📚 AQA A Level Maths Command Words | AQA A Level 数学指令词
In AQA A Level Mathematics, command words are the action verbs in exam questions. They signal the exact type of response required, from a one-line answer to a fully reasoned proof.
在 AQA A Level 数学中，指令词是考试题目里的动作动词。它们提示你答案的确切类型，从一行答案到完整推理证明。
1. Why Command Words Matter | 为什么指令词重要
Command words control how you should respond. For example, 'state' requires only the answer, while 'show that' requires a logical sequence of steps leading to the printed result.
指令词控制你的答题方式。例如 state 只要求答案，而 show that 要求逻辑步骤推出题目给出的结果。
The same mathematical skill can be examined in different ways. Reading the command word carefully helps you decide how much working to show and avoids wasted time.
同一数学技能可以不同的方式考查。仔细阅读指令词有助于你决定展示多少过程，避免浪费时间。
| Command word | Meaning | 中文含义 |
|---|---|---|
| State / Write down | Give the answer only | 只给出答案 |
| Find / Calculate | Obtain with suitable working | 通过适当步骤求出 |
| Show that | Prove a given result | 证明给定结果 |
| Hence | Use the previous result | 利用前面的结果 |
2. State and Write Down | State 与 Write Down
'State' hout explanation or working. For example, state the period of y = sin 2x: the period is π.
State 表示无需解释或步骤，直接给出所需答案。例如，写出 y = sin 2x 的周期：周期是 π。
'Write down' nformation given. If a line has equation y = 3x + 4, you can write down the gradient as 3.
Write down 与之非常相似；它告诉你答案可以直接从所给信息中读出。如果直线方程为 y = 3x + 4，你可以直接写出斜率为 3。
3. Find, Calculate and Evaluate | Find、Calculate 与 Evaluate
'Find' is a general instruction to obtain a result, usually showing necessary working. It may ask for a coordinate, root, derivative or probability.
Find 是一个通用指令，要求得到结果，通常需要展示必要步骤。它可以要求坐标、根、导数或概率。
'Calculate' cal computation, often with a formula such as the trapezium rule or binomial coefficients. 'Evaluate' ns means substitute values and simplify to a single number, for example evaluate ∫₀² 3x² dx = 8.
Calculate 强调数值计算，通常涉及梯形法则或二项式系数等公式。Evaluate 表示代入数值并化简为一个数，例如计算 ∫₀² 3x² dx = 8。
4. Show That and Prove | Show That 与 Prove
'Show that' provides the answer in the question. You must present clear, logical working that arrives at that exact result. Copying the given answer without justification earns no marks.
Show that 在题目中已给出答案。你必须展示清晰、合乎逻辑的过程，得出该确切结果。只抄写给定答案而不加证明不得分。
'Prove' asks for a general argument covering all cases. Proof by deduction, exhaustion or contradiction may be required for identities, inequalities or divisibility statements.
Prove 要求覆盖所有情况的一般性论证。证明恒等式、不等式或整除性时可能需要演绎、穷举或反证法。
5. Solve and Simplify | Solve 与 Simplify
'Solve' fy an means find all values of the unknown that satisfy an equation or inequality. For example, solve 2x² − 5x − 3 = 0 gives x = 3 or x = −1/2.
Solve 表示求出满足方程或不等式的所有未知数值。例如，解 2x² − 5x − 3 = 0 得 x = 3 或 x = −1/2。
'Simplify' means rewrite an expression in its most compact or standard form by cancelling common factors, collecting like terms or using laws of indices. For instance, (x² − 1)/(x − 1) simplifies to x + 1, x ≠ 1.
Simplify 表示通过约去公因式、合并同类项或使用指数律，把表达式化为最简洁或标准形式。例如 (x² − 1)/(x − 1) 化简为 x + 1, x ≠ 1。
6. Factorise, Expand and Express | Factorise、Expand 与 Express
'Factorise' means write an expression as a product of factors. For example, factorise x² − 9 gives (x + 3)(x − 3), and factorise 6x² − 5x − 4 gives (2x + 1)(3x − 4).
Factorise 表示把表达式写成因式乘积。例如 x² − 9 因式分解为 (x + 3)(x − 3)，6x² − 5x − 4 因式分解为 (2x + 1)(3x − 4)。
'Expand' is the opposite process: multiply out brackets and simplify. 'Express' asks you to rewrite in a specified form, such as express 12 as a product of prime factors, or express 2/(√3) in the form a√3.
Expand 是逆过程：去括号并化简。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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