題記：「知識百寶箱」系列是「寶仁工作室」為了實踐2021-2022年度工作願景，而特別設立。目的旨在加快「寶仁工作室」的轉型，全面成為以「知識型專欄」為基礎之「知識主導型」的網誌。期望以協助提升大眾的學術素養為信條，並配合STEM的發展。除了普及科學知識外，也負起潛移默化為大家的人生有所改變的重責大任。將以學術專題探討、學習筆記為內容主體，回饋社會，服務讀者。
内容介紹：本篇屬重啟篇章，會跟讀者分析會考附加數學及現代數學課程，本人將透過多份歷史資料，配合本人對高等數學課程的了解，客觀分析會考附加數學及現代數學課程的歷年沿革。以協助讀者對會考附加數學及現代數學課程的歷年沿革有基本了解，從而幫助有讀者可以選用合適的Past Paper去備試，爭取好成績。以及協助教育工作者在進行數學教育工作時，有更多參考資源可供參考。
各位大家好，本篇為《2024年第14篇：香港中學會考數學科目分析（附加數學及現代數學篇）》的附錄，以中英雙語形式，整理並列出當年的會考數學課程。建議讀者連同正篇一同閲讀，從而令大家更清晰了解歷年會考數學課程之發展。
在本人撰寫正篇及附錄期間，曾研讀大量參考讀物，包括：
Ø 梁操雅和羅天佑合著的《香港考評文化的承與變：從強調篩選到反映能力》
Ø 歷年會考之Regulations and
Syllabues
Ø 中學課程綱要－附加數學中四至中五課程綱要
(1992)
Ø 數學教育學習領域－附加數學課程指引 (中四至中五) (2001)
這些Regulations and Syllabues，以及上述列出之參考讀物，可以在香港中央圖書館、港大參考圖館和中大圖書館中找到。這都幫助本人對會考數學課程有如此透徹的了解，特此鳴謝。
附件1：會考附加數學課程
Version 1: 1967
1.
Indices, logarithms, surds. The
remainder theorem.
2.
Arithmetical and Geometrical
progressions.
3.
Solution of simultaneous linear
equations, involving not more than three unknowns. Simultaneous equations, one
linear, in two unknowns.
4.
Elementary properties of
quadratic equations and functions. Simple problems on arrangements, on choice
and chance, and on the method of induction.
5.
The binomial theorem for a
positive integral index and its use for simple approximation. (Questions on the
greatest terms and on sums and properties of the coefficients will not be
asked).
6.
Functions of a variable and
their graphical representation. Determination of a function from a straight
line graph. Meaning of 
and its determination in simple cases. The
forms, graphs, and derivatives of the function 
, 
(Proofs will be required).
7.
Simple problems on
differentiation of a sum, product and function of a function (Chain Rule).
Applications to small increments, rate of change, speed problems, maxima and
minima (questions will be soluble without the use of the second derivative).
8.
The define integral and its
representation as an area; integration as the inverse of differentiations.
Integration of simple functions (excluding integration by part and by change of
variable other than 
); application to plane areas and
volumes of solids of revolution and to speed-time problems.
9.
Graphs and derivatives of
simple algebraic and trigonometrical functions (including sums, products,
quotients, functions of a function and implicit functions but excluding the
inverse trigonometric functions).
10.
Integration by simple change of
variable. (Integration by parts is excluded).
11.
Elementary two-dimensional
rectangular Cartesian co-ordinate geometry, e.g. distances, angles, area of a
triangle.
12.
The linear equation;
perpendicular distance from a point to a line. Easy locus problems. Equation of
a circle. Equation of tangents to a curve. Simple curvetracing.
13.
Circular measure.
Trigonometrical ratios of angles of any magnitude, Graphs of simple
trigonometrical functions. The solution of triangles and determination of area
(only the sine and cosine formulae and the formulae 
and 
will be needed; proofs will not be required).
Simple trigonometrical problems in three dimensions. General solutions of
simple trigonometrical equations.
14.
Formulae for 
(Proofs will not required). Applications to
multiple angles and simple identities.
（中文參考譯文）
1.
指數、對數、平均數。
餘式定理。
2.
等差和等比級數。
3.
聯立線性方程式的解，涉及不超過三個未知數。
聯立方程式，一為線性，有兩個未知數。
4.
二次方程式和函數的基本性質。
關於安排、選擇和機會以及歸納方法的簡單問題。
5.
正整指數的二項式定理及其在簡單近似的應用。
（不會詢問有關最大項以及係數的和及性質的問題）。
6.
函數之變數及其圖形表示。
從直線圖像確定函數。 簡單情況下的意思及其確定。 函數 、 的形式、圖像和導數（需證明）。
7.
關於函數的和、積和函數之微分（鏈式法則）的簡單問題。
應用到微增量、變率、速度問題、最大值和最小值（不使用二階導數即可解決問題）。
8.
積分的定義及其面積的表示；
積分作為微分的逆運算。 簡單函數的積分（不包括分部積分法和除 以外的變數的變化進行積分）； 應用於旋轉體的平面面積和體積以及速度-時間問題。
9.
簡單代數和三角函數的圖像和導數（包括和、積、商、函數的函數和隱函數，但不包括反三角函數）。
10.
透過簡單代換法進行積分。
（不包括分部積分法）。
11.
基本二維直角笛卡兒坐標幾何，例如：距離、角度、三角形的面積。
12.
線性方程；
從點到線的垂直距離。 簡易軌跡問題。 圓的方程。 曲線的切線方程式。 簡易曲線描繪。
13.
角的測量。
任何大小的角度的三角比，簡易三角函數圖像。 三角形的解和面積的確定（只需要正弦和餘弦公式以及公式 和 ）；不需要證明）。 三維的簡單三角學問題。
簡單三角方程的通解。
14.
公式（不需要證明）。 倍角和簡單恆等式的應用。
Version 2: 1968, 1969, 1970, 1971
Paper 1: Pure Mathematics I
1.
Simple problems on
arrangements, choice and chance.
2.
Simple problems on mathematical
induction.
3.
The binomial theorem for a
positive integral index, and its use for simple approximation. (Question on the
greatest terms and on sums and properties of the coefficients will not be
asked).
4.
Functions of a variable and
their graphical representation. Determination of a function from a straight
line graph. Meaning of the and its determination in simple cases. The
forms, graphs, and derivatives of the function , (Proofs will be required).
5.
Simple problems on
differentiation of a sum, product and function of a function.
6.
Applications to small
increments, rate of change, speed problems, maxima and minima (questions will
be soluble without the use of the second derivative).
7.
The define integral and its
representation as an area; integration as the inverse of differentiations.
Integration of simple functions (excluding integration of 
and excluding integration by part and by
change of variable other than );
application to plane areas and volumes of solids of revolution and to
speed-time problems.
8.
Circular measure.
Trigonometrical ratios of angles of any magnitude, Graphs of simple
trigonometrical functions. The solution of triangles and determination of area
(only the sine and cosine formulae and the formulae 
and will be needed; proofs will not be required).
Simple trigonometrical problems in three dimensions. Harder question may also
be set any item in the syllabus for Mathematics Syllabus A.
Paper II: Pure Mathematics II
1.
Indices, logarithms, surds. The
remainder theorem.
2.
Arithmetical and Geometrical
progressions.
3.
Solution of simultaneous linear
equations, involving not more than three unknowns. Simultaneous equations, one
linear, in two unknowns.
4.
Elementary properties of
quadratic equations and functions.
5.
Graphs and derivatives of
simple algebraic and trigonometrical functions (including sums, products,
quotients, functions of a function and implicit functions but excluding the
inverse trigonometric functions).
6.
Integration by simple change of
variable. (Integration by parts is excluded).
7.
Elementary two-dimensional
rectangular Cartesian co-ordinate geometry, e.g. distances, angles, area of a
triangle.
8.
The linear equation;
perpendicular distance from a point to a line. Easy locus problems. Equation of
a circle. Simple curve-tracing. Equation of tangents to a curve.
9.
Formulae for , 
, 
(Proofs will not required). Applications to
multiple angles and simple identities. General solutions of simple
trigonometrical equations.
Paper 3: Mechanics
1.
Equilibrant and resultant of
coplanar forces acting on a particle. The triangle and parallelogram of forces.
Simple examples on polygon of forces. Solution by composition and resolution of
forces. Lami’s theorem.
2.
Moments of forces, reactions,
parallel forces, couples, centre of gravity. Toppling. The equilibrium of a
rigid body under the action of coplanar forces.
3.
Pulleys, wheel and differential
axle, differential pulley.
4.
Friction. The inclined plane.
5.
Velocity, acceleration,
combined and relative velocities, solutions by vectors and calculation.
Equations of rectilinear motion with uniform acceleration including graphical
solutions. Projectiles on a horizontal plane.
6.
Newton’s laws of motion;
gravitational and absolute system of units. Work, energy any power.
Conservation of energy. Motion of connected particles. Motion in a circle with
uniform speed including centripetal acceleration and centrifugal force. The
conical pendulum, simple governor. Rolling. Torque, work done in rotation.
7.
Impulse. Conservation of
momentum. Impact between inelastic bodies.
（中文參考譯文）
1.
關於安排、選擇和機會的簡單問題。
2.
數學歸納法的簡單問題。
3.
正整指數的二項式定理及其在簡單近似的應用。
（不會詢問有關最大項以及係數的和及性質的問題）。
4.
函數之變數及其圖形表示。
從直線圖像確定函數。
簡單情況下的意思及其確定。
函數
、 的形式、圖像和導數（需證明）。
5.
關於函數的和、積和函數之微分（鏈式法則）的簡單問題。
6.
應用到微增量、變率、速度問題、最大值和最小值（不使用二階導數即可解決問題）。
7.
積分的定義及其面積的表示；
積分作為微分的逆運算。
簡單函數的積分（不包括的積分以及不包括除
以外的變數的變化進行積分）；
應用於旋轉體的平面面積和體積以及速度-時間問題。
8.
角的測量。
任何大小的角度的三角比，簡易三角函數圖像。
三角形的解和面積的確定（只需要正弦和餘弦公式以及公式
和 ）；不需要證明）。
三維的簡單三角學問題。更難的問題也可以設定在數學大綱 A 的大綱中的任何項目。
卷二：純數2
1.
指數、對數、平均數。
餘式定理。
2.
等差和等比級數。
3.
聯立線性方程式的解，涉及不超過三個未知數。
聯立方程式，一為線性，有兩個未知數。
4.
二次方程式和函數的基本性質。
5.
簡單代數和三角函數的圖像和導數（包括和、積、商、函數的函數和隱函數，但不包括反三角函數）。
6.
透過簡單代換法進行積分。
（不包括分部積分法）。
7.
基本二維直角笛卡兒坐標幾何，例如：距離、角度、三角形的面積。
8.
線性方程；從點到線的垂直距離。
簡易軌跡問題。
圓的方程。簡易曲線描繪。曲線的切線方程式。
、、的公式（不需證明）。
倍角和簡單恆等式的應用。簡單三角方程的通解。
卷三：力學
1.
作用在粒子上的共面力的平衡力和合力。
三角形和平行四邊形之力。
關於多邊形之力的簡單範例。
透過力的合成和分解來解決。拉密定理
2.
力、反作用力、平行力、力偶、重心的力矩。
傾倒。
剛體在共面力作用下的平衡。
3.
滑輪、車輪和差速器軸、差速器滑輪。
4.
摩擦。
斜面。
5.
速度、加速度、組合速度和相對速度、向量解和計算。
勻加速直線運動方程，包括圖像解。抛體在水平面上。
6.
牛頓運動定律；
引力和絕對單位制。
作功，能量任何功率。
能量轉換。
連接粒子的運動。
勻速圓周運動，包括向心加速度和離心力。
圓錐擺，簡單調速器。
滾動。
力矩，旋轉所做的功。
7.
衝量。
動量守恆。
非彈性體之間的碰撞。
Version 3: 1972, 1973, 1974 (named
Syllabus B)
Paper 1: Pure Mathematics I
1.
Elementary two-dimensional
rectangular Cartesian co-ordinate geometry, e.g. distances, angles, area of a
triangle.
2.
The linear equation;
perpendicular distance from a point to a line. Easy locus problems. Equation of
a circle. Ability to recognise equations of conics in standard position. Simple
curve-tracing. Equation of tangents to a curve.
3.
Functions of a variable and
their graphical representation. Determination of a function from a straight
line graph. Meaning of and its determination in simple cases. The
forms, graphs, derivatives of the functions , . (Proof will not be required). (until 1973)
Functions of a variable and their graphical representation.
Determination of a function from a straight line graph. Meaning of and its determination in simple cases. Graphs
of the functions , and 
(where
m and c are constants and n a constant integer). Derivatives of the function , and , (where m,
c and n are constants). (1974)
4.
Simple problems on the
differentiation of a sum, product and function of a function. (until 1973)
5.
Applications to small
increments, rates of change, speed problems, maxima and minima (questions will
be soluble without the use of the second derivative). (until 1973)
6.
Differentiation of a sum,
product and function of a function; simple problems; applications to small
increments, rates of change, speed problems, maxima and minima. (1974)
7.
The definite integral and its
representation as an area; integration as the inverse of differentiation.
Integration of simple functions (excluding integration of and excluding integration by parts and by
change of variable other than );
application to plane areas and volumes of solids of revolution add to
speed-time problems. (until
1973)
The define integral; the idea of the definite integral as the limit
of a sum; integration as the inverse of differentiation. Integration of simple
functions (excluding integration of and excluding integration by parts and by
change of variable other than );
application to plane areas and volumes of solids of revolution add to
speed-time problems.
(1974)
8.
Circular measure.
Trigonometrical ratios of angles of any magnitude. Graphs of simple
trigonometrical functions. The solution of triangles and determination of area
(only the sine and cosine formulae and the expressions and will be needed; proofs will not be required/
examined (1973, 1974)).
Simple trigonometrical problems in three dimensions.
Paper II: Pure Mathematics II
1.
Simple problems on
arrangements, choice and chance. (until 1972)
Simple problems on permutations, combinations and probability. (1973, 1974)
2.
Mathematical induction and
simple applications including simple sequences and series.
3.
The binomial theorem for a
positive integral index, and its use for simple approximations. (Questions on
the greatest terms and on sums and properties of the coefficients will not be
asked).
4.
Indices, logarithms, surds.
Functional notation. The remainder theorem and its applications.
5.
Solution of simultaneous linear
equations, involving not more than three unknowns, and of two simultaneous
equations, one linear, in two unknowns. (1974 cancelled)
6.
Elementary properties of
quadratic functions and equations including complex roots. (until 1973)
Elementary properties of quadratic functions in one variable.
Quadratic equations of simple trigonometrical equations. (1974)
7.
Graphs and derivatives of
simple algebraic and trigonometrical functions (including sums, products,
quotients, functions of a function and implicit functions but excluding the
inverse trigonometrical functions).
8.
Integration by simple change of
variable. (Integration by parts is excluded).
9.
Formulae for , , (Proofs will not required/ Formal proofs of
these formulae will not be examined (1973, 1974)). Applications to multiple angles and simple
identities. General solutions of simple trigonometrical equations.
Paper 3: Mechanics
1.
Scalar and vector quantities.
Composition and resolution of vectors. Solution by graphical methods and by
calculation.
2.
Equilibrant and resultant of
coplanar forces acting on a particle. The triangle and parallelogram of forces.
Simple examples on polygon of forces. Solution by composition and resolution of
forces. Lami’s theorem. (until
1973)
Equilibrant and resultant of coplanar forces acting on a particle.
The triangle and parallelogram of forces. Simple examples on polygon of forces.
Lami’s theorem. (1974)
3.
Moments of forces, reactions,
parallel forces, couples, centre of gravity. Toppling. (1974 cancel toppling) The equilibrium of a
rigid body under the action of coplanar forces.
4.
Pulleys, wheel and differential
axle, differential pulley. (until
1973)
Simple machines including pulleys, wheel and differential axle;
differential pulley. (1974)
5.
Friction. The inclined plane. (until 1973)
Coefficient and angle of friction. Inclined plane. (1974)
6.
Velocity, acceleration,
combined and relative velocities, solutions by vectors and calculation.
Equations of rectilinear motion with uniform acceleration including graphical
solutions. Projectiles on a horizontal plane. (until 1973)
Velocity, acceleration, resultant and relative velocities. Equations
of rectilinear motion with uniform acceleration including graphical solutions.
Simple problems on projectiles. (1974)
7.
Newton’s laws of motion;
gravitational and absolute system of units. Work, energy any power.
Conservation of energy. Motion of connected particles. Motion in a circle with
uniform speed including centripetal acceleration and centrifugal force. The
conical pendulum, simple governor. Rolling. Torque, work done in rotation. (until 1973)
Newton’s laws of motion: mass and weight. Work energy and power.
Conservation of energy. Motion of connected particles. Motion in a horizontal
circle with uniform speed including centripetal acceleration. The conical
pendulum. (1974)
8.
Impulse. Conservation of
momentum. Impact between inelastic bodies. (until 1973)
Impulse. Conservation of linear momentum. Impact between inelastic
bodies. (1974)
（中文參考譯文）
卷一：純數1
1.
基本二維直角笛卡兒坐標幾何，例如：距離、角度、三角形的面積。
2.
線性方程；從點到線的垂直距離。
簡易軌跡問題。 圓的方程。能夠辨識標準位置的二次曲線方程式。簡易曲線描繪。曲線的切線方程式。
3.
函數之變數及其圖形表示。
從直線圖像確定函數。 簡單情況下的意思及其確定。 函數 、的形式、圖像和導數。 （不需要證明）。
（直至1973）
函數之變數及其圖形表示。 從直線圖像確定函數。 簡單情況下的意思及其確定。 函數 和
的圖形（其中 m 和 c 是常數，n 是常數整數）。 函數 和
的導數（其中 m、c 和 n 是常數）。 （1974）
4.
關於函數的和、乘積以及函數的微分的簡單問題。（直至1973）
5.
應用到微增量、變率、速度問題、最大值和最小值（不使用二階導數即可解決問題）。（直至1973）
6.
函數的和、積、函數的微分；
簡單問題； 應用到微增量、變率、速度問題、最大值和最小值。（1974）
7.
定積分及其面積表示；
積分是微分的逆運算。 簡單函數的積分（不包括 x^(-1) 的積分，不包括以分部積分法和改變除 以外的變量的積分）；
應用於旋轉體的平面面積和體積以及速度-時間問題。（直至1973）
定積分； 定積分作為和的極限的想法；
積分是微分的逆運算。 簡單函數的積分（不包括 的積分，包括以分部積分法和改變除 
以外的變量的積分）； 應用於旋轉體的平面面積和體積以及速度-時間問題。（1974）
8.
角的測量。
任何大小的角度的三角比，簡易三角函數圖像。 三角形的解和面積的確定（只需要正弦和餘弦公式以及公式 
和 ）；不需要/考查證明（1973、1974）） 。
三維空間的簡單三角學問題。
卷二：純數2
1.
關於安排、選擇和機會的簡單問題。
（直至1972）
關於排列、組合和概率的簡單問題。 （1973、1974）
2.
數學歸納法和簡單應用，包括簡單的數列和級數。
3.
正整指數的二項式定理及其在簡單近似的應用。
（不會詢問有關最大項以及係數的和及性質的問題）。
4.
指數、對數、根式。
函數符號。 餘式定理及其應用。
5.
解聯立線性方程式（涉及不超過三個未知數）和兩個聯立方程式（其中一個為線性方程式）的兩個未知數。
（1974年取消）
6.
二次函數和方程式的基本性質，包括複數根。
（直至1973）
單變量二次函數的基本性質。 簡單三角方程的二次方程。 （1974）
7.
簡單代數函數和三角函數的圖像和導數（包括和、積、商、函數的函數和隱函數，但不包括反三角函數）。
8.
透過簡單代換法進行積分。
（不包括分部積分法）。
9.
、、 的公式（不需要證明/考查這些公式的正式證明（1973、1974））。 多角度和簡單恆等式的應用。
倍角和簡單恆等式的應用。簡單三角方程的通解。
卷三：力學
1.
純量和向量。
向量的組成和分解。 採用圖解法和計算法求解。
2.
作用在粒子上的共面力的平衡力和合力。
三角形和平行四邊形之力。 關於多邊形之力的簡單範例。 透過力的合成和分解來解決。拉密定理。
（直至1973）
作用在粒子上的共面力的平衡力和合力。 三角形和平行四邊形之力。 關於多邊形之力的簡單範例。 拉密定理。
（1974）
3.
力、反作用力、平行力、力偶、重心的力矩。
傾倒。 （1974年取消傾倒）剛體在共面力作用下的平衡。
4.
滑輪、車輪及差速器軸、差速器皮帶輪。（直至1973）
簡單機械，包括滑輪、車輪和差速器軸；差速器滑輪。 （1974）
5.
摩擦力。
斜面。 （至1973 年）
摩擦係數和摩擦角。斜面。 （1974）
6.
速度、加速度、組合速度和相對速度、向量解和計算。
勻加速直線運動方程，包括圖像解。 抛體在水平面上。 （直至1973）
速度、加速度、合速度和相對速度。 勻加速直線運動方程，包括圖形解。抛體上的簡單問題。（1974）
7.
牛頓運動定律；
引力和絕對單位制。 作功，能量任何功率。 能量轉換。連接粒子的運動。
勻速圓周運動，包括向心加速度和離心力。 圓錐擺，簡單調速器。 滾動。 力矩，旋轉所做的功。
（直至1973）
牛頓運動定律：質量和重量。 作功、能量任何功率。能量轉換。連接粒子的運動。 水平圓周上的等速運動，包括向心加速度。
圓錐擺。 （1974）
8.
衝量。
動量守恆。 非彈性體之間的碰撞。（直至1973）
衝量。 線性動量守恆。
非彈性體之間的碰撞。（1974）
Version 4: 1975 (combined English and
Chinese programme), 1976, 1977, 1978, 1979, 1980
1.
The six trigonometric ratios
and their graphs. Trigonometric ratios of angle of any magnitude. Sine and
cosine formulae. Formulae for 
, , (formal proofs of these
formulae will not be required), application to multiple and sub-multiple
angles. Problems in 2 or 3 dimensions. General solutions of simple
trigonometric equations.
2.
Differentiation from first
principles. Differentiation of polynomials and trigonometric functions
(excluding the inverses of trigonometric functions). Differentiation of 
. Second derivatives. Applications to small increments, rates of
change, equation of tangent to a curve, speed problems, maxima and minima,
sketching of simple curves.
3.
Indefinite integration as the
reverse process of differentiation.
4.
Rectangular co-ordinates in
2-dimension space; distance between two points; points dividing line segments
in a given ratio. Equations of a straight line; gradient of a straight line;
angle between two lines; distance from a point to a straight line; intersection;
family of straight lines. Area of triangle. (until 1978)/ Area of rectilinear figures. (1979, 1980)
5.
Linear and quadratic
inequalities in one variable. Inequalities of the form 
and 
and their solutions
algebraically or graphically on the real number line.
6.
Quadratic equations;
discriminant, complex roots. Arithmetic of complex numbers, Argand diagram,
conjugate, modulus. (until
1978)
Quadratic equations:
discriminant, complex roots. Arithmetic of complex numbers, Argand diagram,
conjugate, modulus and amplitude (limited to principal values 
). (since 1979)
7.
Remainder Theorem.
Factorisation of polynomials up to and including the third degree. (added 1979)
Paper II: Pure Mathematics
1.
Mathematical Induction and its
simple applications. (added
1979)
2.
Properties of logarithms
(including change of base).
(added 1980)
3.
The binomial theorem for
positive integral indices, and its applications such as simple approximation
and rate of growth. (Questions on the greatest sums and on sums and properties
of co-efficients will not be asked).
4.
Complex numbers: polar form and
de Moivre’s Theorem.
5.
Differentiation of a product, a
quotient, composite function and implicit function.
6.
Integration of simple functions
(excluding 
). Integration by simple change of variable. Definite integrals as
limit of a sum. Properties of definite integrals. Applications to areas and
volumes. (NOTE: integration by parts is excluded)
7.
Equations of circles,
co-ordinates of centre, length of radius, intersection of straight lines and
circles. Recognition of standard equations of parabola, ellipse and hyperbola.
Easy locus problems. (until
1978)
Equations of circles,
co-ordinates of centre, length of radius, intersection of straight lines and
circles. Family of circles. Standard equations of parabola, ellipse and
hyperbola. Locus problems. (1979)
Paper 3: Mechanics
1.
Scalar and vector quantities.
Composition and resolution of vectors. Solution of vector problems by graphical
methods and by calculation.
2.
Equilibrant and resultant of
coplanar forces acting on a particle. The triangle and parallelogram of forces.
Lami’s theorem. Simple examples on polygon of forces.
3.
Moments of forces, parallel
forces, couples, centre of gravity. The equilibrium of a rigid body under the
action of coplanar forces.
4.
Coefficient and angle of
friction. Inclined plane.
5.
Velocity, acceleration, resultant
and relative velocities. Equations of rectilinear motion with uniform
acceleration including graphical solutions. Simple problems on projectiles. (until 1978)
Displacement, velocity and acceleration. Resultant and relative
velocities. Rectilinear motion with uniform acceleration, including graphical
method. Simple problems on projectiles. (1979)
6.
Rotation about a fixed axis:
angular displacement and angular velocity. (1980 added)
7.
Newton’s laws of motion. Mass
and weight. Work, energy and power. Conservation of energy. Motion of connected
particles.
8.
Simple machines including
pulleys, wheel and differential axle, differential pulley; mechanical
advantage, velocity ratio, efficiency. (1979 cancelled)
9.
Impulse. Conservation of linear
momentum. Impact between inelastic bodies. (until 1979)
Impulse. Conservation of linear momentum. Direct impact of perfect
elastic bodies, and extension to the cases of imperfectly elastic bodies and
inelastic bodies. Loss of kinetic energy at impact. (1980)
（中文版本）
卷一：純數
1.
六三角函數及其圖像，任意角之函數，正弦定律及餘弦定律，，，之公式（此等公式不須證明）及其倍角及半角之應用，平面及空間之應用題，簡易三角方程之通解。
2.
基本原理微分法，多項式及三角函數之微分（反三角函數之微分除外）。之微分，二重導數。微分之應用：微增量，切綫方程，變速，極大與極小等問題及簡易曲綫之繪畫。
3.
不定積分作為微分之倒算法。
4.
平面之直角坐標系，兩點距離，分綫段為定比之點，直綫方程，直綫斜率，二直線之交角，點與直綫之距離，二直綫之交點，直線系，三角形之面積（直到1978）/直線形之面積（1979-1980）。
5.
單變元之一次及二次不等式及二不等式及其代數解法與實線上之圖解法。
6.
二次方程，判別式，複根。複數之算術運算，阿根圖，共軛，模數。（直到1978）
二次方程，判別式，複根。複數之算術運算，阿根圖，共軛，模數及輻角（只限於主值）。（自1979）
7.
餘式定理。不超過三次之多項式之因子分解。
卷二：純數
1.
數學歸納法及其簡易應用。（1979加入）
2.
對數之性質（包括換底）。（1980加入）
3.
正整指數之二項式定理及其在計算簡易近似值及增長率等應用。（求最大項，系數和，及系數性質等問題不包括在內。）
4.
複數：極式及弟美弗定理。
5.
積及商之微分，複函數及隱函數之微分。
6.
簡易函數之積分（除外）。簡易代入法積分。定積分作為和之極限，定積分之性質。計算面積及體積之應用。（註：分部積分不包括在內）
7.
圓之方程，圓心坐標，半徑長、直線與圓之交點。拋物線橢圓及雙曲線標準式之認識。簡易軌跡問題。（直到1978）
圓之方程，圓心坐標，半徑長、直線與圓之交點。圓族。拋物線橢圓及雙曲線標準式。軌跡問題。（自1979）
卷三：力學
1.
純量與向量，向量之合成與分解，向量問題之解法：圖解法及計算法。
2.
同平面力施於一質點是之平衡力與合力。平行四邊形及三角形定律。藍利定理（Lami's Theorem），簡易多邊形定律問題。
3.
力短，平行力，力偶，重心。剛體在數同平面力下之平衡。
4.
摩擦系數及摩擦角；斜面。
5.
速度、加速度、合速度及相對速度，直綫等加速運動方程，包括其圖解法。簡易拋物體問題。（直到1978）
位移，速度及加速度。合速度及相對速度。直綫等加速度運動，包括圖解法。簡易拋物體問題。（自1979）
6.
環繞定軸之旋轉：角位移，角速度。（1980加入）
7.
牛頓運動定律。質量與重量、功、能及功率。能量不滅定律，連系質點運動。
8.
簡單機械，包括滑輪組，輪軸，差動滑輪，機械利益，速度比，機械効率。（1979取消）
9.
衝量，綫動量不滅定律，非彈性物體之撞擊。（直到1979）
衝量，綫動量不滅定律，非彈性物體之撞擊：完全彈性物體，彈性物體，非彈性物體。由撞擊引致之動能損耗。（1980）
Version 5: 1981 (cancel paper 3), 1982,
1983, 1984, 1985, 1986, 1987, 1988
1.
The six trigonometric ratios
and their graphs. Trigonometric ratios of angle of any magnitude. Sine and
cosine formulas. (1984
cancelled two formulas) Formulas for , , (formal proofs of these formulas will not be
required), their application to multiple and submultiple angles. Problems in
two or three dimensions. General solutions of simple trigonometric equations.
2.
Linear inequalities in one or
two variables and their graphical representation; applications to simple
practical problems such as Linear Programming. Quadratic inequalities in one
variable. Use of the absolute signs, e.g. 
. (1984 cancelled)
3.
Quadratic equations:
discriminant, complex roots, relations of the roots with the coefficients.
Algebraic manipulation of complex numbers, Argand diagram, conjugate, modulus
and argument (limited to principal values ). Polar
form and De Moivre’s Theorem. (until 1983)
Quadratic equations: discriminant, complex roots. Solution of linear
and quadratic inequalities in one variable. Use of absolute sign. Algebraic
manipulation of complex numbers, Argand diagram, conjugate, modulus and argument
(limited to principal values ). Polar
form and De Moivre’s Theorem. (since 1984)
4.
Remainder Theorem.
Factorization of polynomials up to and including the third degree. (1984 cancelled)
5.
Mathematical induction and its
simple applications.
6.
Theory of indices. Properties
of logarithm (including change of base). (1984 cancelled)
7.
The binomial theorem for
positive integral indices and its applications such as simple approximation and
rate of growth (questions on greatest terms and on sums and properties of
coefficients will be asked). (until
1983)
The binomial theorem for positive integral indices and its simple
applications (questions on greatest terms and on properties of coefficients
will not be asked). (since
1984)
8.
Rectangular coordinates in two
dimensional space; distance between two points; points dividing the segments in
a given ratio. Equations of a straight line; slope (gradient) of a straight
line; angle between two lines, conditions for two lines to be parallel or
perpendicular; distance from a point to a straight line; intersection; family
of straight lines. Area of rectilinear figures. (until 1983)
9.
Equation of a circle,
coordinates of centre, length of radius, intersection of straight lines and
circles. Equation of a tangent to a circle. Family of circles. (until 1983)
10.
Standard equations of parabola,
ellipse and hyperbola. Simple locus problems. (until 1983)
11.
Rectangular coordinates in
two-dimensional space. Angle between two lines, distance from a point to a
straight line, family of straight lines. Area of rectilinear figures. Equation
of a tangent to a circle, family of circles. Standard equations of parabola,
ellipse and hyperbola. Simple locus problems. (since 1984)
12.
Vectors in 2-dimensional space.
Unit vectors and zero vector. Representation of a vector by ai+bj and by a
directed line segment. Sum and difference of vectors. Multiplication of a
vector by a scalar. Scalar product (dot product) of two vectors. Simple vector
operations in proving properties of parallelism, perpendicularity and the
ration of line segments. (added
1984)
13.
Differentiation from first
principles. Differentiation of polynomials and trigonometric functions
(excluding the inverses of trigonometric functions). Differentiation of ;
differentiation of a product, a quotient; differentiation of a composite and an
implicit function. Second derivatives. Applications to small increments, rates
of change, equation of tangent to a curve, speed problems, maxima and minima,
sketching of simple curves. (until
1983)
Differentiation from first principles. Differentiation of powers of
x and trigonometric functions (excluding the inverses of trigonometric
functions). Differentiation of a sum, of a product, and of a quotient of
functions; differentiation of a composite function and an implicit function.
Second derivatives. Applications to small increments, rates of change,
equations of tangent and normal to a curve, maxima and minima, sketching of
simple curves (excluding points of inflexion). (since 1984)
14.
Indefinite integration as the
reverse process of differentiation. Integration of simple functions (excluding ).
Integration by simple changes of variable. Definite integral as limit of a sum.
Properties of definite integrals (proofs of these properties will not be
required). Applications to areas and volumes. (NOTE: integration by parts is
excluded.) (until 1983)
Indefinite integration as the reverse process of differentiation.
Integration of simple functions (excluding ).
Integration by simple changes of variable (excluding integration by parts).
Definite integral as the limit of a sum. Properties of definite integrals
(proof of these properties will not be required). Applications of areas and
volumes. (since 1984)
（中文版本）
1.
六個三角函數及其圖形。任意角之函數。正弦及餘弦定律。（1984取消這兩條公式）、及之公式（此等公式不需證明）及其於倍角與半角之應用。平面及三維空間之應用題。簡易三角方程之通解。
2.
單變元及雙變元之綫性不等式及其圖形；及其在簡易實際問題之應用，如線性規劃。單變元之二次不等式。絕對值符號之應用，如。（1984取消）
3.
二次方程：判別式，複根，根與系數之關係。複數之代數運算，阿根圖，共軛複數，模數及輻角（只限於之主值範圍內）。極式及棣美弗定理（De Moivre's Theorem）。（直到1983）
二次方程：判別式，複根。單變元之二次不等式。絕對值符號之應用。複數之代數運算，阿根圖，共軛複數，模數及輻角（只限於之主值範圍內）。極式及棣美弗定理（De Moivre's Theorem）。（自1984）
4.
餘式定理。不超過三次多項式之因式分解。（1984取消）
5.
數學歸納法及其簡易應用。
6.
指數定律。對數之性質（包括換底）。（1984取消）
7.
正整指數之二項式定理及其在計算簡易近似值及增長率等應用（最大項、系數和系數性質等問題不包括在內）。（直到1983）
正整指數之二項式定理及其簡易應用（最大項及係數性質等問題不包括在內）。（自1984）
8.
平面之直角坐標系，兩點距離，分綫段為定比之點。直綫方程，直綫斜率，二直線之交角，兩綫平行或垂直之條件，點與綫之距離，二直綫之交點，直線族。直線圖形之面積。（直到1983）
9.
圓之方程，圓心之坐標，半徑長，圓與直線及圓及圓之交點。圓之切綫方程，圓族。（直到1983）
10.
拋物線、橢圓及雙曲線之標準式。簡易軌跡問題。（直到1983）
11.
平面之直角坐標系。二直線之夾角，點與線之距離，直線族。直線圖形之面積。圓之切綫方程，圓族。拋物線、橢圓及雙曲線之標準式。簡易軌跡問題。（自1984）
12.
二維空間之向量。單位向量及零向量。以ai+bj及有向線段表示向量。向量之和及差。純量與向量相乘。兩向量之内積。應用向量方法以證平行、垂直及求線段之比。（1984加入）
13.
基本原理微分法。多項式及三角函數之微分（反三角函數之微分除外）。
之微分；積及商之微分，複合函數及隱函數之微分。二階導數。微分之應用：微增量，變率，切綫方程，速率問題，極大與極小問題及簡易曲綫圖之描繪。（直到1983）
基本原理微分法。x之乘冪及三角函數之微分（反三角函數之微分除外）。函數之和、積及商之微分，複合函數及隱函數之微分。二階導數。微分之應用：微增量、變率、切綫與法線方程、速率問題、極大與極小問題及簡易曲線圖之描繪（拐點除外）。（自1984）
14.
不定積分作為微分之倒算法。簡易函數之積分（除外）。簡易代入法積分。定積分作為和之極限。定積分之性質。定積分在計算面積及體積之應用。（註：分部積分將不包括在內。）（直到1983）
不定積分作為微分之倒算法。簡易函數之積分（除外）。簡易代入法積分（分部積分不包括在內）。定積分作為和之極限。定積分之性質（此等性質不須證明）。定積分在計算面積及體積之應用。（自1984）
1989 (give detail information),
1990-1994, 1995 (use official syllabus), 1996-2003, 2004 (change syllabus),
2005-2011
Until 2000, set paper 1 and paper 2. Since 2001, just set one paper.
1.
The six trigonometric functions
of angles of any magnitude and their graphs. Formula of 
, 
and
, sum and product formulas. General
solution of simple trigonometric equations. Problems in two and three
dimensions.
2.
Quadratics functions and
quadratic equations. Discriminant and complex roots. Inequalities in one
variable. Use of the absolute value sign.
3.
Complex numbers in standard
form and polar form, and their manipulation. Argand diagram, conjugate, modulus
and argument. De Moivre’s theorem and its applications. (2004 cancel)
4.
Mathematical induction and its
simple applications.
5.
The binomial theorem for
positive integral indices and its application to numerical approximation. (until 1991)
The binomial theorem for positive integral indices. (since 1992)
6.
Plane rectangular coordinates.
Area of rectilinear figures. Angle between two lines, distance from a point to
a line, family of straight lines. Equations of tangents to a circle. Family of
circles. Parabola, ellipse and hyperbola. (2004 cancel Conic Sections) Simple locus
problems.
7.
Vectors in the two-dimensional
space. Unit vectors and the zero vector. Position vectors. Representation of a
vector by 
and
by a directed line segment. Sum and difference of vectors. Multiplication of a
vector by a scalar. Scalar product (dot product) of two vectors. Application of
vector method to problems involving parallelism, perpendicularity and division
of a line segment.
8.
Differentiation from first
principles. Differentiation of powers of x and trigonometric functions.
Differentiation of a sum, a product and a quotient of functions.
Differentiation of a composite function and an implicit function. Second
derivatives. Application of differentiation to small increments, gradients,
rates of change, tangents and normal to a curve, maxima and minima, and
sketching of simple curves.
9.
Indefinite integration as the
reverse process of differentiation. Integration of simple functions.
Integration by simple change of variable. Definite integrals and their simple
properties. Applications in find plane areas and volumes of solids of revolution.
(until 2003)
Indefinite integration as the reverse process of differentiation.
The integrals of 
(excluding 
), 
and 
. Definite
integrals and their simple properties. Applications in finding plane areas and
finding volume of solids of revolution formed by revolving about the coordinate
axes. (since 2004)
（中文版本）
2000年以前，設試卷一及試二，2001年起只設一卷。
1.
任意角之六個三角函數及其圖形。、、公式，和積互變公式。簡易交各方程之通解。二維及三維空間問題。
2.
二次函數及二次方程。判別式及複根。單變元不等式。絕對值符號之使用。
3.
複數之標準式及極式及其運算。阿根圖，共軛複數，模數及幅角。棣美弗定理及其應用。（2004取消）
4.
數學歸納法及其應用。
5.
正整指數之二項式定理及其應用於近似數值之計算。（直到1991）
正整指數之二項式定理。（自1992）
6.
平面直角坐標。直線圖形之面積。兩直線之交角，點與線之距離，直線族。圓之切線方程。圓族。拋物線，橢圓及雙曲線。（2004取消圓錐曲線）簡易軌跡問題。
7.
二維空間之向量。單位向量及零向量。位置向量。以及有向線段表示向量。向量之和及差。純量與向量相乘。兩向量之純量積（點積）。應用向量方法以解平行，垂直及線段之分割等問題。
8.
從基本原理求微分。x之乘冪及三角函數之微分。函數之和、積、商之微分。複合函數及隱函數之微分。二階導數。微分之應用：微增量、斜率、變率、曲線之切線及法線、極大及極小、簡易曲線之描繪。
9.
不定積分作為微分之倒算法。簡易函數之積分。簡易代換積分法。定積分及其簡易性質。以定積分計算平面面積及旋轉體之體積。（直到2003）
不定積分作為微分之倒算法。
、及之積分。定積分及其簡易性質。以定積分計算平面面積及繞坐標軸所得旋轉體之體積。（自2004）
附件2：會考現代數學課程
Edition 1: 1969, 1970, 1971
1.
Knowledge of Primary School
Mathematics is assumed.
2.
Rough estimates,
approximations, significant figures and limits of accuracy.
3.
Primes and factorization of natural numbers. Principles
of simple divisibility test for 2, 3, 4, 5, 8, 9, 11. LCM and HCF including the
general principles of finding the HCF (Euclidean algorithm).
4.
Simple statements, the negation of a statement (
), compound statements using
connectives “and” (
), “or” (
), “if… then” (
), “if and only if” (
). Truth values and truth
tables. The use of the above in presenting arguments. (The emphasis will be on
the understanding and presentation of logical arguments rather than on formal
manipulations.)
5.
Principle of mathematical induction.
6.
Sets, member (or element) of a set, subset, union,
intersection, difference, complement, universal set and empty set. Venn
diagrams and their use in illustrating set operations and in solving problems.
(Approved symbols: 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
). The use of composition laws
for sets including 
, 
, 
and 
(formal proofs will not be
required). Order pairs, simple ideas of mappings (or functions).
7.
Representation of integers by means of different bases,
including base 2, (The number a to base b will be expressed as 
with b always in denary). Simple
flow charts.
8.
Informal discussion of integers, rational numbers, the
real number system and the complex number system. (The concept of ordered pairs
applied to the above where appropriate).
9.
Binary operations. Informal discussion of associativity,
commutativity, distributivity, neutral element and inverse. Modulo arithmetic
treated intuitively. The elementary idea of a group and its sub-groups as
illustrated by examples such as modulo arithmetic, integers and addition,
non-zero rational numbers and multiplication, rotation and reflection of
triangles, quadrilaterals and regular n-sided polygons, matrices and matrix
multiplication.
10.
matrices with 
, and operations on them: addition, multiplication and
scalar-multiplication. System of m linear equations in n unknowns with 
. Square matrices and
determinants of order 
. Unit matrices, non-singular matrices and simple numerical cases of
their inverses. Vectors and simple applications in geometry.
11.
Knowledge of the following will
be assumed by no formal proofs of any kind will be required: Parallel lines and
their sets. Angle sums of triangles and polygons, base angles of an isosceles
triangle, equiangular triangles have their corresponding sides proportional,
Pythagoras’ relation, angle in the alternative segment, angles in the same
segment, angles in a cyclic quadrilateral. Lengths, areas and volumes;
mensuration of common plane and solid figures, including polygons, polyhedral,
circle, cylinder, cone and sphere. Plans and maps, areas and volumes of similar
figures.
12.
Simple transformations of the
plane: reflection, rotations and translation, combination of the above
transformations; identity and inverse transformation. The transformations
connecting directly or oppositely congruent figures. The ideas of shearing and
stretching. Transformations in terms of co-ordinates: reflection in the lines 
, 
and 
; rotation
through multiple of 
. Expression, by 
matrices, of reflection,
rotation, enlargement and shearing.
13.
Symmetry about a point, a line
and a plane.
14.
Informal discussion of simple networks; odd nodes, even
nodes, universal (one-stroke) network, matrix description of a network.
15.
Three-dimensional figures:
angle between a straight line and a line and a plane and between two planes,
nets of solids, Euler’s relation for convex polyhedral. Plans and elevations
(ability to produce technically correct figures will not be required).
16.
Polynomials in one variable and
their fundamental operations (questions will not be set on lengthy
multiplication and division). Simple algebraic fractions. Factorization of 
, 
, 
. Easy identities, easy equations
including the general quadratic equation.
17.
Functional relations and graphs. Simple curves including
the curve 
. Gradients of curves by drawing, estimation of area under curves by
square counting or trapezium rule. The idea of rate of change.
18.
Law of indices. Slide rule.
19.
Rectangular Cartesian co-ordinates in 2 and
3-dimentisonal spaces. Equations of lines in 2-dimentsional spaces and planes
in 3-dimensional space. Simple loci in 2 and 3-dimentisonal spaces.
20.
Measurement of angles (degree
and radians). The function since, cosine, tangent and their graphs. The
relation 
, 
. Solution of triangles in cases
reducible to right-angled triangles, Simple 3-dimentsional problems. Courses
and bearings. Latitude, longitude, great and small circles, nautical miles,
distances along parallels of latitudes and along meridians.
21.
Simple probability theory
including applications of the sum and product laws.
22.
Collection and organization of
numerical data, and their graphical representation by bar chart, pie chart,
frequency polygon and cumulative frequency polygon, histogram. Calculation of
the mean. Estimation of the median and quartiles, inter-quartile range.
（中文參考譯文）
1.
假定具備小學數學知識。
2.
粗略估計、近似值、有效數字和準確度限制。
3.
自然數的質數和因式分解。 2、3、4、5、8、9、11的簡單整除性測試原理。最小公倍數及最大公因數包括查找最大公因數（歐幾里得演算法）的一般原理。
4.
簡單命題、命題的否定 ()、使用連接詞「和」()、「或」()、「如果…則」()、「當且僅當」() 的複合語句。 真值和真值表。 在提出論點時使用上述內容。 （重點將放在邏輯論證的理解和表達上，而不是形式操作上。）
5.
數學歸納法原理。
6.
集合、集合的成員（或元素）、子集、併集、交集、差集、補集、全集和空集。 温氏圖及其在說明集合運算和解決問題中的用途。 （認可的符號：
）。 使用組合定律，包括
、、' 和 」（不需要正式證明）。有序對，映射（或函數）的簡單想法。
7.
透過不同底（包括底 2）表示整數（a 到 b 基數將表示為 ，其中 b 始終為十進制數）。 簡單的流程圖。
8.
整數、有理數、實數系統和複數系統的非正式討論。 （有序對的概念在適當的情況下適用於上述內容）。
9.
二元運算。 結合性、交換性、分配性、單位元素和反元素的非正式討論。 直觀地處理模運算。 透過模算術、整數和加法、非零有理數和乘法、三角形、四邊形和正n邊多邊形的旋轉和反射、矩陣和矩陣乘法等範例說明群及其子群的基本思想。
10.
的 矩陣及其運算：加法、乘法和純量乘法。 n 個未知數中的 m 個線性方程組，其中 。方陣和階次 的行列式。單位矩陣、非奇異矩陣及其逆矩陣的簡單數值情況。 向量和幾何中的簡單應用。
11.
假設您了解以下內容，不需要任何形式的正式證明：平行線及其集合。
三角形和多邊形的角和、等腰三角形的底角、等角三角形的對應邊成比例、畢氏關係、交錯線段內的角、同線段內的角、圓內接四邊形內的角。
長度、面積和體積； 常見平面和立體圖形的測量，包括多邊形、多面體、圓形、圓柱體、圓錐體和球體。 類似圖形的平面圖和地圖、面積和體積。
12.
平面的簡單變換：反射、旋轉與平移、上述變換的組合；
恆等式和逆變換。 連接直接或相反全等圖形的變換。 剪切和拉伸的想法。
座標變換：、 和
線上的反射； 旋轉 90° 的倍數。 透過矩陣表達反射、旋轉、放大和剪切。
13.
關於點、線、面的對稱性。
14.
簡單網路的非正式討論； 奇數節點、偶數節點、通用（一筆）網路、網路的矩陣描述。
15.
三維圖形：直線與直線與平面之間以及兩個平面之間的交角、立體摺紙圖樣、凸多面體的歐拉關係。
平面圖和立面圖（不需要能夠產生技術上正確的圖形）。
16.
單變量多項式及其基本運算（不會針對冗長的乘法和除法提出問題）。
簡單的代數分數。 、、 因式分解。
簡單的恆等式，簡單的方程，包括一般的二次方程。
17.
函數關係和圖表。 簡單曲線，包括曲線 。 透過繪製曲線的梯度，透過平方計數或梯形規則來估計曲線下的面積。變率的概念。
18.
指數定律。計算尺。
19.
二維和三維空間中的矩形直角座標。 二維空間中的線方程式和三維空間中的平面方程式。二維和三維空間中的簡單軌跡。
20.
角度測量（度和弧度）。
正弦、餘弦、正切函數及其圖像。 關係式 ，。 在可簡化為直角三角形的情況下三角形的解，簡單的三維問題。
路線和方位。 緯度、經度、大圓和小圓、海裡、沿緯線和經線的距離。
21.
簡單機率論，包括加法和乘法定律的應用。
22.
數據資料的收集和組織，以及用棒形圖、圓形圖、頻數多邊形和累積頻數多邊形、組織圖的圖形表示。
平均數的計算。 估計中位數和四分位數、四分位數間距。
Edition 2: 1972
1.
Knowledge of Primary School
Mathematics is assumed.
2.
Rough estimates, approximation,
significant figures and limits of accuracy.
3.
Primes and factorization of natural numbers. Principles of
simple divisibility tests for 2, 3, 4, 5, 8, 9, 11 LCM and HCF including the
general principles of finding the HCF. (Euclidean algorithm).
4.
Natural numbers, integers, rational numbers, real numbers
and complex numbers; the concept of ordered pairs will be applied where
appropriate.
5.
Representation of integers by means of different bases (the
number a to base b will be expressed as 
with b always in denary).
6.
Polynomials in one variable and
their fundamental operations (questions will not be set on lengthy
multiplication and division. Simple algebraic fractions.)
7.
Factorization of 
, , ; 
where h, k, m and n are integers.
8.
Solution of quadratic equations
involving only one unknown including knowledge of the relations between the sum
and products of the roots and the coefficient of a quadratic equation; the
solution of simultaneous one equations, one linear and one quadratic, involving
two unknowns, simple problems leading to such equations. Variation, ratio and
proportion. Formulae; Construction, change of subject, numerical applications.
Distinction between conditional equations and identities.
9.
Inequalities, linear and
quadratic; their solution, and the representation of the solution on the real
number line. Applications, especially to linear relationships and graphs.
Linear programming in two variables by graphs.
10.
Graphs of simple algebraic
functions of not more than the third degrees.
11.
Law of non-negative integral
indices with extension to fractional and negative indices and logarithms
including use of the root sign. (
to represent the positive square root of “a”
where “a” is any positive number). Calculation by logarithms to base 10 with
the use of four-figure tables.
12.
Measure of angles in degree up
to 
and radians up to 
. Length of
arc and area of sector of a circle. The functions of sine, cosine, tangent and
their graphs. The relations , . Solution
of right-angled triangles, with simple applications. Easy problem in two and
three dimensions soluble by analysis into right-angled triangles.
13.
Knowledge and applications of
the following will be assumed without formal proof: Parallel lines and their
tests. Angle sums of triangles, base angles of an isosceles triangle, similar
triangles, congruent triangles, Pythagoras’ theorem. Angle and tangent
properties of circles, including the alternate segment property. Lengths, areas
and volumes; mensuration of common plane and solid figures, including polygons,
circle, polyhedral, cylinder, cone and sphere. Plans and maps, areas and
volumes of similar figures.
14.
Rectangular co-ordinates in 2-dimensional space: equation
of a straight line; gradient of a straight line; distance between two points;
intersection; easy locus problems; recognition of standard equations of circle,
parabola, ellipse and hyperbola.
15.
Simple statements, the negations of a statement, compound
statements using connectives “and”, “or”, “if…then” and “if and only if”. Truth
values and simple truth tables involving not more than two variables. The use
of the above in presenting arguments. (The emphasis will be on the
understanding and presentation of logical arguments rather than on formal
manipulations).
16.
Set, number (or element) of a set, subset, union,
intersection, complement, universal set and empty set. Venn diagrams and their
use in illustrating set operations and in solving problems. The use of
composition laws for sets (formal proofs will not be required). Ordered pairs,
relations, simple ideas of mapping (or functions) including injective,
surjective and bijective mapping. Graphs of relations and of mapping. (The
emphasis will be on the understanding and presentation rather than on formal
manipulations).
17.
Mathematical induction and simple applications including
simple sequences and series. Compound interest.
18.
Reading and understanding of simple flow charts.
19.
Idea of matric. Operations on 
matrices with 
, 
: addition, multiplication,
scalar-multiplication and transposition. Null matrix. Solution of m linear
equations in n unknowns with , . Square matrices and determinants
of order 
. Unit matrices, non-singular
matrices and simple numerical cases of their inverses. Vector in 2-dimensional
space. Representation of a vector by a 
matric and by a directed line segment. Unit
vector and null vector. Position vector of a point. Sum and difference of two
vectors. Multiplication of a vector of a point. Sum and difference of two
vectors. Multiplication of a vector by a scalar. Scalar product of two vectors.
Simple applications of vector operations in proving properties of parallelism,
perpendicularity and ratio of line segments.
20.
Collection and organization of
numerical data, and their graphical representation by bar chart, frequency
polygon and cumulative frequency polygon, histogram. Calculation of the mean.
Estimation of the median and quartiles, inter-quartile range. Simple ideas of
probability theory with applications of the sum and product laws to easy
problems.
（中文參考譯文）
1.
假定具備小學數學知識。
2.
粗略估計、近似值、有效數字和準確度限制。
3.
自然數的質數和因式分解。 2、3、4、5、8、9、11的簡單整除性測試原理。最小公倍數及最大公因數包括查找最大公因數的一般原理。（歐幾里得演算法）
4.
自然數、整數、有理數、實數和複數； 在適當的情況下將應用有序對的概念。
5.
透過不同底（包括底 2）表示整數（a 到 b 基數將表示為 ，其中 b 始終為十進制數）。 簡單的流程圖。
6.
單變量多項式及其基本運算（不會提出冗長的乘法和除法問題。簡單的代數分式。）
7.
,、、因式分解；其中 h、k、m 和 n 為整數。
8.
僅涉及一個未知數的二次方程式的解，包括了解二次方程式的根和乘積與係數之間的關係；
聯立一個方程式（一個線性方程式和一個二次方程式）的解，涉及兩個未知數，導致此類方程式的簡單問題。
變分、比和比例。 公式； 建立、主項變換、數值應用。
條件方程式和恆等式之間的區別。
9.
線性和二次不等式；
它們的解，以及解在實數線上的表示。應用程序，特別是線性關係和圖形。 透過圖像對兩個變數進行線性規劃。
11.
非負整數指數定律，擴展到分數和負指數以及對數，包括根符號的使用。
（ 表示「a」的正平方根，其中「a」是任意正數）。
使用四位數表，以 10 為底的對數進行計算。
12.
測量最大 360° 的角度和最大 2π 的弧度。 弧長和扇形面積。
正弦、餘弦、正切函數及其圖像。
關係式 ，。 直角三角形的解法，簡單應用。
透過分析直角三角形可以解決二維和三維的簡單問題。
13.
在沒有正式證明的情況下，將假設具備以下知識和應用：平行線及其測試。
三角形的角和、等腰三角形的底角、相似三角形、全等三角形、畢氏定理。
圓的角度和切線特性，包括交錯弓形特性。
長度、面積和體積；
常見平面和立體圖形的測量，包括多邊形、圓形、多面體、圓柱體、圓錐體和球體。
類似圖形的平面圖和地圖、面積和體積。
14.
二維空間中的直角座標：直線方程式； 直線的斜率； 兩點之間的距離； 相交；簡易軌跡問題； 辨識圓、拋物線、橢圓和雙曲線的標準方程式。
15.
簡單命題、命題的否定、使用連接詞「and」、「or」、「if…then」和「if and only if」的複合命題。 涉及不超過兩個變數的真值和簡單真值表。 在提出論點時使用上述內容。 （重點將放在邏輯論證的理解和表達上，而不是形式操作上）。
16.
集合、集合的個數（或元素）、子集、併集、交集、補集、全集和空集。 温氏圖及其在說明集合運算和解決問題中的用途。 使用集合的組合法則（不需要正式證明）。 有序對、關係、映射（或函數）的簡單概念，包括單射、滿射和雙射映射。 關係圖和映射圖。 （重點將放在理解和表達上，而不是正式的操作上）。
17.
數學歸納法和簡單應用，包括簡單的數列和級數。 複利息。
18.
閱讀和理解簡單流程圖。
19.
矩陣的想法。 、 的 矩陣上的運算：加法、乘法、純量乘法和轉置。 零矩陣。 n 個未知數中的 m 個線性方程式的解，其中
、。 方陣與階次
的行列式。 單位矩陣、非奇異矩陣及其逆矩陣的簡單數值情況。 二維空間中的向量。 以 
矩陣和有向線段表示向量。單位向量和零向量。點的位置向量。兩個向量的和與差。 點向量的乘法。 兩個向量的和與差。向量乘以純量。兩個向量的純量積。向量運算在證明線段平行性、垂直性和線段比例的簡單應用。
20.
數據資料的收集和組織，及其透過棒形圖、頻數多邊形和累積頻數多邊形、組織圖的圖形表示。平均數的計算。估計中位數和四分位數、四分位數間距。
概率論的簡單想法以及將加法及乘法法則應用於簡單問題的應用。
Edition 3: 1973
1.
Knowledge of Primary School
Mathematics is assumed.
2.
Rough estimates, approximation,
significant figures and limits of accuracy.
3.
Natural numbers, integers, rational numbers, real numbers
and complex numbers; the concept of ordered pairs will be applied where
appropriate.
4.
Representation of integers by means of different bases (the
number a to base b will be expressed as 
with b always in denary).
5.
Polynomials in one variable and
their fundamental operations (questions will not be set on lengthy
multiplication and division.) Factorisation of , , ; where h, k, m and n are integers. LCM and HCF.
Simple algebraic fractions.
6.
Solution of quadratic equations
involving only one unknown including knowledge of the relations between the sum
and products of the roots and the coefficient of a quadratic equation; the
solution of simultaneous one equations, one linear and one quadratic, involving
two unknowns, simple problems leading to such equations. Variation, ratio and
proportion. Formulae; Construction, change of subject, numerical applications.
Distinction between conditional equations and identities.
7.
Inequalities, linear and
quadratic; their solution, and the representation of the solution on the real
number line. Applications, especially to linear relationships and graphs.
Linear programming in two variables by graphs.
8.
Graphs of simple algebraic
functions of not more than the third degrees.
9.
Law of non-negative integral
indices with extension to fractional and negative indices and logarithms
including use of the root sign. ( to represent the positive square root of “a”
where “a” is any positive number). Calculation by logarithms to base 10 with
the use of four-figure tables.
10.
Measure of angles in degree
range of 
and in radians in the range 
. Length of
arc and area of sector of a circle. The functions of sine, cosine, tangent and
their graphs. The relations , . Solution
of right-angled triangles, with simple applications. Easy problem in two and
three dimensions soluble by analysis into right-angled triangles. Easy
trigonometrical equations.
11.
Knowledge and applications of
the following will be assumed without formal proof: Parallel lines and their
tests. Angle sums of triangles, base angles of an isosceles triangle, similar
triangles, congruent triangles, Pythagoras’ theorem. Angle and tangent
properties of circles, including the alternate segment property. Lengths, areas
and volumes; mensuration of common plane and solid figures, including polygons,
circle, polyhedral, cylinder, cone and sphere. Plans and maps, areas and
volumes of similar figures.
12.
Rectangular co-ordinates in 2-dimensional space: equation
of a straight line; gradient of a straight line; distance between two points;
intersection; easy locus problems; recognition of standard equations of circle,
parabola, ellipse and hyperbola.
13.
Simple statements, the negations of a statement, compound
statements using connectives “and”, “or”, “if…then” and “if and only if”. Truth
values and simple truth tables involving not more than two variables.
14.
Set, number (or element) of a set, subset, union,
intersection, complement, universal set and empty set. Venn diagrams.
Composition laws for sets. Ordered pairs, relations, simple ideas of mapping
(or functions) including injective (one-to-one), surjective (onto) and
bijective (one-one onto) mappings. Graphs of relations and of mapping.
15.
Mathematical induction and simple applications including
simple sequences and series. Compound interest.
16.
Reading and understanding of simple flow charts.
17.
Idea of matrix. Operations on 
matrices with 
, 
: addition, multiplication,
scalar-multiplication and transposition. Null matrix. Solution of m linear
equations in n unknowns with , . Square matrices and determinants
of order 
. Unit matrices, non-singular
matrices and simple numerical cases of their inverses. Vector in 2-dimensional
space. Representation of a vector by a 
matrix and by a directed line segment. Unit
vector and null vector. Position vector of a point. Sum and difference of two
vectors. Multiplication of a vector by a scalar. Scalar product of two vectors.
Simple applications of vector operations in proving properties of parallelism,
perpendicularity and ratio of line segments.
18.
Collection and organisation of
numerical data, and their graphical representation by bar chart, frequency
polygon and cumulative frequency polygon, histogram. Calculation of the mean.
Estimation of the median and quartiles, inter-quartile range. Simple ideas of
probability theory with applications of the sum and product laws to easy
problems.
（中文參考譯文）
1.
假定具備小學數學知識。
2.
粗略估計、近似值、有效數字和準確度限制。
3.
自然數、整數、有理數、實數和複數； 在適當的情況下將應用有序對的概念。
4.
透過不同底表示整數（a 到 b 基數將表示為 ，其中 b 始終為十進制數）。
5.
單變量多項式及其基本運算（不會提出冗長的乘法和除法問題。簡單的代數分式。）,、、因式分解；其中 h、k、m 和 n 為整數。最小公倍數和最大公因數。簡單的代數分式。
6.
僅涉及一個未知數的二次方程式的解，包括了解二次方程式的根和乘積與係數之間的關係；
聯立一個方程式（一個線性方程式和一個二次方程式）的解，涉及兩個未知數，導致此類方程式的簡單問題。
變分、比和比例。 公式； 建立、主項變換、數值應用。
條件方程式和恆等式之間的區別。
7.
線性和二次不等式；
它們的解，以及解在實數線上的表示。應用程序，特別是線性關係和圖形。 透過圖像對兩個變數進行線性規劃。
8.
三次以下的簡單代數函數的圖像。
9.
非負整數指數定律，擴展到分數和負指數以及對數，包括根符號的使用。
（ 表示「a」的正平方根，其中「a」是任意正數）。
使用四位數表，以 10 為底的對數進行計算。
10.
角度測量範圍為
，弧度測量範圍為 。弧長和扇形面積。 正弦、餘弦、正切函數及其圖像。
關係式 ，。 直角三角形的解法，簡單應用。
透過分析直角三角形可以解決二維和三維的簡單問題。簡單三角方程。
11.
在沒有正式證明的情況下，將假設具備以下知識和應用：平行線及其測試。
三角形的角和、等腰三角形的底角、相似三角形、全等三角形、畢氏定理。 圓的角度和切線特性，包括交錯弓形特性。 長度、面積和體積； 常見平面和立體圖形的測量，包括多邊形、圓形、多面體、圓柱體、圓錐體和球體。 類似圖形的平面圖和地圖、面積和體積。
12.
二維空間中的直角座標：直線方程式； 直線的斜率； 兩點之間的距離； 相交；簡易軌跡問題； 辨識圓、拋物線、橢圓和雙曲線的標準方程式。
13.
簡單命題、命題的否定、使用連接詞「and」、「or」、「if…then」和「if and only if」的複合命題。 涉及不超過兩個變數的真值和簡單真值表。
14.
集合、集合的個數（或元素）、子集、併集、交集、補集、全集和空集。 温氏圖及其在說明集合運算和解決問題中的用途。 使用集合的組合法則（不需要正式證明）。 有序對、關係、映射（或函數）的簡單概念，包括單射（一對一）、滿射（到）和雙射（一對一到）映射。 關係圖和映射圖。
15.
數學歸納法和簡單應用，包括簡單的數列和級數。 複利息。
16.
閱讀和理解簡單流程圖。
17.
矩陣的想法。 、 的 矩陣上的運算：加法、乘法、純量乘法和轉置。 零矩陣。 n 個未知數中的 m 個線性方程式的解，其中
、。 方陣與階次
的行列式。 單位矩陣、非奇異矩陣及其逆矩陣的簡單數值情況。 二維空間中的向量。 以 
矩陣和有向線段表示向量。單位向量和零向量。點的位置向量。兩個向量的和與差。 點向量的乘法。 兩個向量的和與差。向量乘以純量。兩個向量的純量積。向量運算在證明線段平行性、垂直性和線段比例的簡單應用。
18.
數據資料的收集和組織，及其透過棒形圖、頻數多邊形和累積頻數多邊形、組織圖的圖形表示。平均數的計算。估計中位數和四分位數、四分位數間距。
概率論的簡單想法以及將加法及乘法法則應用於簡單問題的應用。
Edition 4: 1974
1.
Knowledge of Primary School
Mathematics is assumed.
2.
Rough estimates, approximation,
significant figures and limits of accuracy.
3.
Natural numbers, integers, rational numbers, real
numbers and complex numbers.
4.
Polynomials in one variable and
their fundamental operations (questions will not be set on lengthy
multiplication and division.) Factorisation of , , ; where h, k, m and n are integers. LCM and HCF.
Simple algebraic fractions.
5.
Solution of quadratic equations
involving only one unknown including knowledge of the relations between the sum
and products of the roots and the coefficient of a quadratic equation; the
solution of simultaneous equations, one linear and one quadratic, involving two
unknowns, simple problems leading to such equations. Ratio, proportion,
proportional parts and variation. Formulae: construction, change of subject,
numerical applications. Distinction between conditional equations and
identities.
6.
Inequalities, linear and
quadratic; their solution, and the representation of the solution on the real
number line; applications, especially to linear relationships and graphs.
Linear programming in two variables by graphs.
7.
Graphs of simple algebraic
functions of not more than the third degrees.
8.
Law of non-negative integral
indices with extension to fractional and negative indices and logarithms
including use of the root sign. ( to represent the positive square root of “a”
where “a” is any positive number). Calculation by logarithms to base 10 with
the use of four-figure tables.
9.
Measure of angles in degree
range of and in radians in the range . Length of
arc and area of sector of a circle. The functions of sine, cosine, tangent and
their graphs. The relations , . Solution
of right-angled triangles, with simple applications. Easy problem in two and
three dimensions soluble by analysis into right-angled triangles. Easy
trigonometrical equations (solution in the range ).
10.
Knowledge and applications of
the following will be assumed without formal proof: Parallel lines and their
tests. Angle sums of triangles, base angles of an isosceles triangle, similar
triangles, congruent triangles, Pythagoras’ theorem. Angle and tangent
properties of circles, including the alternate segment property. Lengths, areas
and volumes; mensuration of common plane and solid figures, including polygons,
circle, polyhedral, cylinder, cone and sphere. Plans and maps, areas and
volumes of similar figures.
11.
Rectangular co-ordinates in 2-dimensional space:
equation of a straight line; gradient of a straight line; distance between two
points; intersection; easy locus problems; recognition of standard equations of
circle, parabola, ellipse and hyperbola.
12.
Simple statements, the negations of a statement,
compound statements using connectives “and”, “or”, “if…then” and “if and only
if”. Truth values and simple truth tables involving not more than two
variables.
13.
Set, number (or element) of a set, subset, union,
intersection, complement, universal set and empty set. Venn diagrams.
Composition laws for sets. Ordered pairs, relations, simple ideas of mapping
(or functions) including injective (one-to-one), surjective (onto) and
bijective (one-one onto) mappings. Graphs of relations and of mapping.
14.
Mathematical induction and simple applications including
simple sequences and series. Compound interest.
15.
Idea of matrix. Operations on 
matrices with 
, 
: addition, multiplication,
scalar-multiplication and transposition. Null matrix. Solution of m linear
equations in n unknowns with , . Square matrices and
determinants of order 
. Unit matrices, non-singular
matrices and simple numerical cases of their inverses. Vector in 2-dimensional
space. Representation of a vector by a 
matrix and by a directed line segment. Unit
vector and null vector. Position vector of a point. Sum and difference of two
vectors. Multiplication of a vector by a scalar. Scalar product of two vectors.
Simple applications of vector operations in proving properties of parallelism,
perpendicularity and ratio of line segments.
16.
Collection and organisation of
numerical data, and their graphical representation by bar chart, frequency
polygon and cumulative frequency polygon, histogram. Calculation of the mean.
Estimation of the median and quartiles, inter-quartile range.
17.
Simple ideas of probability
theory with applications of the sum and product laws to easy problems.
（中文參考譯文）
1.
假定具備小學數學知識。
2.
粗略估計、近似值、有效數字和準確度限制。
3.
自然數、整數、有理數、實數和複數。
4.
單變量多項式及其基本運算（不會提出冗長的乘法和除法問題。簡單的代數分式。）,、、因式分解；其中 h、k、m 和 n 為整數。最小公倍數和最大公因數。簡單的代數分式。
5.
僅涉及一個未知數的二次方程式的解，包括了解二次方程式的根和乘積與係數之間的關係；
聯立一個方程式（一個線性方程式和一個二次方程式）的解，涉及兩個未知數，導致此類方程式的簡單問題。
變分、比和比例。 公式； 建立、主項變換、數值應用。
條件方程式和恆等式之間的區別。
6.
線性和二次不等式；
它們的解，以及解在實數線上的表示。應用程序，特別是線性關係和圖形。 透過圖像對兩個變數進行線性規劃。
7.
三次以下的簡單代數函數的圖像。
8.
非負整數指數定律，擴展到分數和負指數以及對數，包括根符號的使用。
（ 表示「a」的正平方根，其中「a」是任意正數）。
使用四位數表，以 10 為底的對數進行計算。
9.
角度測量範圍為，弧度測量範圍為 。弧長和扇形面積。 正弦、餘弦、正切函數及其圖像。
關係式 ，。 直角三角形的解法，簡單應用。
透過分析直角三角形可以解決二維和三維的簡單問題。簡單三角方程（範圍內的解）。
10.
在沒有正式證明的情況下，將假設具備以下知識和應用：平行線及其測試。
三角形的角和、等腰三角形的底角、相似三角形、全等三角形、畢氏定理。 圓的角度和切線特性，包括交錯弓形特性。 長度、面積和體積； 常見平面和立體圖形的測量，包括多邊形、圓形、多面體、圓柱體、圓錐體和球體。 類似圖形的平面圖和地圖、面積和體積。
11.
二維空間中的直角座標：直線方程式； 直線的斜率； 兩點之間的距離； 相交；簡易軌跡問題； 辨識圓、拋物線、橢圓和雙曲線的標準方程式。
12.
簡單命題、命題的否定、使用連接詞「and」、「or」、「if…then」和「if and only if」的複合命題。 涉及不超過兩個變數的真值和簡單真值表。
13.
集合、集合的個數（或元素）、子集、併集、交集、補集、全集和空集。 温氏圖及其在說明集合運算和解決問題中的用途。 使用集合的組合法則（不需要正式證明）。 有序對、關係、映射（或函數）的簡單概念，包括單射（一對一）、滿射（到）和雙射（一對一到）映射。 關係圖和映射圖。
14.
數學歸納法和簡單應用，包括簡單的數列和級數。 複利息。
15.
矩陣的想法。 、 的 矩陣上的運算：加法、乘法、純量乘法和轉置。 零矩陣。 n 個未知數中的 m 個線性方程式的解，其中
、。 方陣與階次
的行列式。 單位矩陣、非奇異矩陣及其逆矩陣的簡單數值情況。 二維空間中的向量。 以 
矩陣和有向線段表示向量。單位向量和零向量。點的位置向量。兩個向量的和與差。 點向量的乘法。 兩個向量的和與差。向量乘以純量。兩個向量的純量積。向量運算在證明線段平行性、垂直性和線段比例的簡單應用。
16.
數據資料的收集和組織，及其透過棒形圖、頻數多邊形和累積頻數多邊形、組織圖的圖形表示。平均數的計算。估計中位數和四分位數、四分位數間距。
17.
概率論的簡單想法以及將加法及乘法法則應用於簡單問題的應用。
Edition 5: 1975 (change syllabus), 1976,
1977, 1978
1.
Statements: negation, conjunction, disjunction,
conditional, bi-conditional, implication and equivalence; applications to
testing validity of simple arguments in not more than 3 variables.
2.
Sets, numbers of a set, subset, union, intersection,
complement, universal set and empty set. Venn diagrams. Composition laws for
sets. Ordered pairs. Relations. Simple ideas of mapping (single-valued
function) including injective (one-one), surjective (onto) and bijective
(one-one onto) mappings. Graph of relations and mappings.
3.
Elementary operations in number systems, including
complex numbers.
4.
Polynomials in one variable and
their fundamental operations. Factorization of , , ; where h, k, m and n are integers. LCM and HCF.
Simple algebraic fractions.
5.
Formulae: their manipulation
and numerical applications.
6.
Solution of linear equations in
one unknown and simultaneous linear equations in two unknowns, and of quadratic
equations in one unknowns including knowledge of the relations between the
roots and the coefficients. Solution of simultaneous equations, one linear and
one quadratic, in two unknowns. Simple problems leading to such equations.
Distinction between equations and identities.
7.
Ratio, proportion and
variation.
8.
Graph of linear and quadratic
functions.
9.
Linear inequalities in one or
two variables and applications. Quadratic inequalities in one variable.
Graphical representation of linear inequalities with applications to simple
practical problems such as Linear Programming.
10.
Law of rational indices.
Calculation using common logarithms.
11. Mathematical
Induction and its simple applications including sequences and series.
Arithmetic and geometric progression.
12.
The meaning of nPr and nCr.
Simple ideas of probability theory with applications of the addition law and
multiplication law to easy problems.
13.
Collection and organization of
numerical data, and their graphical representation by bar charts, pie charts,
histograms, frequency polygons and curves, cumulative frequency polygons and
curves. Calculation of the mean. Determination of the median and quartiles;
inter-quartile range as a simple measure of dispersion.
14.
Measure of angles in degrees
and in radians. Lengths of arc and area of sector of a circle. The function
sine, cosine, tangent and their graphs in the interval 0 to . The
relations of , .
15.
Solution of right-angles
triangles, with simple applications. Easy problems in two and three dimensions
soluble by analysis into right-angles triangles.
16.
Easy trigonometric equations
(solution in the interval 0 to ).
17.
Elementary mensuration of the
rectangle, triangle, parallelogram, trapezium, polygon, circle, rectangular
block, prism, cylinder, pyramid, right circular cone and sphere. (since 1977)
18. Rectangular
co-ordinates in 2-dimensional space. Distance between two points. Points
dividing line segments in a given ratio. Equations of a straight line; gradient
of a straight line; perpendicularity; intersection; family of straight lines.
Equations of circle. Recognition of standard equations of parabola, ellipse and
hyperbola. Easy locus problems. (until 1977)
Rectangular
co-ordinate in 2-dimensional space. Distance between two points. Points
dividing line segments in a given ratio. Equations of a straight line; gradient
of a straight line; perpendicularity; intersection; family of straight lines.
Equations of circles, co-ordinate of centre, length of radius. Intersection of
straight line and circles. (1978)
19. Vectors in
2-dimensional space. Unit vectors and zero vector. Representation of a vector
by 
and by a directed line segment. Sum and
difference of vectors. Multiplication of a vector by a scalar. Scalar product
(dot product) of two vectors. Simple vector operations in proving properties of
parallelism, perpendicularity and the ratio of line segments.
（中文版本）
1.
命題：否定，合取，析取，條件式，雙條件式，蘊涵與等價；及其應用於不多於三變元命題真值之驗定。
2.
集及集之元素，子集，併集，交集，餘集，泛集及空集。温氏圖解。集之運算。序偶，關係及映射之簡易概念，包括直射，全射及對射，關係及映射之圖像。
3.
數系之運算，包括複數系。
4.
單元多項式及其基本運算，下列各式之因子分解：，，及，其中h，k，m，n為整數，最大公約及最小公倍，簡易分式。
5.
公式：計算之應用。
6.
一元綫性方程，二元綫性方程組，一元二次方程，根與係數之關係，二元聯立方程組（一為一次，一為二次）。各類方程之應用題。
7.
比，比例及變數法。
8.
綫性及二次函數之圖解。
9.
單變元及雙變元之綫性不等式及其應用，單變元之二次不等式，綫性不等式之圖像及其在簡易實際問題中之應用，如綫性規劃。
10.
有理指數定律，用常用對數之計算。
11. 數學歸納法及其簡易應用，包括數列及數串，等差級數，等比級數。
12.
nPr及nCr之意義，簡易概率論，和積定理及簡易應用。
13.
數據之搜集，組織及其表示法，長條圖，圓形圖，直方圖，頻數折綫及曲線，累積頻數折綫及曲綫，平均值之計算，中位數及四分位數之計算，分四位數距作為分佈之初步量度。
14.
角之量度：以度及徑為單位。弧長及扇形面積。正弦，餘弦，正切在0至區間之函數。三角函數之基本關係：及。
15.
直角三角形解法及其應用。二維及三位空間之簡易應用題，只限能用直角三角形求解者。
16.
簡易三角方程（答案在0至區間）。
17.
面積及體積之計算，包括矩形，三角形，平行四邊形，梯形，多邊形，圓形，長方體，柱體，錐體，圓錐體和球體。（自1977）
18. 平面之直角坐標系。兩點距離，分綫段為定比之點，直綫方程，直線斜率，垂直之條件，兩直綫交點，直線系。圓之方程，圓心坐標，半徑長，直線與圓之交點。拋物線，橢圓及雙曲線標準式之認識。簡易軌跡。（直至1977）
平面之直角坐標系。兩點距離，分綫段為定比之點，直綫方程，直線斜率，垂直之條件，兩直綫交點，直線系。圓之方程，圓心坐標，半徑長，直線與圓之交點。（1978）
19. 二維空間之向量，單位向量及零向量，以及有向直綫表示向量。向量之和及差。純量向量相乘，兩向量之內積應用向量運算，以證平行，垂直及求綫段之比例等。
Edition 6: 1979, 1980, 1981 (change name
as Syllabus 1), 1982
1.
Sets, numbers of a set, subset, union, intersection,
complement, universal set and empty set. Venn diagrams. Composition laws for
sets. Ordered pairs. Relations. Simple ideas of mapping (single-valued
function) including one-one, onto and one-one onto mappings. Graphs of
relations and mappings.
2.
Addition, subtraction, multiplication and division of
real numbers and complex numbers.
3.
Polynomials in one variable and
their fundamental operations. Factorization of 
, , ; where h, k, m and n are integers. LCM and HCF.
Simple algebraic fractions.
4.
Formulae: their manipulation
and numerical applications. (1979, 1980)
Formulas: their manipulation and numerical applications. (1981,
1982)
5.
Solution of linear equations in
one unknown and simultaneous linear equations in two unknowns, and of quadratic
equations in one unknown. Relations between the roots and the coefficients of
quadratic equations in one unknown. Solution of simultaneous equations, one
linear and one quadratic, in two unknowns. Simple problems leading to such
equations. Distinction between equations and identities.
6.
Problems of simple interest,
profit and loss, percentage, averages.
7.
Ratio, proportion and
variation.
8.
Graphs of linear and quadratic
functions; travel graphs. (until 1981)
Graphs of 
and 
; travel
graphs. (1982)
9.
Linear inequalities in one or
two variables and their applications. Quadratic inequalities in one variable.
Graphical representation of linear inequalities with applications to simple
practical problems such as Linear Programming.
10.
Laws of rational indices.
Calculation using common logarithms. (1979)
Laws of rational indices. Calculation using common logarithms.
Equations with unknown indices. (1980, 1981, 1982)
11.
Arithmetic and geometric
progressions. Insertion of arithmetic and geometric means, sum to n terns,
summation of geometric progressions to infinity, compound interest, growth and
depreciation.
12.
Simple ideas of probability
theory with applications of the addition law and multiplication law to easy
problems.
13.
Collection and organization of
numerical data, and their graphical representation by bar charts, pie charts,
histograms, frequency polygons and curves, cumulative frequency polygons and
curves. Calculation of the mean. Determination of the median and quartiles;
inter-quartile range as a simple measure of dispersion.
14.
Measures of angles in degrees
and in radians. Length of arc and area of sector of a circle. The functions
sine, cosine, tangent and their graphs in the interval 0 to . The
relation , .
15.
Solution of right-angles
triangles, with simple applications. Easy problems in two and three dimensions
soluble by analysis into right-angles triangles.
16.
Easy trigonometric equations
(solution in the interval 0 to ). (until
1981)
Easy trigonometric equations (solution in the interval 0 to radians). (1982)
17.
Elementary mensuration of the
rectangle, triangle, parallelogram, trapezium, polygon, circle, rectangular
block, prism, cylinder, pyramid, right circular cone and sphere. Similar plane
figures and solids; relation of areas and volumes to their corresponding
dimensions. (until 1981)
Elementary mensuration of the rectangle, triangle, parallelogram,
trapezium, polygon, circle, rectangular block, prism, cylinder, pyramid, right
circular cone and sphere. Similar plane figures and solids, their areas and
volumes. (1982)
18.
Rectangular co-ordinate in
2-dimensional space. Distance between two points. Points dividing line segments
in a given ratio. Equations of a straight line; gradient of a straight line;
perpendicularity; intersection; family of straight lines. Equations of circles,
co-ordinate of centre, length of radius. Intersection of straight line and
circles.
19. Vectors in
2-dimensional space. Unit vectors and zero vector. Representation of a vector
by 
and by a directed line segment. Sum and
difference of vectors. Multiplication of a vector by a scalar. Scalar product
(dot product) of two vectors. Simple vector operations in proving properties of
parallelism, perpendicularity and the ratio of line segments.
20.
Easy application of the
following:
Angles at a point; parallel lines; sum of angles of a triangle;
congruent triangle; isosceles triangles; parallelograms; Pythagoras’ theorem;
circles: arc, chords, angle in a segment, cyclic quadrilaterals, tangents,
angle in the alternative segment; similar triangles. (No proof will be
required.)
（中文版本）
1.
集，集之元素，子集，併集，交集，餘集，泛集及空集。温氏圖解。集之運算定律。序偶。關係。映射（單值函數）之簡易概念，包括一對一，映成，及一對一映成之映射。關係及映射之圖像。
2.
實數及複數之加、減、乘、除運算。
3.
單變元多項式及其基本運算。下列各項之因子分解：，，及，其中h、k、m、n為整數。LCM及HCF。簡易分式。
4.
公式：計算上之應用。
5.
一元線性方程、二元聯立線性方程組及一元二次方程之解法。一元二次方程之根與係數關係。二元聯立方程組（一為一次，一為二次）之解法。各類方程之簡易應用題。方程與恒等式之區別。
6.
單利息問題，盈利及賠本，百分率，平均值。
7.
比，比例及變數法。
8.
線性及二次函數之圖像；行情圖像。（直到1981）
及
之圖形；行程圖形。（1982）
9.
單變元及雙變元之綫性不等式及其應用。單變元之二次不等式。線性不等式之圖像及其在簡易實際問題之應用，如線性規劃。
10.
有理指數定律。用常用對數之計算。（1979）
有理指數定律。用常用對數之計算。指數方程。（1980至1982）
11.
等差級數。等比級數。等差中項及等比中項之插入，n項和，等比級數無限項之和。複利息，增長及折舊。
12.
簡易概率論。加法定律，乘法定律及其簡易應用。
13.
數據之搜集，組織及其表示法，長條圖，圓形圖，直方圖，頻數折綫及曲綫，累積頻數折線及曲線。平均值之計算。中位數及四分位數之確定，四分位數距作為分佈之初步量度。
14.
角之量度：以度及弳為單位。弧長及扇形面積。正弦，餘弦，正切在0至2π區間之函數及其圖像。三角函數基本關係：及。
15.
直角三角形解法及其簡以應用。二維及三維空間之簡易應用題，只限於能用直角三角形求解者。
16.
簡易三角方程（在區間0至之解）。（直到1981）
簡易三角方程（在區間0至弧度之解）。（1982）
17.
面積及體積之計算，包括矩形、三角形、平行四邊形、梯形、多邊形、圓形、長方體、角柱、圓柱、角錐、直圓錐及球體。相似形及相似體，面積、體積與對應線段之關係。（直到1981）
面積及體積之計算，包括矩形、三角形、平行四邊形、梯形、多邊形、圓形、長方體、角柱、圓柱、角錐、直圓錐及球體。相似形及相似體，其面積及體積。（1982）
18.
平面之直角座標系。兩點距離，分綫段為定比之點。直綫方程，直綫斜率，垂直之條件，兩直線交點，直線系。圓之方程，圓心座標，半徑長，直線與圓之交點。
19. 二維空間之向量。單位向量及零向量。以ai+dj及有向直綫表示向量。向量之和及差。純量向量相乘。兩向量之內積。應用向量運算以證平行、垂直及求綫段之比。
20.
下列各項之簡易應用：
同頂角，平行綫，三角形之內角和，全等三角形，等腰三角形，平行四邊形。畢氏定理。圓：弧及弦，對同弧圓周角，圓內接四邊形，切綫，弦切角。相似三角形。
（本該將不測驗幾何證明題。）
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