Year 11 Edexcel Maths: Core Topics Revision | Edexcel 11年级数学核心知识点梳理

📚 Year 11 Edexcel Maths: Core Topics Revision | Edexcel 11年级数学核心知识点梳理

As Year 11 students prepare for their Edexcel GCSE Mathematics exams, a solid understanding of the core topics is essential. This guide revisits key concepts from number, algebra, geometry, statistics, and beyond, presented in a clear bilingual format to support both English and Chinese learners.

对于11年级学生来说，在备战Edexcel GCSE数学考试时，牢固掌握核心知识点至关重要。本指南以清晰的中英双语形式，回顾了数字、代数、几何、统计等关键内容，帮助英汉双语学习者全面巩固。

1. Number: Fractions, Decimals and Percentages | 数字：分数、小数与百分比

Fractions represent parts of a whole. To add or subtract fractions, find a common denominator first.

分数表示整体的一部分。进行分数加减时，需先找到公分母。

Multiplying fractions is straightforward: multiply the numerators and denominators separately. For division, flip the second fraction and multiply.

分数乘法直接：分子乘分子，分母乘分母。除法时，将第二个分数颠倒后再相乘。

Decimals and percentages are interchangeable. To convert a decimal to a percentage, multiply by 100; to convert a percentage to a decimal, divide by 100.

小数与百分比可以互相转换。将小数乘以100可转为百分比，百分比除以100可转为小数。

To find a percentage of an amount, multiply the amount by the percentage as a decimal. Percentage increase and decrease can be calculated using multipliers (e.g., 1.15 for a 15% increase).

求某数的百分比，将总数乘以该百分比对应的小数。计算百分比增减可使用乘数（如增加15%，乘数为1.15）。

---

2. Surds and Indices | 根式与指数

Surds are irrational roots like √2 or √3. Simplify surds by factoring out perfect squares: √(a²b) = a√b.

根式是无理数的根号形式，如√2或√3。化简根式可提取完全平方因子：√(a²b) = a√b。

Rationalising the denominator involves removing a surd from the bottom of a fraction, e.g., by multiplying numerator and denominator by √a or the conjugate.

分母有理化即消除分母中的根号，通常分子分母同乘以√a或用共轭式。

Indices (powers) follow laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a⁻¹ = 1/a, a^(1/n) = ⁿ√a.

指数（幂）遵循运算法则：aᵐ × aⁿ = aᵐ⁺ⁿ，aᵐ ÷ aⁿ = aᵐ⁻ⁿ，(aᵐ)ⁿ = aᵐⁿ，a⁰=1，a⁻¹=1/a，a^(1/n) = ⁿ√a。

Fractional indices: a^(m/n) = (ⁿ√a)ᵐ or ⁿ√(aᵐ).

分数指数：a^(m/n) = (ⁿ√a)ᵐ 或 ⁿ√(aᵐ)。

---

3. Algebraic Expressions and Equations | 代数表达式与方程

Simplify expressions by collecting like terms and using the distributive law: a(b + c) = ab + ac.

化简表达式：合并同类项并运用分配律 a(b + c) = ab + ac。

Factorising reverses expansion. Common methods include taking out a common factor, difference of two squares: a² – b² = (a + b)(a – b), and quadratic trinomials.

因式分解是展开的逆过程。常用方法包括提取公因式、平方差公式 a² – b² = (a+b)(a-b) 以及二次三项式分解。

Solving linear equations: isolate the variable by performing inverse operations on both sides.

解一元一次方程：通过等式两边逆运算，使未知数单独出现。

Quadratic equations can be solved by factorising, completing the square, or using the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a).

解二次方程可用因式分解法、配方法或求根公式：x = (-b ± √(b² – 4ac)) / (2a)。

Simultaneous equations can be solved by elimination or substitution. Linear and quadratic pairs often require substitution.

联立方程组可用消元法或代入法求解。当一个方程为一次、另一个为二次时，通常使用代入法。

---

4. Inequalities and Sequences | 不等式与数列

Inequalities use signs: <, >, ≤, ≥. Solve similarly to equations, but reverse the sign when multiplying or dividing by a negative number.

不等式使用 <, >, ≤, ≥ 符号。解法与方程类似，但乘以或除以负数时，不等号方向要改变。

Represent inequalities on a number line with open or closed circles, and shade the appropriate region.

在数轴上表示不等式时，使用空心或实心圆点，并涂出正确区域。

Graphical inequalities are shown by shading regions on a coordinate plane, bounded by straight or curved lines.

图形不等式在坐标系中通过阴影区域表示，边界可为直线或曲线。

Sequences: an arithmetic sequence has a common difference d, and the nth term is a + (n-1)d.

数列：等差数列有公差 d，第 n 项公式为 a + (n-1)d。

Quadratic sequences have a second difference that is constant. The nth term is of the form an² + bn + c.

二次数列的二次差为常数，第 n 项通常形式为 an² + bn + c。

---

5. Graphs and Functions | 图形与函数

Straight-line graphs have equation y = mx + c, where m is gradient (rise/run) and c is y-intercept.

直线图方程为 y = mx + c，其中 m 为斜率（纵差/横差），c 为 y 截距。

Parallel lines have the same gradient; perpendicular lines have gradients whose product is -1.

平行线斜率相等；垂直线的斜率乘积为 -1。

Quadratic graphs (parabolas) are U-shaped or n-shaped. The roots are where y = 0; the turning point can be found by completing the square.

二次函数图像为抛物线，开口向上或向下。与 x 轴交点为根；可通过配方法求顶点（转折点）。

Cubic, reciprocal and exponential graphs each have distinctive shapes. Recognise and sketch them.

三次、倒数及指数函数图像各有特点，需能识别并草图绘制。

Functions f(x) can be transformed: f

Published by TutorHao | Year 11 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）