新加坡劍橋O水准考試(Singapore-Cambridge General Certificate of Education Ordinary Level Examinations,簡稱GCE ‘O’ Level),是由新加坡教育部MOE和新加坡考試與評鑒局SEAB共同主辦的國家級統一考試,也是新加坡的中學生在4年中學教育結束後參加的考試。
考試一年舉辦一次,考生可以用獲得的成績爲標准申請進入新加坡初級學院、理工學院或工藝教育學院。考試成績也爲英聯邦各個國家所承認和接受,可用于申請海外英聯邦國家的初級學院或是大學預備班。
貫穿新加坡中學四年教育的,仍是3+1的教學體系,三大模塊數學知識和貫穿始終的數學過程思維訓練,如下圖所示。
數學過程思維這一環節最爲關鍵的是思維技巧和策略思維方法。這部分內容是要求學生在掌握數學知識點的基礎上,能活學活用,經過訓練,學會常用的思維方法。
新加坡中學一年級的知識點如下。
一、代數部分
N1. Number & operations 數及運算
1.1. primes and prime factorisation 質數和質因數分解
1.2. finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation
1.3. negative numbers, integers, rational numbers, real numbers and their four operations 通過質因數分解求最大公因子、最小公倍數、平方數、立方數、平方根、立方根
1.4. calculations with calculator 使用計算器
1.5. representation and ordering of numbers on the number line 在數軸線上對數進行標注和排序
1.6. use of <,>, ≤, ≥ 使用<,>, ≤, ≥符號
1.7. approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, and estimating the results of computation)
近似計算和估算(包括按要求對特定數位及小數位或有效數字進行取整,及估算結果)
N2. Ratio & proporation 比率和比例
2.1. ratios involving rational numbers
有理數比率
2.2. writing a ratio in its simplest form
比率的最簡單形式,化簡
2.3. problems involving ratio
涉及比率的問題求解
N3. Percentage 百分比
3.1. expressing one quantity as a percentage of another
將數量寫成百分比形式
3.2. comparing two quantities by percentage
按百分比比較兩個量(數量)
3.3. percentages greater than 100%
多于100%的百分比
3.4. increasing/decreasing a quantity by a given percentage (including concept of percentage point)
用給定的百分比增減某個量
3.5. reverse percentages
反向百分比
3.6. problems involving percentages
百分比問題求解
N4. Rate & Speed 速率
4.1. concepts of average rate, speed, constant speed and average speed
平均速率、恒定速率的概念
4.2. conversion of units (e.g. km/h to m/s)
速度單位轉換
4.3. problems involving rate and speed
速度/速率問題求解
N5. Algebraic expression & formulate 代數表達式
5.1. using letters to represent numbers
用字母代表數字
5.2. interpreting notations:
解析上述標記
5.3. evaluation of algebraic expressions and formulae
計算代數表達式,表達式規範化
5.4. translation of simple real-world situations into algebraic expressions
將現實場景轉換爲代數表達式
5.5. recognising and representing patterns/relationships by finding an algebraic expression for the nth term
識別模式關系,並能含第N項的代數表達式呈現
5.6. addition and subtraction of linear expressions
線性表達式的加減法
5.7. simplification of linear expressions
線性表達式化簡
5.8. use brackets and extract common factors
使用括號,及提取公因式
N6. Functions & graphs 函數和圖
6.1. Cartesian coordinates in two dimensions
二維迪卡爾坐標系
6.2. graph of a set of ordered pairs as a representation of a relationship between two variables
用給定的代表兩元變量關系的數對作圖(在坐標系上繪制點線)
6.3. linear functions = +
一元線性函數
6.4. graphs of linear functions
線性函數對應的圖
6.5. the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
線性圖對應的斜率
N7. Equations & inequities 等式和不等式
7.1. concept of equation
等式的概念
7.2. solving linear equations in one variable
求解一元線性等式
7.3. solving simple fractional equations that can be reduced to linear equations
求解簡單分數方程(可化簡爲線性等式的)
7.4. formulating a linear equation in one variable to solve problems
規範化線性等式,並求解
二、幾何和測量
G1. Angles, triangles & polygons 角度/三角形/多邊形
1.1. right, acute, obtuse and reflex angles
直角、銳角、鈍角和reflex angles
1.2. vertically opposite angles, angles on a straight line, angles at a point
1.3. angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
平行線與直線相交形成的角
1.4. properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties
三角形、特殊四邊形、正多邊形的性質
1.5. classifying special quadrilaterals on the basis of their properties
依據特性對特殊四邊形分類
1.6. angle sum of interior and exterior angles of any convex polygon
凸多邊形的內角和/外角和
1.7. construction of simple geometrical figures from given data using compasses, ruler, set squares and protractors, where appropriate
使用圓規、直尺、半圓板等工具繪制幾何圖形
G2. Mensurations
5.1. area of parallelogram and trapezium
平行四邊形和梯形的面積
5.2. problems involving perimeter and area of composite plane figures
組合平面圖形的面積及周長問題求解
5.3. volume and surface area of prism and cylinder
棱柱和圓柱體的體積和表面積
5.4. conversion between cm2 and m2 , and between cm3 and m3
cm2 和m2 ,cm3 和m3單位轉換
5.5. problems involving volume and surface area of composite solids
組合立體形狀的體積及表面積問題求解
三、統計和概率
S1. Data handling & analysis 數據處理和分析
1.1. simple concepts in collecting, classifying and tabulating data
數據采集、分類和圖表化的基本概念
1.2. analysis and interpretation of:
tables
bar graphs
pictograms
line graphs
pie charts
分析並解析圖表、棒圖、折線圖和餅圖
1.3. purposes and uses, advantages and disadvantages of the different forms of statistical representations
陳述不同形式的統計呈現方式的目的、用途和優缺點
1.4. explaining why a given statistical diagram leads to misinterpretation of data
陳述爲何某些特定的統計圖會導致誤讀數據