IB OCR Math: Calculation Practice Drills | IB OCR 数学：计算题专项训练

📚 IB OCR Math: Calculation Practice Drills | IB OCR 数学：计算题专项训练

Fluent calculation is the bedrock of high achievement in IB Mathematics, whether you are taking Analysis and Approaches (AA) or Applications and Interpretation (AI). These targeted practice drills cover the most common computational question types, from algebra to statistics. Each step is presented in English first followed by its Chinese equivalent, so you can strengthen both your mathematical reasoning and your bilingual command of the subject.

流利的计算是 IB 数学高分的基石，无论你选修 分析与方法 (AA) 还是 应用与解释 (AI)。本次专项训练涵盖了从代数到统计最常见的计算题型。每一步都先用英文给出、再配上中文对应内容，帮助你同步强化数学推理和双语学科能力。

1. Algebraic Simplification and Equations | 代数化简与解方程

Simplify (3x² – 2x + 5) – (x² + 4x – 1).

化简 (3x² – 2x + 5) – (x² + 4x – 1)。

Distribute the minus sign: 3x² – 2x + 5 – x² – 4x + 1.

分配负号：3x² – 2x + 5 – x² – 4x + 1。

Group like terms: (3x² – x²) + (–2x – 4x) + (5 + 1).

合并同类项：(3x² – x²) + (–2x – 4x) + (5 + 1)。

Result: 2x² – 6x + 6.

结果：2x² – 6x + 6。

Now solve 2x² – 5x – 3 = 0 by factorising.

现在用因式分解法解 2x² – 5x – 3 = 0。

Multiply a×c = 2×(–3) = –6. Find two numbers with product –6 and sum –5: –6 and +1.

计算 a×c = 2×(–3) = –6。找出乘积为 –6 且和为 –5 的两个数：–6 和 +1。

Rewrite: 2x² – 6x + x – 3 = 0. Group: 2x(x – 3) + 1(x – 3) = 0 → (2x+1)(x–3)=0.

改写：2x² – 6x + x – 3 = 0。分组：2x(x – 3) + 1(x – 3) = 0 → (2x+1)(x–3)=0。

Solutions: x = –1/2 and x = 3.

解得：x = –1/2 与 x = 3。

2. Functions and Inverse Functions | 函数与反函数

Given f(x) = √(3x – 2) for x ≥ 2/3, find its inverse f⁻¹(x) and state its domain.

已知 f(x) = √(3x – 2) ，x ≥ 2/3，求反函数 f⁻¹(x) 并写出定义域。

Write y = √(3x – 2). Swap x and y: x = √(3y – 2).

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