📚 Year 8 Edexcel Maths: Core Knowledge Summary | Year 8 Edexcel 数学：核心知识点梳理
Year 8 Mathematics under the Edexcel curriculum builds on the foundations laid in Year 7, introducing more sophisticated number work, algebraic manipulation, geometric reasoning, and data handling. This article summarises the essential knowledge that every student should master, providing clear explanations in both English and Chinese to support bilingual learners.
Year 8 Edexcel 数学课程在 Year 7 的基础上进一步深化，引入了更复杂的数字运算、代数操作、几何推理和数据处理。本文梳理了每位学生必须掌握的核心知识点，并以中英双语提供清晰解释，帮助双语学习者巩固理解。
1. Working with Integers, Powers and Roots | 整数、幂与根的运算
You need to confidently add, subtract, multiply and divide positive and negative integers. Remember: multiplying or dividing two numbers with the same sign gives a positive answer; different signs give a negative answer.
你需要熟练进行正负整数的加、减、乘、除运算。记住：同号两数相乘或相除得正，异号得负。
Powers (indices) tell us how many times to multiply a number by itself. For example, 5² = 5 × 5 = 25, and 2³ = 2 × 2 × 2 = 8. The square root √ undoes squaring, so √25 = 5. You should also know simple cube roots, e.g. ∛27 = 3.
幂（指数）表示一个数自乘的次数。例如 5² = 5 × 5 = 25，2³ = 2 × 2 × 2 = 8。平方根 √ 是平方的逆运算，所以 √25 = 5。你还需要知道简单的立方根，例如 ∛27 = 3。
Order of operations (BIDMAS/BODMAS: Brackets, Indices, Division/Multiplication, Addition/Subtraction) must be followed exactly. For 3 + 4 × 2, we multiply first: 4 × 2 = 8, then add 3 to get 11.
运算顺序（BIDMAS/BODMAS：括号、指数、乘除、加减）必须严格遵守。对于 3 + 4 × 2，先乘：4 × 2 = 8，再加 3 得 11。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
Equivalent fractions simplify to the same value, e.g. 1/2 = 2/4 = 4/8. To add or subtract fractions, find a common denominator first: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Multiply fractions by multiplying numerators and denominators separately; to divide, flip the second fraction and multiply.
等价分数化简后值相同，如 1/2 = 2/4 = 4/8。加减分数时，先通分找公分母：1/3 + 1/4 = 4/12 + 3/12 = 7/12。分数乘法是分子乘分子、分母乘分母；除法则是将第二个分数倒转再相乘。
Decimals represent tenths, hundredths, etc. Multiply decimals as if they were whole numbers, then count the total decimal places. For 0.3 × 0.2, 3 × 2 = 6, and with two decimal places in total we get 0.06. Division by a decimal is easier if you move the decimal point in both numbers the same number of places.
小数表示十分之几、百分之几等。小数乘法先按整数乘，再数出总的小数位数。如 0.3 × 0.2，3 × 2 = 6，共有两位小数，结果为 0.06。小数除法时，将除数与被除数的小数点同时右移可简化计算。
Percent means ‘out of 100’. To convert a fraction to a percentage, find an equivalent fraction with denominator 100, or multiply the fraction by 100%. 3/5 = (3 × 20) / (5 × 20) = 60/100 = 60%. Percentage increase or decrease problems involve finding a percentage of an amount then adding or subtracting.
百分数表示“每百分”。分数转百分数，可化为分母为 100 的等价分数，或乘以 100%。3/5 = (3 × 20) / (5 × 20) = 60/100 = 60%。百分比增减问题则是先求出一个数量的百分比，再加或减。
3. Ratio and Proportion | 比与比例
A ratio compares parts of a whole, written as a:b. Simplify ratios by dividing both sides by their highest common factor. The ratio 6:9 simplifies to 2:3 (divide by 3). If the ratio of boys to girls is 2:3 and there are 30 children in total, 2+3=5 parts, so one part is 30 ÷ 5 = 6. Boys = 2 × 6 = 12, girls = 3 × 6 = 18.
比用于比较整体各部分，写作 a:b。化简比时两边同时除以最大公因数。6:9 化简为 2:3（同除以 3）。若男生与女生的比是 2:3，总共有 30 个孩子，则 2+3=5 份，每份为 30 ÷ 5 = 6。男生 = 2 × 6 = 12，女生 = 3 × 6 = 18。
Proportion describes how one quantity changes with another. Direct proportion means as one doubles, the other doubles; the graph is a straight line through the origin. Use the unitary method: if 5 pens cost £2, one pen costs £0.40, so 8 pens cost 8 × £0.40 = £3.20.
比例描述一个量随另一个量变化的关系。正比例表示一个量加倍，另一个也加倍；其图像是一条过原点的直线。常用归一法：若 5 支笔 2 英镑，则 1 支 0.40 英镑，8 支就是 8 × 0.40 = 3.20 英镑。
4. Algebraic Expressions and Simplifying | 代数表达式与化简
Algebra uses letters to stand for unknown numbers. We can collect like terms: 3a + 2b + 2a − b = (3a+2a) + (2b−b) = 5a + b. Remember that a × a = a², and a × a × a = a³. When multiplying terms, multiply the numbers and then the letters: 4x × 2y = 8xy.
代数用字母表示未知数。我们可以合并同类项：3a + 2b + 2a − b = (3a+2a) + (2b−b) = 5a + b。记住 a × a = a²，a × a × a = a³。单项式相乘时，系数相乘，字母相乘：4x × 2y = 8xy。
Expanding brackets uses the distributive law: 5(x + 3) = 5x + 15; −2(3y − 4) = −6y + 8. Factorising is the reverse process. Look for the highest common factor: 6x + 9 = 3(2x + 3). This skill is essential for solving equations.
展开括号运用分配律：5(x + 3) = 5x + 15；−2(3y − 4) = −6y + 8。因式分解是逆向过程，寻找最大公因数：6x + 9 = 3(2x + 3)。这一技能是解方程的基础。
5. Solving Equations and Inequalities | 解方程与不等式
To solve linear equations like 2x + 5 = 13, perform inverse operations on both sides: subtract 5 → 2x = 8, divide by 2 → x = 4. Always check your answer by substituting it back. For equations with unknowns on both sides, collect terms first: 5x − 3 = 2x + 9 → 5x − 2x = 9 + 3 → 3x = 12 → x = 4.
解如 2x + 5 = 13 的一元一次方程，在等式两边同时执行逆运算：减 5 → 2x = 8，除以 2 → x = 4。务必代入原方程检验。若未知数在两边，先移项：5x − 3 = 2x + 9 → 5x − 2x = 9 + 3 → 3x = 12 → x = 4。
Inequalities use the symbols < (less than), ≤ (less than or equal to), > (greater than), ≥ (greater than or equal to). Solve them like equations, but if you multiply or divide by a negative number, you must flip the inequality sign. Graph inequalities on a number line using open or closed circles.
不等式用符号 <（小于）、≤（小于等于）、>（大于）、≥（大于等于）。解法同方程，但若乘以或除以负数，不等号方向必须反转。在数轴上用空心或实心圆点表示不等式的解集。
6. Sequences and the nth Term | 数列与第 n 项
A number sequence follows a rule. In an arithmetic sequence, the difference between consecutive terms is constant. For the sequence 3, 7, 11, 15, …, the term-to-term rule is ‘add 4’. The position-to-term rule (nth term) is 4n − 1 because when n=1, 4(1)−1=3; n=2, 4(2)−1=7, etc.
数列按规律排列。在等差数列中，相邻两项的差不变。对于数列 3, 7, 11, 15, …，递推规则是“加 4”。其通项公式（第 n 项）为 4n − 1，因为 n=1 时 4×1−1=3；n=2 时 4×2−1=7，等等。
If the first difference is not constant, look for a second difference pattern. This might indicate a quadratic sequence, but in Year 8 you mostly deal with linear sequences. Always check if the given nth term formula works for the first few terms.
若一次差不是常数，可观察二次差是否恒定，这通常是二次数列的特征。但在 Year 8 阶段，主要掌握线性数列。给定通项公式后，务必验证前几项是否符合。
7. Graphs and Coordinates | 图形与坐标
Plot points in all four quadrants using coordinates (x, y), where x is the horizontal position and y the vertical. The origin is (0,0). You should be able to draw straight-line graphs from a table of values. For y = 2x + 1, choose x values, calculate y, plot the points, and draw a line.
用坐标 (x, y) 在四个象限中描点，x 表示水平位置，y 表示垂直位置。原点是 (0,0)。你需要能通过列出数值表来绘制直线图像。如 y = 2x + 1，选取 x 值，算出 y 值，描点并连线。
Identify parallel lines by having the same gradient (coefficient of x). Perpendicular lines have gradients that multiply to give −1. Also be able to read and interpret real-life graphs, such as distance-time graphs. A horizontal line means no movement; a steeper slope means faster speed.
斜率（x 的系数）相同的直线相互平行。垂直直线的斜率乘积为 −1。此外，要能读取和解释实际生活图像，如距离-时间图。水平线段表示静止；斜率越大，速度越快。
8. Angles, Polygons and Parallel Lines | 角、多边形与平行线
Know angle facts: angles on a straight line sum to 180°; angles around a point sum to 360°; vertically opposite angles are equal. In a triangle, interior angles sum to 180°; in a quadrilateral, 360°. For a polygon with n sides, sum of interior angles = (n−2) × 180°.
熟悉角度事实：直线上的邻角和为 180°；一点周角为 360°；对顶角相等。三角形内角和为 180°；四边形内角和为 360°。对于 n 边形，内角和 = (n−2) × 180°。
When parallel lines are cut by a transversal, identify corresponding angles, alternate angles and co-interior (allied) angles. Corresponding angles are equal; alternate angles are equal; co-interior angles sum to 180°. Use these to find missing angles and prove lines are parallel.
当平行线被一条截线所截，识别同位角、内错角和同旁内角。同位角相等；内错角相等；同旁内角互补（和为 180°）。运用这些性质求未知角并证明直线平行。
9. Perimeter, Area and Volume | 周长、面积与体积
Perimeter is the distance around a 2D shape. For a rectangle, P = 2(l+w). Area measures the surface; formulas needed: rectangle A = lw; triangle A = ½ bh; parallelogram A = bh; trapezium A = ½(a+b)h. Areas of compound shapes can be found by splitting into simpler shapes.
周长是二维图形一周的长度。矩形周长 P = 2(l+w)。面积度量表面大小，需记忆公式：矩形 A = lw；三角形 A = ½ bh；平行四边形 A = bh；梯形 A = ½(a+b)h。组合图形的面积可通过拆分为基本图形求得。
Volume is the space a 3D solid occupies. A cuboid’s volume V = l × w × h, measured in cubic units. Surface area is the total area of all faces. For a cube with side s, SA = 6s². Prisms have constant cross-section; volume = area of cross-section × length.
体积是三维立体所占空间。长方体体积 V = l × w × h，单位为立方单位。表面积是所有面的总面积。边长为 s 的立方体，表面积为 6s²。棱柱具有恒定截面，体积 = 截面积 × 长。
10. Statistics and Probability | 统计与概率
Collect and represent data using bar charts, line graphs, pie charts and scatter graphs. When drawing pie charts, each category’s angle = (frequency ÷ total frequency) × 360°. Interpret scatter graphs by looking for correlation: positive, negative or none. A line of best fit can help estimate values.
用条形图、折线图、饼图和散点图收集与展示数据。绘制饼图时，每个类别的角度 = (频数 ÷ 总频数) × 360°。解读散点图时，观察相关性：正相关、负相关或无相关。最佳拟合线有助于估值。
Calculate the mean, median, mode and range of a set of data. The mean is the sum divided by the number of values. The median is the middle value when ordered. The mode is the most frequent. The range = maximum − minimum, measuring spread.
计算一组数据的平均数、中位数、众数和极差。平均数是总和除以数值个数。中位数是将数据排序后最中间的值。众数是出现次数最多的值。极差 = 最大值 − 最小值，衡量数据的离散程度。
Probability is the chance of an event happening, expressed as a fraction, decimal or percentage. Probability of event A = number of favourable outcomes ÷ total number of outcomes. The probability scale goes from 0 (impossible) to 1 (certain). For mutually exclusive events, P(A or B) = P(A) + P(B).
概率表示事件发生的可能性，可用分数、小数或百分数表示。事件 A 的概率 = 有利结果的数目 ÷ 所有可能结果的数目。概率范围从 0（不可能）到 1（必然）。对于互斥事件，P(A 或 B) = P(A) + P(B)。
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