GCSE OCR Maths: Mind Map Quick Revision | GCSE OCR 数学：思维导图速记

📚 GCSE OCR Maths: Mind Map Quick Revision | GCSE OCR 数学：思维导图速记

Mind maps offer a visual and structured way to revise GCSE OCR Mathematics, linking key ideas across the syllabus. This guide presents a complete mind map of essential topics, including Number, Algebra, Geometry, Statistics and Probability, with quick-reference formulas, rules and memory aids to boost your exam performance.

思维导图提供了一种可视化且结构化的方式来复习GCSE OCR数学，将课程中的关键思想联系起来。本指南呈现了核心主题的完整思维导图，包括数字、代数、几何、统计和概率，并提供快速参考公式、法则和记忆辅助，以提升你的考试成绩。

---

1. Number Branch | 数字分支

The Number branch covers types of numbers, operations, and numerical reasoning. Start from the central node: Number.

数字分支涵盖数字类型、运算和数值推理。从中心节点“数字”开始。

Types of Numbers: Natural numbers (ℕ), Integers (ℤ), Rational numbers (ℚ), Irrational numbers (surds and π), Real numbers (ℝ).

数字类型：自然数(ℕ)、整数(ℤ)、有理数(ℚ)、无理数(根式和π)、实数(ℝ)。

Prime Factors, HCF & LCM: Use factor trees to express a number as a product of primes; HCF = product of common prime factors with lowest powers; LCM = product of all prime factors with highest powers.

质因数、HCF和LCM：使用因子树将数字表示为质数的乘积；HCF = 取公共质因数的最小幂次之积；LCM = 取所有质因数的最高幂次之积。

Fractions, Decimals & Percentages: Convert between them. Key operations: add/subtract fractions by finding common denominator; multiply across; divide by multiplying by the reciprocal.

分数、小数和百分比：相互转换。关键运算：加减分数找公分母；分子乘分子，分母乘分母；除法乘以倒数。

Standard Form: Write numbers as a × 10ⁿ where 1 ≤ a < 10 and n is an integer. Useful for very large or very small numbers.

标准形式：将数字写成 a × 10ⁿ 的形式，其中 1 ≤ a < 10，n为整数。适用于非常大或非常小的数字。

Rounding & Estimation: Round to decimal places or significant figures. Estimate by rounding to 1 significant figure.

四舍五入与估算：四舍五入到小数位或有效数字。通过四舍五入到一位有效数字进行估算。

---

2. Algebra Branch | 代数分支

Algebra includes simplifying expressions, solving equations, and working with formulae. The mind map sub-branches cover linear, quadratic, and simultaneous equations.

代数包括化简表达式、解方程和处理公式。思维导图子分支涵盖线性、二次和联立方程。

Simplifying Expressions: Collect like terms, expand brackets using the distributive law (e.g., a(b+c) = ab + ac), and factorise by extracting the highest common factor.

化简表达式：合并同类项，使用分配律展开括号（例如 a(b+c) = ab + ac），并通过提取最高公因式进行因式分解。

Linear Equations: Solve by isolating the variable using inverse operations. Always perform the same operation on both sides of the equation.

线性方程：通过逆运算隔离变量来求解。恒等变形，等式两边进行相同操作。

Quadratic Equations: Solve by factorising into two brackets, completing the square, or using the formula: x = [-b ± √(b² – 4ac)] / (2a).

二次方程：通过因式分解为两个括号、配方法或使用公式：x = [-b ± √(b² – 4ac)] / (2a) 求解。

Simultaneous Equations: Solve by elimination (add/subtract equations) or substitution (replace one variable with an expression).

联立方程组：通过消元法（方程相加/相减）或代入法（用一个变量的表达式替换另一个变量）求解。

Sequences: nth term of an arithmetic sequence: a + (n-1)d, where a = first term, d = common difference. Quadratic sequences: find the second difference which is constant.

数列：等差数列的第n项：a + (n-1)d，其中a为首项，d为公差。二次序列：寻找常数二阶差分。

---

3. Graphs & Functions | 图形与函数

Visual representation of functions helps connect algebra and geometry. Key graph types must be memorised.

函数的可视化表示有助于连接代数和几何。必须记住关键的图形类型。

Linear Graphs: y = mx + c, where m = gradient, c = y-intercept. Parallel lines have equal gradients; perpendicular lines have gradients whose product is -1.

线性图：y = mx + c，其中m = 斜率，c = y轴截距。平行线斜率相等；垂直线斜率乘积为-1。

Quadratic Graphs: Parabolas, y = ax² + bx + c. If a > 0, u-shaped (minimum); if a < 0, n-shaped (maximum). Roots are the x-intercepts.

二次函数图：抛物线，y = ax² + bx + c。若a > 0，开口向上（最小值）；若a < 0，开口向下（最大值）。根为x轴截距。

Cubic, Reciprocal & Exponential: y = x³ (s-shaped), y = 1/x (hyperbola with asymptotes), y = kˣ (exponential growth or decay).

三次、反比例和指数函数：y = x³（S形），y = 1/x（带渐近线的双曲线），y = kˣ（指数增长或衰减）。

Transformations: f(x) + a (vertical shift), f(x + a) (horizontal shift), -f(x) (reflection in x-axis), f(-x) (reflection in y-axis).

变换：f(x) + a（垂直平移），f(x + a)（水平平移），-f(x)（x轴对称），f(-x)（y轴对称）。

Real-life Graphs: Distance-time, velocity-time, conversion graphs. Gradient of distance-time gives speed; area under velocity-time gives distance.

实际图形：距离-时间图、速度-时间图、换算图。距离-时间图的斜率给出速度；速度-时间图下的面积给出距离。

---

4. Ratio, Proportion & Rates of Change | 比例、比率与变化率

This branch connects multiplicative reasoning across many topics.

此分支将乘法推理贯穿多个主题。

Simplifying Ratios: Divide all parts by their HCF. Write in the form 1:n where appropriate.

化简比例：将所有部分除以其最高公因数。适当时写成 1:n 的形式。

Direct Proportion:Published by TutorHao | GCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）