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數 學 Mathematics
David Chiu
考試形式 Paper I 卷一 問答題 (60%) 2小時 內容
分數
一般情況下，考生取得
選題
出題範圍
A，Paper I 要取得90分以上
Section A (1) 甲部(一)
33分
8-10題 (必答)
剪裁課程
Section A (2) 甲部(二)
33分
4-5 題 (必答)
剪裁課程
Section B 乙部
33分
4題選3題答
整體範圍 (深入的長題目)
Paper II 要答對50題以上 C，Paper I 要取得70分以上 Paper II 要答對38題以上
Paper II 卷二 MC選擇題 (40%) 1.5小時 內容
E，Paper I 要取得35分以上
選題
出題範圍
Section A 甲部
36題 (必答)
剪裁課程 (問題由30題開始會較難)
Section B 乙部
18題 (必答)
整體範圍
備註：
Paper II 要答對20題以上
得分
(1) 剪裁課程是從整體課程中選出部分內容，使成績稍遜的學生能先專注 選答這一部份的基礎內容，熟讀剪裁課程可保合格。 (2) 時間分配是十分重要，卷一甲應於1小時10分鐘內完成，卷二乙平均 15分鐘1題（共三題），最後考生應預留不少於五分鐘覆核全卷。卷 二共有54題選擇題，平均分半鐘一題，最後用大約五分鐘去覆核全卷。
扣分
A : Accuracy
P.P: poor presentation
即是答案正確而取得的分數，應以真
即是表達不清楚而扣去的分數
確值(exact value)或三位有效數字(3 significant figures) 表示。在運算過 程中，答案應多取一些有效數字，否 則最終的答案會出現偏差。
(3) 在卷一中考生答題時必須列出計算步驟，以確保在不小心錯算答案時， 仍可取得步驟的分數。卷二的首三十六題比較容易。
M: Method
U: Unit
評核技巧和方法正確的分數
因欠單位而扣的分數 全卷最多可扣 2 分 P.P. 及 1 分 U
主要課程比較 新增重點
刪減重點 1. 根與係數間的關係 (sum of root, product of root) [90 #5, 96 #11, 03 #41]
一元二次方程
2. 進行分母如
Quadratic Equations in One Unknown
(Rationalization the denominators of expression in the form
等差及等比數列
現實生活問題，例如利息、增長、折舊及幾何問題等
Arithmetic & Geometric Sequences
(Real-life problems such as interest, growth and depreciation, geometric problems etc)
函數及其圖像
從給出的代數關係，將經變換後的函數圖像形像化 The effect of transformation on the graphs of functions
Functions and Graphs
指數函數及對數函數 Exponential and Logarithmic Functions
(全新課題)
等的公式之有理化
E.g. How to obtain
以
) [90#4, 00#40]
符號表示多項的求和，以及涉及 符號的 代數運算 (The use of notation)
from
1. 有理數指數定律 the laws of rational indices 2. 對數及指數函數之圖像特性 the properties of the graphs of exponential and logarithmic functions
求直線與圓的交點 軌跡及坐標幾何問題 Locus & Coordinate Geometry
會考 指南
2006 學友社
(Intersection of a straight line and a circle)
直線與圓相交、相切及不相交的情況 (The cases of a straight line intersects, touch and do not touch a circle) [98 #52, 00 #49]
數學 Mathematics
9
新增重點
刪減重點 1. 以弧度 (radian) 為單位量度角度
續三角 More about
2. 弧長及扇形的面積 (Arc length and the area of sector)
Trigonometry
離差的量度 Measures of Dispersion
在不同情況對數據離差所產生的影響，例如：
1. 計算平均差 (mean deviation)
1. 剔除數據中某個項 removal of a certain item from the data
2. 計算方差 (variance) 3. 正態分佈 (normal distribution)
2. 在整組數據中每一項加入一個共同常數 adding a common constant to the whole set of data
4. 加權平均數 (weighted mean)
3. 把整組數據中每一項乘以一個共同常數 multiplying the whole set of data by a constant 4. 在該組數據中加入「零」項 insertion of zero in the data set E.g. The mean of a group of 20 numbers is 36. Four numbers, each equals to 100, are added to the group. What is the new mean?
統計的應用及誤用 Uses & Abuses of Statistics
1. 認識抽取樣本的不同技巧和選擇搜集數據的法則 (Recognize different techniques in choosing samples and the criteria in choosing data collection method)
(全新課題)
2. 研究日常生活中統計的應用及誤用 (Investigate methods in which statistical surveys are used and misused in various daily-life activities)
半分法
整個課題刪去 [ 94 #4, 02#41]
(Method of bisection)
另外，考生亦要留意以下點 1. 不要答非所問和粗心大意 [03#7] If
, then y=
[05#17] The figure shows a solid right circular cone if height 5cm and slant height 13cm. Find the total surface area of the cone.
A. 0 B. 13 C. 0 or -3 D. 4 or 13
A. 144π cm B. 156π cm 2 C. 240π cm 2 D. 300π cm 2
[03#31] P(-10, -8) and Q(4,6) are two points. If R is a point on the x axis such that PR=RQ, then the coordinates of R are
[05#42] If four arithmetic means are inserted between 12 and 27, then the sum of the four means is
A. (-4,0) (24.60%) B. (-3,-1) (35.45%) C. (-3,0) D. (-2,0)
A. 78 B. 90 C. 105 D. 117
[05#31] A(2,5) and B(6,-3) are two points. If P is a point lying on the straight line x=y such that AP=PB, then the coordinates of P are
[05#44] o _ x < _ 360 o , how many distinct roots does the For 0 < equation cosx (sinx-1) =0 have?
A. (-2,-2) (30.01%) B. (-2,4) C. (1,1) D. (4,1) (40.29%)
A. 2 B. 3 C. 4 D. 5
10 數學 Mathematics
2
學友社 2006
會考 指南
2.留意未知數的可能性 [98#10] Solve (x-1) (x-3) = x-3 A. x=1 B. x=2 C. x=0 or 3 D. x=1 or 3 E. x=2 or 3
[91#10] If (x-2) (x-3) = (a-2) (a-3), solve for x. A. x=0 or 5 B. x=2 or 3 C. x=a or 2 D. x=a or 3 E. x=a or 5-a
常犯錯誤 1. 指數 (indices) x
x
5(5 ) = 25 x x+1 5(5 ) = 5 x 2
x+2
(4 ) =4 2 2x (4 x) = 4 x 0 =0 x 0 =1 2. 對數
log x log x- log y = log y x log x- log y = log y log x 2 y 2 - log xy = log xy (xy - 1) log x 2 y 2 - log xy = log xy
[99#44] The sum of the first two terms of a geometric sequence is 3 and the sum to infinity of the sequence is 4. Find the common ratio of the sequence. A. -1/7 B. 1/7 C. 1/4 D. -1/2 E. -1/2 or 1/2 [Example] Solve
7-x = x-5
A. 6 B. 3 or 6 C. -3 or -6 D. 6 or -6
3. 因式分解 (x+y) 2 =x 2 +y 2 2 (x+y) 2 =x 2 +2xy+y x 2 -25y 2 =(x-25y) (x+25y) x 2 -25y 2 =(x-5y) (x+5y) 4. 等差及等比數列 (Arithmetic & Geometric Sequences) T(n) = a+(n+1)d T(n) = a+(n-1)d S(n) = a(1-Rn)/1-R S(n) = a(Rn-1)/R-1 5. 續三角 (More about Trigonometry) Given B= C then AB=AC (base s, isos. )
3.小心閱讀題目和留意題目用字 [03#33] The median of the five numbers 15, x-1, x-3, x-4 and x+17 is 8. Find the mean of the five numbers. A. 8 B. 12 (33.60%) C. 13.6 (45.49%) D. 14.4
Given B= C then AB=AC (sides opp. equal
A
s)
B
C
6. 百分比 (percentage) Find the amount of $10000 at 12% p.a., compounded monthly, for 2 years. $10000(1+12/100)
2
$10000(1+12/100)
24
由David Chiu提供的常用方程式(Useful Formula)可於學友社網頁(www.hyc.org.hk)或學生專線網頁(www.student.hk)下載。 會考 指南
2006 學友社
數學 Mathematics 11
David Chiu
考試形式 Paper I 卷一 問答題 (60%) 2小時 內容
分數
一般情況下，考生取得
選題
出題範圍
A，Paper I 要取得90分以上
Section A (1) 甲部(一)
33分
8-10題 (必答)
剪裁課程
Section A (2) 甲部(二)
33分
4-5 題 (必答)
剪裁課程
Section B 乙部
33分
4題選3題答
整體範圍 (深入的長題目)
Paper II 要答對50題以上 C，Paper I 要取得70分以上 Paper II 要答對38題以上
Paper II 卷二 MC選擇題 (40%) 1.5小時 內容
E，Paper I 要取得35分以上
選題
出題範圍
Section A 甲部
36題 (必答)
剪裁課程 (問題由30題開始會較難)
Section B 乙部
18題 (必答)
整體範圍
備註：
Paper II 要答對20題以上
得分
(1) 剪裁課程是從整體課程中選出部分內容，使成績稍遜的學生能先專注 選答這一部份的基礎內容，熟讀剪裁課程可保合格。 (2) 時間分配是十分重要，卷一甲應於1小時10分鐘內完成，卷二乙平均 15分鐘1題（共三題），最後考生應預留不少於五分鐘覆核全卷。卷 二共有54題選擇題，平均分半鐘一題，最後用大約五分鐘去覆核全卷。
扣分
A : Accuracy
P.P: poor presentation
即是答案正確而取得的分數，應以真
即是表達不清楚而扣去的分數
確值(exact value)或三位有效數字(3 significant figures) 表示。在運算過 程中，答案應多取一些有效數字，否 則最終的答案會出現偏差。
(3) 在卷一中考生答題時必須列出計算步驟，以確保在不小心錯算答案時， 仍可取得步驟的分數。卷二的首三十六題比較容易。
M: Method
U: Unit
評核技巧和方法正確的分數
因欠單位而扣的分數 全卷最多可扣 2 分 P.P. 及 1 分 U
主要課程比較 新增重點
刪減重點 1. 根與係數間的關係 (sum of root, product of root) [90 #5, 96 #11, 03 #41]
一元二次方程
2. 進行分母如
Quadratic Equations in One Unknown
(Rationalization the denominators of expression in the form
等差及等比數列
現實生活問題，例如利息、增長、折舊及幾何問題等
Arithmetic & Geometric Sequences
(Real-life problems such as interest, growth and depreciation, geometric problems etc)
函數及其圖像
從給出的代數關係，將經變換後的函數圖像形像化 The effect of transformation on the graphs of functions
Functions and Graphs
指數函數及對數函數 Exponential and Logarithmic Functions
(全新課題)
等的公式之有理化
E.g. How to obtain
以
) [90#4, 00#40]
符號表示多項的求和，以及涉及 符號的 代數運算 (The use of notation)
from
1. 有理數指數定律 the laws of rational indices 2. 對數及指數函數之圖像特性 the properties of the graphs of exponential and logarithmic functions
求直線與圓的交點 軌跡及坐標幾何問題 Locus & Coordinate Geometry
會考 指南
2006 學友社
(Intersection of a straight line and a circle)
直線與圓相交、相切及不相交的情況 (The cases of a straight line intersects, touch and do not touch a circle) [98 #52, 00 #49]
數學 Mathematics
9
新增重點
刪減重點 1. 以弧度 (radian) 為單位量度角度
續三角 More about
2. 弧長及扇形的面積 (Arc length and the area of sector)
Trigonometry
離差的量度 Measures of Dispersion
在不同情況對數據離差所產生的影響，例如：
1. 計算平均差 (mean deviation)
1. 剔除數據中某個項 removal of a certain item from the data
2. 計算方差 (variance) 3. 正態分佈 (normal distribution)
2. 在整組數據中每一項加入一個共同常數 adding a common constant to the whole set of data
4. 加權平均數 (weighted mean)
3. 把整組數據中每一項乘以一個共同常數 multiplying the whole set of data by a constant 4. 在該組數據中加入「零」項 insertion of zero in the data set E.g. The mean of a group of 20 numbers is 36. Four numbers, each equals to 100, are added to the group. What is the new mean?
統計的應用及誤用 Uses & Abuses of Statistics
1. 認識抽取樣本的不同技巧和選擇搜集數據的法則 (Recognize different techniques in choosing samples and the criteria in choosing data collection method)
(全新課題)
2. 研究日常生活中統計的應用及誤用 (Investigate methods in which statistical surveys are used and misused in various daily-life activities)
半分法
整個課題刪去 [ 94 #4, 02#41]
(Method of bisection)
另外，考生亦要留意以下點 1. 不要答非所問和粗心大意 [03#7] If
, then y=
[05#17] The figure shows a solid right circular cone if height 5cm and slant height 13cm. Find the total surface area of the cone.
A. 0 B. 13 C. 0 or -3 D. 4 or 13
A. 144π cm B. 156π cm 2 C. 240π cm 2 D. 300π cm 2
[03#31] P(-10, -8) and Q(4,6) are two points. If R is a point on the x axis such that PR=RQ, then the coordinates of R are
[05#42] If four arithmetic means are inserted between 12 and 27, then the sum of the four means is
A. (-4,0) (24.60%) B. (-3,-1) (35.45%) C. (-3,0) D. (-2,0)
A. 78 B. 90 C. 105 D. 117
[05#31] A(2,5) and B(6,-3) are two points. If P is a point lying on the straight line x=y such that AP=PB, then the coordinates of P are
[05#44] o _ x < _ 360 o , how many distinct roots does the For 0 < equation cosx (sinx-1) =0 have?
A. (-2,-2) (30.01%) B. (-2,4) C. (1,1) D. (4,1) (40.29%)
A. 2 B. 3 C. 4 D. 5
10 數學 Mathematics
2
學友社 2006
會考 指南
2.留意未知數的可能性 [98#10] Solve (x-1) (x-3) = x-3 A. x=1 B. x=2 C. x=0 or 3 D. x=1 or 3 E. x=2 or 3
[91#10] If (x-2) (x-3) = (a-2) (a-3), solve for x. A. x=0 or 5 B. x=2 or 3 C. x=a or 2 D. x=a or 3 E. x=a or 5-a
常犯錯誤 1. 指數 (indices) x
x
5(5 ) = 25 x x+1 5(5 ) = 5 x 2
x+2
(4 ) =4 2 2x (4 x) = 4 x 0 =0 x 0 =1 2. 對數
log x log x- log y = log y x log x- log y = log y log x 2 y 2 - log xy = log xy (xy - 1) log x 2 y 2 - log xy = log xy
[99#44] The sum of the first two terms of a geometric sequence is 3 and the sum to infinity of the sequence is 4. Find the common ratio of the sequence. A. -1/7 B. 1/7 C. 1/4 D. -1/2 E. -1/2 or 1/2 [Example] Solve
7-x = x-5
A. 6 B. 3 or 6 C. -3 or -6 D. 6 or -6
3. 因式分解 (x+y) 2 =x 2 +y 2 2 (x+y) 2 =x 2 +2xy+y x 2 -25y 2 =(x-25y) (x+25y) x 2 -25y 2 =(x-5y) (x+5y) 4. 等差及等比數列 (Arithmetic & Geometric Sequences) T(n) = a+(n+1)d T(n) = a+(n-1)d S(n) = a(1-Rn)/1-R S(n) = a(Rn-1)/R-1 5. 續三角 (More about Trigonometry) Given B= C then AB=AC (base s, isos. )
3.小心閱讀題目和留意題目用字 [03#33] The median of the five numbers 15, x-1, x-3, x-4 and x+17 is 8. Find the mean of the five numbers. A. 8 B. 12 (33.60%) C. 13.6 (45.49%) D. 14.4
Given B= C then AB=AC (sides opp. equal
A
s)
B
C
6. 百分比 (percentage) Find the amount of $10000 at 12% p.a., compounded monthly, for 2 years. $10000(1+12/100)
2
$10000(1+12/100)
24
由David Chiu提供的常用方程式(Useful Formula)可於學友社網頁(www.hyc.org.hk)或學生專線網頁(www.student.hk)下載。 會考 指南
2006 學友社
數學 Mathematics 11
