q3
A number is selected at random from the integers 1 to 40 inclusive. Find the probabilities of getting a multiple of 5 or 9.

Q4
A letter is chosen from the words THIRTY and EIGHT each. Find the PROBABILITY of choosing two vowels.

2012/02/04

培正數學邀請賽 2012:初賽題目及答案

0 回應
今日帶班黃毛小子去參加「第11屆培正數學邀請賽」,
心裡頗感到惋惜......大好的天賦,
那麼晚才告知我做領隊的事,
早知道的話,恨不得跟他們來個特訓!
(下次應該一報名就做 training)



事後,我當然不放過機會,跟他們即場討論解題方法。
希望今年有半數同學殺入決賽啦~
中一組中二組中三組中四組高中組
答案

高中組我當下的做法
(3分題)
Q1 各項之間的差分別是5、3、4,故16應改為15,使之為等差數列。
Q2 事關$2012=4\times503$ 且503是質數(如何證明?),故無兩位正整數是 2012 的因數。
Q3 (送分題?)$n=3^5+1=244$
Q4 考慮 $x=2.5$,則$2.5^2-5\times2.5+k=2012$,故 $k=2018.25$
Q5 考慮「圓內接四邊形對角互補」,x 必須是 130o或120o
Q6 每D四次個函數的正負值均相等,故答案是 $2^{12} =4096$

(4分題)
Q7 馬上分解1888($1888=32\times59$),由於比正確答案大,故正確答案是 $23\times59$ 而不會是 $32\times95$。
Q8 把裡面的六邊形「一開六」(變成六個等邊三角形),再把每個三角形由重心「一開三」,故答案是 $\frac{18}{24}$=75%。
Q9 (腦海諗著 1, 6, 15, 20, 15, 6, 1)
$2.012^6$
$=(2+0.012)^6=64+6(32)(0.012)+15(16)(0.000144)+...$(應該可省略)
$=64+2.304+...=66.304...$

(5分題)
Q10
Q11 要做到「數字之積是0」,四個數字之中最少要有一個0(別忘記千位不可以是0),諗清楚思路,答案顯然就是 $9\times10\times10\times10-9\times9\times9\times9=2439$

(6分題)
Q12 (大膽假設) $n+3210<4000$,那麼 n 必然是三位數而個位數字等於3(故百位數字同樣是3),$n+3210=3553$,$n=343$(感覺呢條數幾好玩)。
Q13
Q14 方程可簡化成 $s^2-2sc-c^2=0$

(7分題)
Q15 (又大膽假設) $BO_1$的延線與$CO_2$的延線相交於兩圓的另一交點,利用cosine law,考慮兩員直徑及120o夾角,計算 $BC$ 的長度。
Q16 (那是我最唔喜歡玩的算食蟲題目,謝謝智軒出手)
ABC
x  CBA
------
GJGC
GHIF
DEBF
------
GBGGBF

從下邊加數B+F=B,可以推出F必然為0,
從而ABCxB與ABCxA的個位值=0
當個位值=0,乘式為(偶數x5)或(任意數x0)的組合,
由於0已經使用,只剩下(偶數x5)的組合。
然後觀察A和B不能同時為5,因此C為5。

觀察ABCxC=GJGC
已知C=5,A、B為偶數,因此G只能是2。
要使AB5x5的千位為2,A只能為4或5,而5已被使用,A只能為4

現在:

4B5
x  5B4
------
2J25
2HI0
DEB0
------
2B22B0

在B是偶數的條件中,只剩下B=6和B=8的可能
經驗算ABC=465是唯一可能解

Q17 「最多有多少交點?」掉翻轉諗,任何交點都由兩條線段相交而成,即兩條線段對應的四個在圓周上的點,故考慮「20個點任選4個點」的組合,答案是$\frac{20!}{4!(20-4)!}=4845$
Q18
Q19
Q20

========
暫時有60分咁上下啦...夠入決賽先