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，會跟讀者分析高等程度會考數學課程，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，客觀分析中文中學會考數學課程的歷年沿革。以協助讀者對高等程度會考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，有更多參考資源可供參考。
各位大家好，本篇為《2024年第27篇：香港高等程度會考數學科目分析》的附錄，以中英雙語形式，整理並列出當年的高等程度會考數學課程。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 歷年高等程度會考之考試規則及課程
Ø 歷年之香港中文大學入學資格考試規則及課程
這些考試規則及課程，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。這都幫助本人對高等程度會考數學課程有如此透徹的了解，特此鳴謝。
附錄1：高等程度會考普通數學考試範圍
Version 1: 1966-1971
1.
邏輯與集：
命題之運算，包括命題之析取，合取及蘊涵。真值表，集的概念和記號。子集與空集，集的併，交和餘集，De Morgan's公式。
2.
代數：
基本運算。整數的二，三和十進位表示多項式及簡單的因子分解。餘式定理，分式，簡易最大公約和最小公倍，一元一次及二次方程式。二元聯立方程式其中一為一次，一為二次者。
代數函數之圖像及其簡易應用。對數及其應用。算術級數，調和級數。幾何級數（包括無限項幾何級數）。小數之展開式。
3.
幾何：
角。疊合公理及平行公理。三角形，多邊形。相似變換。面積。圓。軌跡。簡易作圖題。
4.
三角：
角之量度，三角函數及簡易恆等式。三角函數之圖像。互餘，互補及共扼角之三角關係。複角及半角公式。兩三角函數之和及積，任意三角形之解法。簡易三角方程。
Version 2: 1972-1976
1.
簡易命題運算：否定，析取，合取及蕴涵。真值表。
2.
集之概念及記號，空集，子集及餘集，交集及併集，温氏圖，德摩根定律，有限集之交集及併集中元素之個數應用問題。
3.
基本代數運算，整數對於各種底的表示與運算，簡易不等式，綫性規劃，多項式及簡易因式分解，餘式定理。
4.
矩陣之代數運算，其中
。行列式之性質，包括
。滿秩方陣及簡易數值方陣之逆方陣。
5.
二元及三元聯立方程，其中一可為二次但其它為一次方程，算術級數，調和級數及幾何級數（包括無限項幾何級數）。數學歸納法原理。
6.
二維空間之直交卡氏坐標，直綫及圓，代數函數之圖像及簡易應用，參數方程及簡易軌跡。
7.
三角函數及其圖像，基本恆等式，簡易三角方程之通解。
8.
簡易概率論，數據之圖象表示，中心趨勢之量度：平均值，中位數與四分位數。
（考生應具備下列幾何性質之知識，但不要求其證法：三角形，多邊形及圓之性質，相似變換，面積。）
Version 3: 1977-1979
1.
簡易命題運算，命題之否定，析取，合取，藴含及等價。*
2.
簡易演繹推理。
3.
三角形，多邊形及圓形之基本性質。相似變換，面積。三維空間向量。*
4.
集之概念及記號，子集及餘集，併集及交集。温氏圖。狄摩根公式。有限集之併集及交集中元素之個數及其應用。
5.
數學歸納法及其應用。
6.
基本代數運算。正整數在各種底數之表示及計算。多項式及因式分解，餘式定理。
7.
型矩陣之計算，其中。行列式之性質，包括
。滿秩方陣及其逆方陣（限於簡單數值問題）。
8.
二元及三元聯立方程組，其中一個方程可能為二次，但餘皆一次之情形。等差級數及等比級數（包括無限等比級數）。
9.
不等式。綫性規劃。
10.
二維空間之直角卡氏坐標。直綫及圓。二次曲綫之標準式及參數表示。
11.
三角函數及其圖象。基本三角恆等式，包括倍角公式。簡易三角方程之通解。
12.
簡易概率。數據之搜集與整理及各種表示法：圖像，圖解，頻率及累積頻率多邊形與曲綫，及其釋義。平均數，標準離差，中位數，百份位數及其應用。
考生只須具備此等項目知識，試題將不涉及此項目中結論之證明。*
(English Version)
1.
Elementary propositional
calculus, negation, disjunction, conjunction, implication and equivalence.
Simple arguments.*
2.
Basic properties of triangles,
polygons and circles, similarity transforms, areas. Vectors in 3-dimensional
space.*
3.
The concept of a set and
notations Subsets and complements. Unions and intersection of sets. Venn
diagrams. De Morgan’s formulae. The number of elements in finite sets and in
their unions and intersections. Applications.
4.
The principle of mathematical
induction and applications.
5.
Basic algebraic operations.
Representation and manipulation of integers in different bases. Polynomials and
simple factorisation. The remainder theorem.
6.
The algebra of matrices with .
Determinants and their properties, including .
Non-singular matrices and simple numerical cases of their inverses,
7.
Simultaneous equations in two
or three variables in which one equation may be quadratic and the others
linear. Arithmetic and geometric series (including infinite geometric series).
8.
Inequalities. Linear
programming.
9.
Rectangular cartesian
coordinates in 2-dimensional space. Straight lines and circles. The equations
of conics in standard and parametric form.
10.
The trigonometric functions and
their graphs. Basic identities, including compound angles formulae. General
solutions of simple trigonometric equations.
11.
Elementary probability. The
collection, organisation and presentation of numerical data by graphs, charts,
frequency and comluative frequency polygons and curves. Their interpretation.
Mean, standard deviation, median, percentiles and their use.
*Knowledge of the Items in these paragraphs
will be assumed but no formal proofs will be set.
Version 4: 1980, 1981, 1982
考生須具備下列項目知識，惟試題將不涉及此等項目中結論之證明：
Ø 簡易命題運算，命題之否定、析取、合取、藴含及等價。
Ø 簡易演繹推理。
Ø 數系：自然數、整數、有理數、無理數、實數、複數。
Ø 三角形、多邊形及圓形之基本性質，相似形，面積及體積。
課程綱要
1.
集之概念，子集、併集、交集；差集（包括餘集）。温氏圖。狄摩根公式。有限集之併集及交集中元素之個數及其應用。
2.
數學歸納法及其應用。
3.
基本代數運算：多項式及有理式之運算；餘式定理；多項式，包括對稱為及輪換對稱式之因式分解；正整數在各種底數之表示及計算；指數及對數之性質。(until 1981)
函數之概念及符號。基本代數運算：多項式及有理式之運算；餘式定理；多項式，包括對稱式及輪換對稱式之因式分解；正整數在各種底數之表示及計算；指數及對數之性質。(1982)
4.
型矩陣之運算，其中；滿秩方陣及其逆方陣。行列式之性質及其應用，包括及齊次方程組的解。
5.
二次方程論。二元及三元聯立方程組，其中一個方程可能為二次，但餘皆為一次之情形。
6.
等差級數及等比級數（包括無限項等比級數）。(until 1981)
等差級數及等比級數（包括無限項等比級數）。Σ符號之應用。(1982)
7.
不等式，包括
定理（本定理之證明至四個變量為止，但應用則推廣至n個變量）。(until 1982)
不等式，包括絕對值符號之應用及定理（本定理之證明至四個變量為止，但應用則推廣至n個變量）。兩變量之線性規劃。(1982)
8.
二維空間之直角坐標。直綫及圓錐曲綫之標準式及參數表示。
9.
三角函數及其圖像。基本三角恒等式，包括複角公式、倍角公式、半角公式、和積互變公式。正弦定律、餘弦定律及其在三維空間之應用。三角方程之通解。(until 1981)
三角函數及其圖像，反三角函數。基本三角恒等式，包括複角公式、倍角公式、半角公式、和積互變公式。正弦定律、餘弦定律及其在三維空間之應用。三角方程之通解。(1982)
10.
簡易概率論，概率加法及乘法，單純事件之重複試驗。(until 1981)
簡易排列與組合及其簡易概率論之應用，概率加法及乘法，單純事件之重複試驗。(1982)
11.
數據之搜集與整理及各種表示法：圖像、圖解、頻數及累積頻數多邊形與曲綫，及其釋義。相對頻率、平均數、標準差、中位數、百份位數及其應用。
(English Version)
Knowledge of the following items is
assumed, but no formal proofs will be set on them:
Ø Elementary propositional calculus, negation, disjunction,
conjunction, implication and equivalence. Simple arguments.
Ø Number systems: natural numbers, integers, rational numbers,
irrational numbers, real numbers and complex numbers.
Ø Basic properties of triangles, polygons and circles, similar
figures, area and volume.
Syllabus
1.
The concept of a set, subsets,
union and intersection. Complement with respect to the universal set and to
other sets. Venn diagrams. De Morgan’s formulas. The number of elements in
finite sets and in their unions and intersections, applications.
2.
Mathematical induction and its
applications.
3.
Basic algebraic operations:
operations on polynomial and rational expressions; remainder theorem;
factorization of polynomials including symmetric and cyclic expressions;
representation and manipulation of positive integers in different bases;
properties of indices and logarithms. (until 1981)
The concept and notation of a function. Basic algebraic operations:
operations of polynomial and rational expressions; remainder theorem;
factorization of polynomials including symmetric and cyclic expressions;
representation and manipulation of positive integers in different bases;
properties of indices and logarithms. (1982)
4.
The algebra of matrices with .
Non-singular matrices and their inverses. Properties of determinants and their
applications, including and solution of system of homogeneous
equations.
5.
Theory of quadratic equations.
Simultaneous equations in two or three unknowns in which one equation may be
quadratic and the other linear.
6.
Arithmetic progressions and
geometric progressions (including infinite geometric progression). (until 1981)
Arithmetic progressions and geometric progressions (including
infinite geometric progressions). Use of the Σ notation. (1982)
7.
Inequalities, including the
theorem . (The
proof of this theorem is restricted to 4 variables but its application extends
to n variables.) (until 1981)
Inequalities, including the use of the absolute value sign and the
theorem (The proof of this theorem is restricted to 4
variables but its applications may extend to n variables.) Linear programming
in two variables. (1982)
8.
Rectangular coordinates in the
two-dimensional space. Straight lines. Equations of conics in standard forms
and in parametric forms.
9.
Trigonometric functions and
their graphs. Basic identities including compound angle formulas. The sine law,
the cosine law and their applications in the three-dimensional space. General
solutions of trigonometric equations. (until 1981)
Trigonometric functions and their graphs. Inverse trigonometric
functions. Basic identities including compound angle formulas, multiple-angle
formulas, half-angle formulas, sums and products formulas. The sine law, the
cosine law and their applications in the three-dimensional space. General
solution of trigonometric equations. (1982)
10.
Elementary probability theory,
addition and multiplication of probabilities. Repeated trials of a simple
event. (until 1981)
Simple permutations and combinations and their application to
elementary probability theory. Addition and multiplication of probabilities.
Repeated trials of a simple event. (1982)
11.
The collection, organization
and presentation of numerical data by graphs, charts, frequency and cumulative
frequency polygons and curves and their interpretation. Relative frequency,
mean, standard deviation, median, percentiles and their use.
Version 5: 1983-1986 (give detail
information and change syllabus), 1987-1992
考生須具備下列項目知識，惟試題將不涉及此等項目中結論之證明：
Ø 簡易命題運算，命題之否定、析取、合取、藴含及等價。
Ø 簡易演繹推理。
Ø 數系：自然數、整數、有理數、無理數、實數、複數。
Ø 三角形、多邊形及圓形之基本性質，相似形，面積及體積。
Ø 普通平面及立體圖形之面積及體積之計算，包括多邊形、圓形、多面體、柱體、角錐及球體。
課程綱要
1.
集之概念：集之語言及符號。子集。交集及併集。差集（包括餘集）。對稱差集。狄摩根公式。温氏圖。有限集、有限集之併集及交集中元素之個數及其應用。
2.
數學歸納法及其應用。
3.
基本代數運算。多項式及有理式。餘式定理。多項式之因式分解，包括對稱式及輪換式。正整數在各種底數之表示及計算。指數及對數之性質。(until 1986)
基本代數運算。多項式及有理式。餘式定理。多項式之因式分解，包括對稱式及輪換式。指數及對數之性質。(1987-1992)
4.
m×n型矩陣之運算，其中m,n≤3。滿秩方陣及其逆方陣。行列式之性質及其應用。
5.
二次方程論。二元及三元聯立方程組。
6.
等差級數及等比級數（包括無限項等比級數）。首n個自然數之平方、立方之總和及其應用。
7.
不等式及線性規劃。AM≥GM (until 1986)
條件不等式。絕對不等式。(1987-1992)
8.
二維空間之直角笛卡兒坐標。直線。圓錐曲線之標準式及參數式。簡易軌跡問題。
9.
三角函數及其圖像。基本三角恒等式，包括補角公式、倍角公式、半角公式、和積互變公式。反三角函數之定義及符號。一變元三角方程之通解。正弦定律、餘弦定律及其在三維空間之應用。
10.
樣本空間。事件。概率之基本概念。加法定律。獨立事件；乘法定律。單純事件之重複試驗。
11.
數據之搜集與整理及各種表示法。分組數據，組距；相對頻率。平均數，方差，標準差，中位數，眾數，百份位數及其應用。(until 1986)
數據之搜集與整理及各種表示法。分組數據，組距；相對頻率。平均數，方差，標準差，中位數，眾數及其應用。(1987-1992)
(English Version)
Knowledge of the following items is
assumed, but questions that require formal proofs on them will not be set:
Ø Elementary propositional calculus, negation, disjunction,
conjunction, implication and equivalence. Simple arguments.
Ø Number systems: natural numbers, integers, rational numbers,
irrational numbers, real numbers and complex numbers.
Ø Basic properties of triangles, polygons and circles; similar
figures, area and volume.
Ø Mensuration of common plane and solid figures including polygons,
circles, polyhedral, cylinders, cones and spheres.
Syllabus
1.
The concept of a set; set
language and notation. Subsets. Union and intersection. Complement with respect
to a universal set and to other sets. Symmetric difference. De Morgan’s
formulas. Venn diagrams. Number of elements in finite sets and in their unions
and intersections; applications.
2.
Mathematical induction and its
applications.
3.
Basic algebraic operations.
Polynomials and rational expressions. Remainder theorem. Factorisation of
polynomials including symmetric expressions and cyclic expressions. Representation
and manipulation of positive integers in different bases. Properties of indices
and logarithms. (until 1986)
Basic algebraic operations. Polynomials and rational expressions.
Remainder theorem. Factorisation of polynomials including symmetric expressions
and cyclic expressions. Properties of indices and logarithms. (1987-1992)
4.
The algebra of m×n matrices
with m,n≤3. Non-singular matrices and their inverses. Properties of
determinants and their applications.
5.
Theory of quadratic equations.
Simultaneous equations in two or three unknowns.
6.
Arithmetic progression and
geometric progression (including infinite geometric series). The sum of the
squares or cubes of the first n natural numbers and their applications.
7.
Inequalities and their
programming. AM≥GM. (until 1986)
Conditional inequalities. Absolute inequalities. (1987-1992)
8.
Rectangular Cartesian
coordinates in the two-dimensional space. Straight lines. Equations of conics
in standard forms and in parametric forms. Easy problems on loci.
9.
Trigonometric functions and
their graphs. Basic formulas, multiple-angle formulas, half-angle formulas,
sums and products formulas. Definition and notation of inverse trigonometric
functions. General solution of trigonometric equations in one unknown. The sine
law, cosine law and their applications to problems in the two or
three-dimensional spaces.
10.
Sample space. Events.
Elementary probability concept. Addition law. Independence; multiplication law.
Repeated trials of a simple event.
11.
The collection, organization
and presentation of numerical data. Grouped data; class intervals; relative
frequency. Mean, variance, standard deviation, median, mode, percentiles and
their use. (until 1986)
The collection, organization and presentation of numerical data.
Grouped data; class intervals; relative frequency. Mean, variance, standard
deviation, median, mode and their use. (1987-1992)
附錄2：高等程度會考高級數學考試範圍
Version 1: 1966-1971
高級數學課程包括普通數學課程内容及以下各項：
1.
數系之描述：
整數及其唯一分解性。有理數。無理數。代數數。超越數及實數。
2.
代數：
二次函數及二次方程論。排列，組合及其概率論（或然率Theory of Probability）之簡單應用。正整幕之二項定理。分數幕與負數幕之二項式定理（只限應用，證明可畧）。簡易不等式。數學歸納法。部份分式。
3.
幾何：
平面直角坐標（包括參數表示）直線。圓。抛物線、橢圓及雙曲線。簡易軌跡問題。空間直角坐標。直線與直線與平面之交角。平面與平面之交角。常見立體之量度及其簡單性質（包括四面體，柱體，錐體及球）。
4.
微積分：
函數之極限及連續性，導數之定義，函數之和與積之微分，微分之連鎖法則。初等函數之微分法。簡易定積分及不定積分。代換積分法及分部積分法。
簡易應用：變化率。極大與極小。切線與法線。面積與體積。曲線繪畫法。
Version 2: 1972-1976
高級數學課程大綱包括普通數學課程大綱所有内容以及下列各項：
1.
命題運算中推理的簡易法則。
2.
複數之代數運算，阿氏圖，模數，輻角及共軛數。二次函數及二次方程之理論。杜美弗定理及單位數之根。
3.
二項式定理，其冪為正數、分數及負數之各種情形。
4.
二維及三維空間之直交卡氏坐標，二維空間之二次曲綫，二直綫間之交角，一直綫與一平面交角及二平面間之交角，二維空間之坐標變換。
5.
等距變換：反射，旋轉，平移及其復合變換，直接疊合圖形與反疊合圖形之變換。平面上變換之矩陣表示。
6.
函數之極限與連續性。微分法及其應用：變率，極大與極小值，簡易曲線之描繪。簡易定積分及不定積分。變量找換，面積與體積之求法。
（考生應具備下列幾何性質之知識，但不要求其證法：一般平面與立體形之測量，例如多邊形，圓，多面體，柱面，錐面與球。）
Version 3: 1977-1979
高級數學課程大綱將包括普通數學課程大綱全部及下列項目：
1.
普通平面及立體圖形之各種量度，包括多邊形，圓形，多面體，圓柱體，圓錐，及球體。*
2.
流程圖使用法。*
3.
命題運算之簡易推理法則。*
4.
複數運算，阿氏圖解，絕對值，幅角，共軛複數。二次三項式及二次方程論。杜美佛定理及單位根。
5.
有理指數之二項式定理。
6.
三維空間直角卡氏坐標。直線與直線，直線與平面及平面與平面之交角。二維空間之坐標變換及其矩陣表示。
7.
函數之定義。等價關係及等價類。模算術。代數結構之概念。可換羣及非可換羣之定義及簡例。同構概念。
8.
數貫（序列）之極限。函數之極限及連續性。微分法及其應用：極大，極小及簡易曲線繪圖法。簡易定積分及不定積分，變數變換，面積及體積之求法。
考生只須具備此等項目知識，試題將不涉及此項目中結論之證明。*
(English Version)
The Higher Mathematics syllabus comprises
the contents of the General Mathematics Syllabus and the following:
1.
Measurement of common plane and
solid figures, including the polygon, circle, polyhedral, cylinder, cone and
sphere.
2.
Use of flow diagrams.
3.
Simple rules of inference in
propositional calculus.
4.
Algebra of complex numbers, the
Argand diagram, modulus, argument and conjugate. The theory of quadratic
functions and equations. De Moivre’s theorem and roots of unity.
5.
Binomial theorem for rational
indices.
6.
Rectangular cartesian
coordinates systems in 2 and 3-dimensional space. Angles between two lines,
between a line and a plane between two planes. Transformation of coordinates in
the plane. Matrix representation of transformations in the plane.
7.
Definition of a function.
Equivalence relations and equivalence classes. Modulo arithmetic. The concept
of algebraic structures. Definition and simple examples of abelian and
non-abelian groups. Isomorphism.
8.
Limits of sequences. Limit and
continuity of a function. Differentiation and its applications: maxima and
minima, simple curve sketching. Simple definite and indefinite integrations.
Change of variable. Applications to area and volume.
*Knowledge of the Items in these paragraphs
will be assumed but no formal proofs will be set.
Version 4: 1980, 1981, 1982
考生須具備下列項目知識，惟試題將不涉及此等項目中結論之證明：
Ø 普通平面及立體圖形之各種量度，包括多邊形，圓形，多面體，柱體，錐體及球體。
課程綱要
1.
普通數學課程綱要之内容。(until 1981)
普通數學課程綱要之内容（試題可要求考生對其内容有較深入之認識）。
2.
整數系之等價關係及等價類，模算術（只涉及一次同餘式）。
3.
複數運算，阿氏圖解，模數，輻角，共軛複數。棣美弗定理及其應用。
4.
有理指數之二項式定理及其應用。
5.
二維空間直角坐標之平移及旋轉變換。
6.
三維空間直角坐標：點、綫、面間之距離（兩直綫不共面之情形除外）；直綫與直綫，直綫與平面及平面與平面之交角。
7.
數貫（序列）之極限。函數之極限及連續性。微分，定積分，不定積分及其應用。
註：(1) 極限，不要求嚴謹之ε-δ方法。
(2) 函數，包括在不同區間用不同公式定義函數。
(3) 微分部份，包括高階導數。
(4) 積分部份，包括變數變換及分部積分法及簡易廣義積分。
(5) 應用部份包括變率，極大，極小，曲綫繪劃法，面積及體積之求法。
(English Version)
Knowledge of the following items is assumed
but no formal proofs will be set of them:
Ø Mensuration of common plane and solid figures, including polygons,
circles, polyhedral, cylinders, cones and spheres.
Syllabus
1.
The content of the syllabus of
General Mathematics. (until 1981)
All topics of the syllabus of General Mathematics. (Questions which
require a deeper understanding may be set.) (1982)
2.
Equivalence relation and
equivalence class among the integers, modulo arithmetic (only linear congruence
is required).
3.
Algebra of complex numbers,
Argand diagram, modulus, argument and conjugate. De Moivre’s theorem and its
applications.
4.
Binomial theorem for rational
indices and its applications.
5.
Translation and rotation of
rectangular coordinate axes in the two-dimensional space.
6.
Rectangular coordinates in the
three-dimensional space: distance between points, lines and planes (excluding
the case where two lines are not coplanar), angles between two lines, between a
line and a plane and between two planes.
7.
Limit of a sequence. Limit of a
function, continuity. Differentiation, definite integration, indefinite
integration and their applications.
8.
Notes: For limits, formal ε-δ technique is not
required.
9.
For functions, those that are
defined by different formulas in different domains are included.
10.
In differentiation, derivatives
of higher orders are included.
11.
In integration, change of
variables, integration by parts and simple improper integrals are included.
12.
Applications include rates of
change, maxima and minima, curve sketching, calculation of areas and volumes.
Version 5: 1983-1986 (give detail
information and change syllabus), 1987-1992
1.
普通數學之全部課程綱要，並須包括下列項目：柯西不等式。反三角方程。條件概率。(until 1986)
普通數學之全部課程綱要，並須包括下列項目：圓錐曲線之參數方程式。柯西不等式。反三角方程。條件概率。(1987-1992)
2.
等價關係；整數系之等價類，模算術。(until 1986)
等價關係。(1987-1992)
3.
複數運算，阿氏圖，模數，輻角，共軛複數。棣美弗定理之證明及其應用。
4.
有理指數之二項式定理及其應用。
5.
二維空間直角坐標之平移及旋轉變換。三維空間直角坐標。點、線、面間之距離。直線與直線，直線與平面及平面與平面之交角。
6.
微分。微分之應用。不定積分。定積分及其應用。
(English Version)
1.
All topics of the syllabus of
General Mathematics. In addition, the following items are required:
Cauchy-Schwarz inequality. Equations involving inverse trigonometric functions.
Conditional probability. (until 1986)
All topics of the syllabus of General Mathematics. In addition, the
following items are required: Equations of conics in parametric form.
Cauchy-Schwarz inequality. Equations involving inverse trigonometric functions.
Conditional probability. (1987-1992)
2.
Equivalence relations;
equivalence classes among the integers, modulo arithmetic. (until 1986)
Equivalence relations. (1987-1992)
3.
Algebra of complex numbers,
Argand Diagram, modulus, argument and conjugate. The proof of DeMoivre’s
theorem and its applications.
4.
The binomial theorem for rational
indices and its applications.
5.
Translation and rotation of
rectangular coordinate axes in the two-dimensional space. Rectangular
coordinates in the three-dimensional space. Distance between points, lines and
planes. Angle between two lines, between a line and a plane and between two
planes.
6.
Differentiation. Applications
of differentiation. Indefinite integration. Definite integration and its
applications.
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