📚 Year 9 OCR Further Maths: Quick Reference Formula & Theorem Handbook | Year 9 OCR 进阶数学：公式定理速查手册
This quick reference handbook brings together the essential formulas, identities, and theorems you need for the Year 9 OCR Further Mathematics course. Use it to revise key algebraic techniques, geometric relationships, trigonometric ratios, and statistical measures. Each entry is stated clearly and compactly so you can check your memory or look up a rule during practice.
本速查手册汇集了 Year 9 OCR 进阶数学课程所必需的基本公式、恒等式和定理。可用于复习关键的代数技巧、几何关系、三角比和统计度量。每一条目表述清晰简洁，便于你在练习时核对记忆或查阅规则。
1. Algebraic Expressions and Identities | 代数表达式与恒等式
Distributive law: a(b + c) = ab + ac. Multiply each term inside the bracket by the term outside.
分配律： a(b + c) = ab + ac。将括号外的项乘以括号内的每一项。
Difference of two squares: a² – b² = (a + b)(a – b). This is particularly useful for factorising.
平方差公式： a² – b² = (a + b)(a – b)。这在因式分解时特别有用。
Perfect square expansion: (a + b)² = a² + 2ab + b² and (a – b)² = a² – 2ab + b².
完全平方展开： (a + b)² = a² + 2ab + b² 以及 (a – b)² = a² – 2ab + b²。
Factorising by grouping: For an expression like ax + ay + bx + by, group as a(x + y) + b(x + y) = (a + b)(x + y).
分组分解法： 对于 ax + ay + bx + by，可分组为 a(x + y) + b(x + y) = (a + b)(x + y)。
2. Linear Equations and Inequalities | 线性方程与不等式
Solving a linear equation: Use inverse operations to isolate the variable. E.g., 2x + 3 = 11 → 2x = 8 → x = 4.
解线性方程： 使用逆运算将变量分离。例如 2x + 3 = 11 → 2x = 8 → x = 4。
Solving linear inequalities: , : Treat like equations, but reverse the inequality sign when multiplying or dividing by a negative number. E.g., –2x < 6 → x > –3.
解线性不等式： 与解方程类似，但当乘以或除以负数时要反转不等号。例如 –2x < 6 → x > –3。
Graphing inequalities on a number line: Open circle for < or >, closed circle for ≤ or ≥. Shade the solution region.
在数轴上表示不等式： 对于 < 或 > 用空心圆圈，≤ 或 ≥ 用实心圆圈。涂出解集区域。
3. Quadratic Equations | 二次方程
Standard form: ax² + bx + c = 0, where a ≠ 0.
标准形式： ax² + bx + c = 0，其中 a ≠ 0。
Factorising quadratics: : Find two numbers that multiply to ac and add to b. For x² + 5x + 6, the numbers 2 and 3 give (x + 2)(x + 3) = 0.
因式分解二次式： 找到两个数其积为 ac，和为 b。例如 x² + 5x + 6，2 和 3 满足，得 (x + 2)(x + 3) = 0。
Quadratic formula: x = [–b ± √b² – 4ac] / (2a). Use when factorising is difficult.
二次公式： x = [–b ± √b² – 4ac] / (2a)。当因式分解困难时使用。
Discriminant: Δ = b² – s: Δ > 0 → two distinct real roots; Δ = 0 → one real repeated root; Δ < 0 → no real roots.
判别式： Δ = b² – 4ac。它决定根的性质：Δ > 0 → 两个不等实根；Δ = 0 → 一个实重根；Δ < 0 → 无实数根。
Completing the square: Write x² + bx as (x + b/2)² – (b/2)². E.g., x² + 6x = (x + 3)² – 9.
配方法： 将 x² + bx 写成 (x + b/2)² – (b/2)²。例如 x² + 6x = (x + 3)² – 9。
Published by TutorHao | Year 9 进阶数学 Revision Series | aleveler.com
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