2012/09/21

DSE 摘星奇緣:常犯錯誤篇(序)

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前言:曾有段時間,自己很厭倦批改家課,
尤其發現很多同學得個「抄」字!
「阿Sir,我好用心去做架!」
「你應該高興我肯交功課!」
趁我仲未看化之前,很想分享一些「心得」。
不,應該是昔日自己的「教訓」才對...

  • 錯解題目

不只錯解,不理解甚至答題欄留白,
這都令人惋惜,甚至擔心(合格率)。

  • 公式混淆

就好似事前無充份認識一件工具的
正確用法及可用之處,這都是低級錯誤

  • 抄錯題目

衰在不上心,與人無尤。
也是我近年睡眠匱乏下的副產品!

  • 運算出錯

忘記先乘除後加減,
或是開方後無考慮正負值
甚或無習慣驗算答案

  • 單位錯誤

因寫錯或漏寫(甚至寫多)
而扣一分,可免則免啦

  • 時間錯配

平日操數 Hea 住咁做又無計時,
在香港考試都係輸蝕!

總結:
以上都是老生正常談,最好是先知先覺,
但更多學生往往是得到足夠的教訓
才能汲取丁點的經驗......

「保要保守你心,勝過保守一切!」(聖經)


後話:難得失眠,好想在此整理一些常犯錯誤,
好給自己提醒,也為他日重看舊文,有所反思...


2012/05/06

[夢遊mode] 2013 HKDSE 數學科試題

打開試卷,首先是 Section A1 部份
Q1. 指數定律,Q2. 主項變換,Q3. 因式分解(不錯不錯)
Q4. 百分率,Q5.  二次方程 ,Q6. 三角函數(咁又做完兩頁)
Q7. 不等式,Q8. 平面/圓形幾何,Q9. 求積法(唷!輕鬆過關,估不到會有第9題)

其實 A1 部份佔 35 分,
諗 8-9 個題目應該唔難估,
這裡 35 分我全取啦~

伸展懶腰,接著是 Section A2 部份
Q10. 變分法,Q11. 多項式因式定理(同校內試一樣既?)
Q12. 二次方程的圖像,Q13. 線性圖像(最怕睇圖了...嗚嗚)Q14. 統計
(甚麼?要人把中一學的幹葉圖重畫成中五學的箱形圖?)
(仲要問埋標準差會點變?只怪自己沒留心上堂 ...嗚嗚嗚)

看看手錶,時間尚餘一小時?
靠,怎麼我這麼慢?

「阿美,你怎麼啦?...甚麼?現在考試中,你竟睡起來?」

糟糕!原剛才是發夢,
看到眼前的 Probability 同 Linear Programming竟睡起來...
後面的是...3-dimensional Problem 同 Geometric Progression?甚麼東東?

2012/04/28

聯立方程(哲理篇)

喜樂 = 人生 + 愛......(1)
困乏 = 人生 - 愛........................(2)

(1)+(2)
2人生 = 喜樂 + 困乏 ,
人生 = 喜樂/2 + 困乏/2

結論:人生路上,喜樂有時,困乏有時
大家還想到其他嗎?

2012/03/12

薪俸稅的累進稅率 Progressive Rate in Salary Tax

2 回應
春節前後,適逢財政司發表財政預算,想到打工仔交稅的問題,
本文嘗試深入淺出介紹本港的情況,以下是一些基本概念。
(中三級數學至 Year1 讀 Finance 的入門知識都會談的)

原則 Principle
  • 按年度計算(由四月一日起計算)
  • 能者多付(以 % 計算)


免稅額 Tax allowance
  • 每年約 12 萬(基本免稅額)
  • 政府不收取任何稅款(0%稅率)
  • 應付生活開支
  • 應課稅入息 = 全年入息 - 免稅額
  • (Net Chargeable Income = Annual Income - Tax allowance)


稅階 Tax band
  • 入息以特定金額分為四個階級
  • 每個稅階徵收不同稅率

累進稅率 Progressive Rate
首 $120000 徵收 0%(即月薪過萬才須交稅)
之後 $40000 徵收 2%
之後 $40000 徵收 7%
之後 $40000 徵收 12%
如有餘額,徵收 17%

中產爸爸個案探討 Case Study (1)
全年入息= $300,000(我以「◎」表示一萬元啦)
◎◎◎◎◎ ◎◎◎◎◎
◎◎◎◎◎ ◎◎◎◎◎
◎◎◎◎◎ ◎◎◎◎◎


應課稅入息
= 300,000 - 120,000 = $180,000

應繳稅款
=40,000 x 2% + 40,000 x 7% + 40,000 x 12% + (180,000-120,000) x 17%
=800 + 2,800 + 4,800 + 10,200 = 18,600

基層爸爸個案探討 Case Study (2)
全年入息= $130,000(我以「◎」表示一萬元啦)
◎◎◎◎◎ ◎◎◎◎◎
◎◎◎

應課稅入息
= 130,000 - 120,000 = $10,000

應繳稅款
=10,000 x 2% = 200

個案一實際稅率$=\frac{18600}{300000}$ = 6.2%(實際稅率以 15% 為上限)

個案二實際稅率$=\frac{200}{130000}$ = 0.15%

希望大家明白,按「能者多付」的原則,按比重而論,
中產人仕所付出的遠高於收入較低人仕。根據下表,
大家估算自己將來要交多少的稅啦...



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