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Syllabus Topics
課程綱要
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Note
筆記
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Exercise
練習
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Test
測驗
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1.
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The six trigonometric functions
of angles of any magnitude and their graphs. 任意角之六個三角函數及其圖像。
Formulas for sin ( A  B ), cos ( A
B ) and tan ( A B ),
sum and product formulas. 公式，和積互變公式。
General solution of simple trigonometric equations. 簡易三角方程之通解。
Problems in two and three dimensions.三維及三維空間問題。
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1
解 |
1 |
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2.
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Quadratic
functions and quadratic equations.二次函數及二次方程。
Discriminant and complex roots. 判別式及複根。
Inequalities in one variable. 單變元不等式。
Use of the absolute value sign. 絕對值符號之使用。 |
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1
解
2 解 |
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2 3 |
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3.
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Mathematical
induction and its simple applications.數學歸納法及其簡易應用。 |
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1
解 |
1 |
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4.
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The binomial
theorem for positive integral indices.正整指數之二項式定理。 |
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1
解 |
1
2 3 4 |
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5.
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Plane
rectangular coordinates. Area of rectilinear figures. Angle between two
lines, distance from a point to a line, family of straight lines. 平面直角坐標。直線圖形之面積。兩直線之夾角，點與線之距離，直線族。
Equations of tangents to a circle. 圓之切線方程。
Family of circles. 圓族。
Simple locus problems. 簡易軌跡問題。 (圖例) |
1 2 3 |
1 解
2 解
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1 |
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6.
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Vectors in
the two-dimensional space. Unit vectors and the zero vector. Position vectors.
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.二維空間之向量。單位向量及零向量。位置向量。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。兩向量之純量積(點積)。
Application of vector method to problems involving parallelism,
perpendicularity and division of a line segment.應用向量方法以解平行，垂直及線段之分割等問題。
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中文
1 2 3
英文
1 2 3
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1 解 |
1 |
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7.
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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.從基本原理求微分。x之乘幕及三角函數之微分。函數之和、積、商之微分。複合函數及隱函數之微分。二階導數。
Application of differentiation to gradients, rates of change,
tangents and normals to a curve, maxima and minima, and sketching of simple
curves.微分之應用:斜率、變率。曲線之切線及法線、極大及極小、簡易曲線之描繪。 |
1 2 3 |
1
解 |
1
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8.
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Indefinite
integration as the reverse process of differentiation. Integration of simple
functions. Integration by simple change of variable.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。
Definite integrals and their simple properties.定積分及其簡易性質。
Applications in finding plane areas and volumes of solids
of revolution.以定積分計算平面面積及旋轉體之體積。 |
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1
解 |
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