數學課程數與代數範疇 - bca.hkeaa.edu.hk ·...

數學課程

第三學習階段基本能力 (試用稿 )

數與代數範疇

學習單位編碼基本能力重點

數與數系

有向數及數線

NA1

KS3-NA1-1

學生能 :

利用正數、負數及零去描述如盈利

與虧損、相對於地面的樓宇層數的

情況等

KS3-NA1-2 展示對整數在數線上的序的認識

KS3-NA1-3 作有向數加、減、乘、除運算 (每一

數式中作不超過 3 次運算 )

數值估算

NA2

KS3-NA2-1

學生能 :

在簡易情境中判斷何時須作估算或

何時須計算準確值

KS3-NA2-2 估計數值並作出合理解釋

KS3-NA2-3 無須實質計算，鑑定計算結果的合

理性

近似與誤差

NA3

KS3-NA3-1

學生能 :

捨入某數至指定的

(a) 小數位

(b) 有效數字 (至最多 3 位有效數字 )

KS3-NA3-2 以科學記數法表示一數值大或數值小的數

©2011 香港考試及評核局版權所有 A-10


KS3-NA3-3 將一以科學記數法表示的數化為整數或小數

有理數及無理數

NA4

KS3-NA4-1

學生能 :

無須利用計算機，展示對 a 的整數部分的認識，其中 a 是一不大於 200的正整數

KS3-NA4-2 在數線上表達實數

比較數量

百分法

NA5

KS3-NA5-1

學生能 :

解簡單買賣問題

KS3-NA5-2 解涉及單利息的問題

KS3-NA5-3 解涉及按年以複利息計算的簡單問題 (當不用複利息公式時，只限不多於 3 年的計算；不包括求年期和利率的問題 )

KS3-NA5-4 解涉及增長和折舊的簡單問題 (只限計算最多 3 次重複增長／折舊的新數值 )

(備註：在這單位，所有涉及的數量應給予數值。 )



續百分法

NA6

率及比

NA7

KS3-NA7-1

學生能 :

展示對率及比的差異的認識

KS3-NA7-2 以 a： b (或 ba

)， a： b： c 的形式

表示比

KS3-NA7-3 從已知的比 a： b 及 a 或 b 的值，求餘下的數量 (包括從 a： b： c 作類似計算 )

KS3-NA7-4 運用率及比解簡單現實生活中的問

題，包括求積問題

觀察規律及表達通則

以代數語言建立

問題

NA8

KS3-NA8-1

學生能 :

辨別 2x 及 2+x；(–2)n 及 –2n；x2 及2x 等的差異

KS3-NA8-2 把文句／情境改寫為代數語言

KS3-NA8-3 將數值代入某些常見及簡易的公式中，然後求某一指定變數的值

KS3-NA8-4 由簡易的情境建立簡易方程／不等式

KS3-NA8-5 從已知數個連續項 (均為整數 )的等差數列、等比數列、斐波那契數列

或多邊形數中，寫出其後數項去描

述數列的規律



KS3-NA8-6 從已知簡易數列的首數項，直觀地求該數列的第 n 項 (各項必須是非負整數，第 n 項只限於 kn， n+k， nk

及 kn 的形式 )

KS3-NA8-7 從已知數列的第 n 項，求數列的各

項

簡易多項式的運

算

NA9

KS3-NA9-1

學生能 :

從代數式中分辨多項式

KS3-NA9-2 展示對有關詞彙的認識，例如：次數、遞升 /遞降序、係數、項數、不同類項及同類項、常數及變數

KS3-NA9-3 加或減最多 4 項的多項式

KS3-NA9-4 (a) 單項式乘以單項式

(b) 二項式乘以單項式

(c) 三項式乘以單項式

KS3-NA9-5 二項式乘以二項式

(備註：在這單位，涉及的項可包含最多兩個變數。 )

整數指數律

NA10

KS3-NA10-1

學生能 :

求 an 的值，其中 a 及 n 是整數



KS3-NA10-2 運用整數指數律來化簡簡易代數式 (每個代數式只限於最多兩個變數及化簡時只涉及運用整數指數律最

多兩次 )

簡易多項式的因

式分解

NA11

KS3-NA11-1

學生能 :

展示對因式分解是展開的逆運算的

認識

KS3-NA11-2 利用提取公因式及／或併項法分解不超過 4 項的簡易代數式

KS3-NA11-3 利用平方差或完全平方式 (只應用一次 )作因式分解

KS3-NA11-4 利用十字相乘法分解形如 ax2 + bx + c 的代數式，其中 a 是 1、 2 或 3而 c 是數值上不大於 20 的整數

代數關係式與函數

一元一次方程

NA12

KS3-NA12-1

學生能 :

由簡易情境中建立一元一次方程

KS3-NA12-2 解簡易方程

KS3-NA12-3 展示對方程的根的理解

KS3-NA13-1

學生能 :

繪畫二元一次方程的圖像

二元一次方程

NA13

KS3-NA13-2 展示對形如 ax + by + c = 0 的方程的圖像為直線的認識

KS3-NA13-3 從給出的直線方程，判定一點是否

在該直線上



KS3-NA13-4 由簡易情境中建立聯立方程

KS3-NA13-5 (a) 以代數方法 (學生可選擇運用消去法或代入法 )

(b) 以圖解法

解簡易聯立方程 (只限於係數、常數均為整數及有唯一解的聯立方

程 )

KS3-NA13-6 認識由圖解法所得的根並不一定精

確

恆等式

NA14

KS3-NA14-1

學生能 :

指出某一等式是方程或恆等式

KS3-NA14-2 運用平方差及完全平方展開簡易代

數式

公式

NA15

KS3-NA15-1

學生能 :

對分子及分母均為一項的分式作出

運算，例如 x1， y

x23

等

KS3-NA15-2 把數值代入所有指數均為正整數的公式，然後求某一指定變數的數值

KS3-NA15-3 變換不涉及根號的簡易公式的主項

一元一次不等式

NA16

KS3-NA16-1

學生能 :

運用不等號 ≥、>、≤ 及 < 去比較數字



KS3-NA16-2 展示對下列不等式性質的認識及應用以下性質﹕

對於 x y， ≥

(a) x + c ≥ y + c (b) cx ≥ cy (c＞ 0)；

cx ≤ cy (c＜ 0)

KS3-NA16-3 由簡易的情境建立一元一次不等式

KS3-NA16-4 解係數及常數均為整數的簡易一元一次不等式

KS3-NA16-5 在數線上表示如 x＜ –2， x 3 等的數學語句，以及將數線上不等式的

解寫成數學語句

≥


數學課程

第三學習階段基本能力 (第四試用稿 )

度量、圖形與空間範疇


平面及立體圖形的度量

量度方面的估計

MS1

KS3-MS1-1

學生能 :

由已知量度的準確度找出度量的範

圍

KS3-MS1-2 就現實生活的量度，選用適當的量度工具和策略

KS3-MS1-3 就現實生活的量度，選用適當的度

量單位和準確度

KS3-MS1-4 估計度量並給予合理解釋

KS3-MS1-5 減低量度的誤差

學生能 : 面積和體積的簡單概念

MS2 KS3-MS2-1 運用圓周和圓形面積的公式

KS3-MS2-2 運用正方體、長方體、稜柱和圓柱表面面積的公式

KS3-MS2-3 運用稜柱和圓柱體積的公式

KS3-MS3-1

學生能 :

計算弧長

續面積和體積

MS3

KS3-MS3-2 計算扇形的面積



KS3-MS3-3 計算稜錐、圓錐和球形的體積

KS3-MS3-4 計算直立稜錐、直立圓錐和球形的表面面積

KS3-MS3-5 運用相似物體的邊和表面面積／體積之間的關係解有關問題 (不包括與平截頭體有關的計算 )

KS3-MS3-6 以維數分辨長度、面積、體積的度

量公式

以直觀法學習幾何

幾何簡介

MS4

KS3-MS4-1

學生能 :

展示對幾何學常用的詞彙的認識，

例如線段、角、多邊形、正多邊形、

正方體、長方體和正多面體 (柏拉圖立體 )

KS3-MS4-2 運用常用的記號去表示點、線段、角和多邊形

KS3-MS4-3 根據角的大小去識別不同類別的角

KS3-MS4-4 判定一多邊形是否正、凸、凹、等

邊或等角

KS3-MS4-5 根據給出的摺紙圖樣，製作立體模

型

KS3-MS4-6 繪畫簡單立體的圖像

KS3-MS4-7 繪畫簡單立體的橫切面



變換及對稱

MS5

KS3-MS5-1

學生能 :

由圖形判定對稱軸的數目及繪畫對

稱軸

KS3-MS5-2 由圖形判定旋轉對稱折的數目及標

示旋轉中心

KS3-MS5-3 從比較原物與其所涉及一次變換後的影像，寫出該變換的名稱

KS3-MS5-4 識別圖形經一次變換後的影像

KS3-MS5-5 展示一次變換對圖形大小及形狀的

影響的認識

KS3-MS6-1

學生能 :

展示對三角形的全等及相似條件的

認識

全等及相似

MS6

KS3-MS6-2 判定兩個三角形是屬於全等三角形或是相似三角形並列舉簡單理由

KS3-MS6-3 展示對全等三角形及相似三角形性質的認識



與線及直線圖形

有關的角

MS7

KS3-MS7-1

學生能 :

從直線及多邊形相對的位置，展示

對以下有關角詞彙的認識

鄰角

同頂角

對頂角

多邊形的內角及外角

與線及其截線有關的角

KS3-MS7-2 運用與相交線／平行線相關的角的性質來解簡單的幾何問題 (相關的逆定理將會在「以演繹法學習幾何」

單位中處理 )

KS3-MS7-3 運用三角形角的性質來解簡單幾何問題

KS3-MS7-4 運用等腰三角形／等邊三角形邊和角的關係來解簡單幾何問題

KS3-MS7-5 運用凸多邊形內角和及外角和的公式

(備註：在這單位，學生不須作幾何證明。 )



續立體圖形

MS8

KS3-MS8-1

學生能 :

由正方體，寫出其反射對稱平面的

名稱

KS3-MS8-2 由正方體，寫出其旋轉對稱軸的名

稱

KS3-MS8-3 識別正方體、正四面體及底為等邊三角形的直立稜柱的摺紙圖樣

KS3-MS8-4 根據立體的不同角度所得的平面圖形，配對相應的立體 (立體須由正方體組成及以不超過 10 個正方體為限 )

KS3-MS8-5 寫出

(a) 邊在水平 /鉛垂平面上的投影

(b) 線與水平 /鉛垂平面的交角

(c) 兩平面的交角，其中一平面是水平 /鉛垂

的名稱

以演繹法學習幾何

KS3-MS9-1

學生能 :

就與角和線有關的簡單幾何問題列

述證明

演繹幾何簡介

MS9

KS3-MS9-2 運用構成全等三角形和相似三角形的條件，進行簡單證明

KS3-MS9-3 識別三角形的中線、垂直平分線、

高線及角平分線

畢氏定理

MS10

KS3-MS10-1

學生能 :

運用畢氏定理解簡單問題



KS3-MS10-2 運用畢氏定理的逆定理解簡單問題

四邊形

MS11

KS3-MS11-1

學生能 :

運用平行四邊形、正方形、長方形、

菱形、鷂形及梯形的性質計算數值

以解析法學習幾何

KS3-MS12-1

學生能 :

利用極坐標描述平面圖上點的位置

坐標簡介

MS12

KS3-MS12-2 利用直角坐標系統的序偶描述點的位置及從已知直角坐標的點找出該

點的位置

KS3-MS12-3 在直角坐標平面的一次變換中，配對某點及其影像 ( 變換只包括平移、與 x 軸、 y 軸平行的線作反射和繞原點旋轉 90°， 180° 及 270°)

KS3-MS12-4 計算能被分割成常見平面直線圖形

或由它們構成的簡單圖形的面積

KS3-MS13-1

學生能 :

應用距離公式

直線的坐標幾何

MS13

KS3-MS13-2 應用公式：斜率 =12

12

xxyy

−− (不須計

算斜角 )

KS3-MS13-3 應用中點公式

KS3-MS13-4 展示對兩線平行及兩線垂直所需條件的認識



三角學

KS3-MS14-1

學生能 :

找出 0° 至 90° 之間的角的正弦、餘弦和正切，及找出對應已知的正

弦、餘弦和正切 0° 至 90° 之間的角

三角比和三角的

應用

MS14

KS3-MS14-2 解直角三角形

KS3-MS14-3 展示對方位、斜率、仰角和俯角概念的認識

KS3-MS14-4 解只涉及一直角三角形的簡單平面

問題

備註﹕ 在數值計算的題目中，學生不須寫幾何理由。惟在幾何證明的題目

中，學生須列出可接受的理由。


數學課程

第三學習階段基本能力 (第四試用稿 )

數據處理範疇


數據的組織及表達

學生能 : 統計工作的各個步驟簡介

DH1 KS3-DH1-1 展示對統計工作各個步驟的認識，包括數據的收集、組織、表達及分析

KS3-DH1-2 使用簡單方法收集數據

KS3-DH1-3 分辨離散數據及連續數據

KS3-DH1-4 以不同分組方法組織同一組數據

簡單圖表及圖像

的製作及闡釋

DH2

KS3-DH2-1

學生能 :

製作簡單統計圖表，包括幹葉圖、圓

形圖、組織圖、散點圖、折線圖、頻

數多邊形及頻數曲線、累積頻數多邊

形及累積頻數曲線

KS3-DH2-2 闡釋簡單統計圖表，包括幹葉圖、圓形圖、組織圖、散點圖、折線圖、頻

數多邊形及頻數曲線、累積頻數多邊

形及累積頻數曲線

KS3-DH2-3 選用適當的圖表／圖像來表達數據

KS3-DH2-4 使用統計圖來比較同一組數據的表達(統計圖可包括各類圖像或同類但比例不同的圖像 )




KS3-DH2-5 從圖像／圖表中讀取資料 (包括百分位數、四分位數、中位數 ) 及頻數

KS3-DH2-6 找出圖表／隨附字句的誤導成份

數據的分析及闡釋

集中趨勢的量度

DH3

KS3-DH3-1

學生能 :

從一組不分組數據中找出算術平均

數、中位數和眾數

KS3-DH3-2 從一組分組數據中找出中位數 (只限由累積頻數多邊形／累積頻數曲線中

找出 )、算術平均數和眾數組

KS3-DH3-3 從一組數據中計算加權平均數

KS3-DH3-4 從誤用平均值的例子，找出誤導成份

概率

KS3-DH4-1

學生能 :

計算經驗概率

概率的簡單概念

DH4

KS3-DH4-2 以列舉的方法計算理論概率

©2011 Hong Kong Examinations and Assessment Authority All rights reserved

A-26

Mathematics Curriculum

Basic Competency for Key Stage 3 (Tryout Version)

Number and Algebra Dimension

Learning Unit Code Descriptors

Number and Number Systems

Directed Numbers and the Number Line

NA1

KS3-NA1-1

Student can:

use positive numbers, negative numbers and zero to describe situations like profit and loss, floor levels relative to the ground level

KS3-NA1-2 demonstrate recognition of the ordering of

integers on the number line

KS3-NA1-3 add, subtract, multiply and divide directed numbers (with at most 3 operations in each expression)

Numerical Estimation

NA2

KS3-NA2-1

Student can:

determine whether to estimate or to compute the exact value in a simple context

KS3-NA2-2 estimate values with reasonable justifications

KS3-NA2-3 judge, without actual calculations, the

reasonableness of answers from computations

Approximation and Errors

NA3

KS3-NA3-1

Student can:

round off a number to a certain number of

(a) decimal places

(b) significant figures (at most 3 sig. fig.)

KS3-NA3-2 represent a large or a small number in scientific notation


KS3-NA3-3 convert numbers in scientific notation to integers or decimals

Rational and Irrational Numbers

NA4

KS3-NA4-1

Student can:

demonstrate, without using calculators, recognition of the integral part of a , where a is a positive integer not greater than 200

KS3-NA4-2 represent real numbers on the number line

Comparing Quantities

Using Percentages

NA5

KS3-NA5-1

Student can:

solve simple selling problems

KS3-NA5-2 solve problems on simple interest

KS3-NA5-3 solve simple problems on compound interest, compounded yearly (confined to calculations for at most 3 years when not using the compound interest formula; excluding problems to find the number of years and the interest rate)

KS3-NA5-4 solve simple problems on growths and depreciations (confined to calculations of new values for at most 3 repeated growths/depreciations)

(Note: In this unit, numerical values should be provided to all quantities involved.)


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More about Percentages

NA6

Rate and Ratio

NA7

KS3-NA7-1

Student can:

demonstrate recognition of the difference between rate and ratio

KS3-NA7-2 represent a ratio in the form a : b (or ba

),

a : b : c

KS3-NA7-3 find the other quantity from a given ratio a : b and the value of either a or b (including similar calculations for the case of a : b : c)

KS3-NA7-4

use rate and ratio to solve simple real-life problems including mensuration problems

Observing Patterns and Expressing Generality

Formulating Problems with Algebraic Language

NA8

KS3-NA8-1

Student can:

distinguish the difference between 2x and 2 + x; (–2)n and –2n; x2 and 2x, etc.

KS3-NA8-2 translate word phrases/contexts into algebraic languages

KS3-NA8-3 substitute values into some common and simple formulas and find the value of a specified variable

KS3-NA8-4 formulate simple equations/inequalities from simple contexts

KS3-NA8-5 describe patterns by writing the next few terms in arithmetic sequences, geometric sequences, Fibonacci sequence or sequences of polygonal numbers from several consecutive terms of integral values


A-28


A-29


KS3-NA8-6 find intuitively the nth term of a simple number sequence from the first few given terms (the terms given should be non-negative integers and the nth term is limited to the forms kn, n + k, nk and kn)

KS3-NA8-7 find the terms of the sequence from a given

nth term

Manipulations of Simple Polynomials

NA9

KS3-NA9-1

Student can:

distinguish polynomials from algebraic expressions

KS3-NA9-2 demonstrate recognition of terminologies such as degree, ascending/descending orders, coefficients, number of terms, unlike terms and like terms, constants and variables

KS3-NA9-3 add or subtract polynomials of at most 4

terms

KS3-NA9-4 multiply (a) a monomial by a monomial

(b) a binomial by a monomial

(c) a trinomial by a monomial

KS3-NA9-5 multiply a binomial by a binomial

(Note: In this unit, the terms involved contain at most two variables.)

Laws of Integral Indices

NA10

KS3-NA10-1

Student can:

find the value of an, where a and n are integers

KS3-NA10-2 use the laws of integral indices to simplify simple algebraic expressions (up to 2 variables and at most 2 applications of integral index laws)


A-30


Factorization of Simple Polynomials

NA11

KS3-NA11-1

Student can:

demonstrate recognition of factorization as a reverse process of expansion

KS3-NA11-2 factorize simple polynomials of not more than 4 terms by taking out common factors and/or grouping terms

KS3-NA11-3 factorize simple polynomials by using the difference of two squares or the perfect square expressions once

KS3-NA11-4 use the cross method to factorize expressions of the form ax2 + bx + c, where a is 1, 2 or 3 and c is an integer numerically not greater than 20

Algebraic Relations and Functions

Linear Equations in One Unknown

NA12

KS3-NA12-1

Student can:

formulate linear equations in one unknown from simple contexts

KS3-NA12-2 solve simple equations

KS3-NA12-3 demonstrate understanding of the meaning of

roots of equations

KS3-NA13-1

Student can:

plot graphs of linear equations in 2 unknowns

Linear Equations in Two Unknowns

NA13 KS3-NA13-2 demonstrate recognition that graphs of

equations of the form ax + by + c = 0 are straight lines

KS3-NA13-3 determine whether a point lies on a straight

line with a given equation

KS3-NA13-4 formulate simultaneous equations from simple contexts


KS3-NA13-5 solve a system of simple linear simultaneous equations (with integral coefficients and constants) which has a unique solution

(a) by algebraic methods (students can choose either the method of elimination or the method of substitution)

(b) by the graphical method

KS3-NA13-6 be aware that the root obtained by the

graphical method may not be exact

Identities

NA14

KS3-NA14-1

Student can:

tell whether an equality is an equation or an identity

KS3-NA14-2 expand simple algebraic expressions by using the difference of two squares and the perfect square expressions

Formulas

NA15

KS3-NA15-1

Student can:

manipulate algebraic fractions with only one term in both the numerator and denominator

such as yx

x 23,1 , etc.

KS3-NA15-2 substitute values of formulas (in which all exponents are positive integers) and find the value of a specified variable

KS3-NA15-3 perform change of subject in simple formulas

but not including radical sign

Linear Inequalities in One Unknown

NA16

KS3-NA16-1

Student can:

use inequality signs ≥ , > , ≤ and < to compare numbers


A-31


A-32


KS3-NA16-2 demonstrate recognition of and apply the following properties of inequalities:

For x ≥ y,

(a) x + c ≥ y + c

(b) cx ≥ cy ( c > 0 ); cx ≤ cy ( c < 0 )

KS3-NA16-3 formulate linear inequalities in one unknown from simple contexts

KS3-NA16-4 solve simple linear inequalities in one unknown with integral coefficients and constants

KS3-NA16-5 represent inequalities, such as x < –2, x ≥

3, etc., on the number line and vice versa


A-33

Mathematics Curriculum Basic Competency for Key Stage 3 (The 4th Tryout Version)

Measures, Shape and Space Dimension


Measures in 2-D and 3-D Figures

Estimation in Measurement

MS1

KS3-MS1-1

Student can:

find the range of measures from a measurement of a given degree of accuracy

KS3-MS1-2 choose an appropriate measuring tool and technique for real-life measurements

KS3-MS1-3 choose an appropriate unit and the degree

of accuracy for real-life measurements

KS3-MS1-4 estimate measures with justification

KS3-MS1-5 reduce errors in measurements

Student can: Simple Idea of Areas and Volumes

MS2 KS3-MS2-1 use the formulas for circumferences and areas of circles

KS3-MS2-2 use the formulas for surface areas of cubes, cuboids, prisms and cylinders

KS3-MS2-3 use the formulas for volumes of prisms and

cylinders

KS3-MS3-1

Student can:

calculate arc lengths

More about Areas and Volumes

MS3 KS3-MS3-2 calculate areas of sectors


A-34


KS3-MS3-3 calculate volumes of pyramids, circular

cones and spheres

KS3-MS3-4 calculate surface areas of right pyramids, right circular cones and spheres

KS3-MS3-5 use the relationships between sides and surface areas/volumes of similar figures to solve related problems (calculations related to frusta are not expected)

KS3-MS3-6 distinguish among formulas for lengths,

areas, volumes by considering dimensions

Learning Geometry through an Intuitive Approach

Introduction to Geometry

MS4

KS3-MS4-1

Student can:

demonstrate recognition of common terms in geometry such as line segments, angles, polygons, regular polygons, cubes, cuboids and regular polyhedra (Platonic solids)

KS3-MS4-2 use common notations to represent points, line segments, angles and polygons

KS3-MS4-3 identify types of angles with respect to

their sizes

KS3-MS4-4 determine whether a polygon is regular, convex, concave, equilateral or equiangular

KS3-MS4-5 make 3-D solids from given nets

KS3-MS4-6 sketch simple solids

KS3-MS4-7 sketch cross-sections of simple solids


A-35


Transformation and Symmetry

MS5

KS3-MS5-1

Student can:

determine the number of axes of symmetry from a figure and draw the axes of symmetry

KS3-MS5-2 determine the order of rotational symmetry from a figure and locate the centre of rotation

KS3-MS5-3 name the single transformation involved in comparing the object and its image

KS3-MS5-4 identify the image of a figure after a single transformation

KS3-MS5-5 demonstrate recognition of the effect on the size and shape of a figure under a single transformation

KS3-MS6-1

Student can:

demonstrate recognition of the conditions for congruent and similar triangles

Congruence and Similarity

MS6

KS3-MS6-2 identify whether 2 triangles are congruent/similar with simple reasons

KS3-MS6-3 demonstrate recognition of the properties of congruent and similar triangles


A-36


Angles related with Lines and Rectilinear Figures

MS7

KS3-MS7-1

Student can:

demonstrate recognition of the following terminologies on angles with respect to their positions relative to lines and polygons:

adjacent angles angles at a point vertically opposite angles interior angles and exterior angles of

polygons angles associated with lines and their

transversals

KS3-MS7-2 use the angle properties associated with intersecting lines/parallel lines to solve simple geometric problems (related converse theorems are to be treated in the learning unit “Learning Geometry through a Deductive Approach”)

KS3-MS7-3 use the properties of angles of triangles to solve simple geometric problems

KS3-MS7-4 use the relations between sides and angles associated with isosceles/equilateral triangles to solve simple geometric problems

KS3-MS7-5 use the formulas for the sums of the interior angles and exterior angles of convex polygons

(Note: In this unit, students are not required to prove geometric facts.)


A-37


More about 3-D Figures

MS8

KS3-MS8-1

Student can:

name planes of reflectional symmetries of cubes

KS3-MS8-2 name axes of rotational symmetries of

cubes

KS3-MS8-3 identify the nets of cubes, regular tetrahedra and right prisms with equilateral triangles as bases

KS3-MS8-4 match 3-D objects built up of cubes (not more than 10) from 2-D representations from various views

KS3-MS8-5 name

(a) the projection of an edge on a horizontal/vertical plane

(b) the angle between a line and a horizontal/vertical plane

(c) the angle between 2 planes, one of the planes being horizontal/vertical

Learning Geometry through a Deductive Approach

KS3-MS9-1

Student can:

present proofs of simple geometric problems related with angles and lines

Simple Introduction to Deductive Geometry

MS9

KS3-MS9-2 use the conditions for congruent and similar triangles to perform simple proofs

KS3-MS9-3 identify medians, perpendicular bisectors, altitudes and angle bisectors of a triangle


Pythagoras’ Theorem

MS10

KS3-MS10-1

Student can:

use Pythagoras’ Theorem to solve simple problems

KS3-MS10-2 use the converse of Pythagoras’ Theorem to solve simple problems

Quadrilaterals

MS11

KS3-MS11-1

Student can:

use the properties of parallelograms, squares, rectangles, rhombuses, kites and trapeziums in numerical calculations

Learning Geometry through an Analytic Approach

KS3-MS12-1

Student can:

use polar coordinates to describe positions of points in a plane

Introduction to Coordinates

MS12

KS3-MS12-2 use an ordered pair to describe the position of a point in the rectangular coordinate plane and locate a point of given rectangular coordinates

KS3-MS12-3 match a point under a single transformation with its image in the rectangular coordinate plane (the transformation includes only translation, reflection with respect to lines parallel to the x-axis, y-axis and rotation about the origin through 90°, 180° and 270°)

KS3-MS12-4 calculate areas of simple figures that can be cut into or formed by common 2-D rectilinear figures

KS3-MS13-1

Student can:

use the distance formula

Coordinate Geometry of Straight Lines

MS13

KS3-MS13-2 use the formula slope = 12

12

xxyy

−−

(calculations on inclinations are not required)


A-38


A-39


KS3-MS13-3 use the mid-point formula

KS3-MS13-4 demonstrate recognition of the conditions

for parallel lines and perpendicular lines

Trigonometry

KS3-MS14-1

Student can:

find the sine, cosine and tangent ratios for angles between 0° to 90° and vice versa

Trigonometric Ratios and Using Trigonometry

MS14

KS3-MS14-2 solve right-angled triangles

KS3-MS14-3 demonstrate recognition of the ideas of bearing, gradient, the angle of elevation and the angle of depression

KS3-MS14-4 solve simple 2-D problems involving one

right-angled triangle

Remarks: Students are not required to state geometric reasons for numerical problems. However, they are expected to give acceptable reasons in geometric proofs.


A-40

Mathematics Curriculum Basic Competency for Key Stage 3 (The 4th Tryout Version)

Data Handling Dimension


Organization and Representation of data

Student can: Introduction to Various Stages of Statistics

DH1 KS3-DH1-1 demonstrate recognition of various stages of

Statistics including collection, organization, representation and analysis of data

KS3-DH1-2 use simple methods to collect data

KS3-DH1-3 distinguish discrete and continuous data

KS3-DH1-4 organize the same set of data by different

grouping methods

Construction and Interpretation of Simple Diagrams and Graphs

DH2

KS3-DH2-1

Student can:

construct simple statistical charts including stem-and-leaf diagrams, pie charts, histograms, scatter diagrams, broken line graphs, frequency polygons and curves, cumulative frequency polygons and curves

KS3-DH2-2 interpret simple statistical charts including stem-and-leaf diagrams, pie charts, histograms, scatter diagrams, broken line graphs, frequency polygons and curves, cumulative frequency polygons and curves

KS3-DH2-3 choose appropriate diagrams/graphs to present a set of data

KS3-DH2-4 compare the presentations of the same set of data by using statistical charts (statistical charts including various types of charts or the same type of charts but in different scales)


A-41


KS3-DH2-5 read information (including percentiles, quartiles, median) and frequencies from diagrams/graphs

KS3-DH2-6 identify sources of deception in misleading

graphs/accompanying statements

Analysis and Interpretation of data

Measures of Central Tendency

DH3

KS3-DH3-1

Student can:

find mean, median and mode from a set of ungrouped data

KS3-DH3-2 find median (from cumulative frequency polygons/curves only), mean and modal class from a set of grouped data

KS3-DH3-3 calculate the weighted mean of a set of data

KS3-DH3-4 identify sources of deception in cases of misuse

of averages

Probability

KS3-DH4-1

Student can:

calculate the empirical probability

Simple Idea of Probability

DH4 KS3-DH4-2 calculate the theoretical probability by listing

C_BC_Math_KS3_4th version_22NOV07數學課程第三學習階段基本能力 (試用稿)數與代數範疇學習單位編碼基本能力重點數學課程第三學習階段基本能力 (第四試用稿)度量、圖形與空間範疇

學習單位編碼基本能力重點數據處理範疇

學習單位編碼基本能力重點

E_BC_Math_KS3_4th version_22Nov07Number and Algebra DimensionLearning UnitCodeDescriptorsMeasures, Shape and Space Dimension

Learning UnitCodeDescriptorsData Handling Dimension

Learning UnitCodeDescriptors

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數學課程數與代數範疇 - bca.hkeaa.edu.hk ·...