Math Problem Solving: Test Prep | 数学解题：考试准备

📚 Math Problem Solving: Test Prep | 数学解题：考试准备

Success in mathematics is not only about knowing formulas; it is about applying the right strategies to solve problems clearly and efficiently. This guide provides a step-by-step approach to tackling math problems in your exams, with practical tips for IGCSE and beyond.

数学考试的成功不仅在于掌握公式，更在于运用正确的策略来清晰、高效地解题。本指南为你的数学考试提供一套循序渐进的解题方法，并附有实用的技巧，适用于 IGCSE 及其他考试。

1. Understand the Problem | 理解题目

Before you start calculating, read the question carefully. Ask yourself: What is given? What is being asked? Underline key numbers and mathematical words such as “sum,” “difference,” “product,” or “ratio.” This prevents careless errors from misreading.

在开始计算之前，请仔细阅读题目。问问自己：已知条件是什么？要求解的是什么？用下划线标出关键数字和数学关键词，如“和”“差”“积”“比”等。这样可以避免因误读题目而产生的粗心错误。

Identify the unknown variable and express it with a symbol such as x or y.

找出未知量，并用 x 或 y 等符号表示。
Rewrite the problem in your own words to confirm you understand the goal.

用自己的话复述题目，以确认你理解了目标。

2. Devise a Plan | 制定计划

Once the problem is clear, choose an appropriate strategy. Common strategies include: drawing a diagram, making a table, looking for a pattern, working backward, or solving a simpler version of the problem. For algebraic problems, this means setting up an equation.

一旦问题清晰，就要选择合适的解题策略。常见策略包括：画图、列表、找规律、倒推，或是先解决一个更简单的版本。对于代数问题，这通常意味着建立方程。

Example: The sum of a number and 15 is 32. Find the number.

x + 15 = 32 → x = 32 − 15 → x = 17

Here, the plan is to use inverse operations to isolate x.

这里的计划是使用逆运算来求出 x。

3. Solve Step by Step | 逐步求解

Execute your plan one step at a time, writing clearly. Show all working lines, because in IGCSE exams partial credit is awarded for correct methods even if the final answer is wrong. Arrange your calculations neatly so you can review them later.

一步一步执行你的计划，并清晰写出过程。展示所有计算步骤，因为在 IGCSE 考试中，即使最终答案错误，正确的方法也能获得部分分数。整齐排列你的计算过程，以便之后复查。

Step	Operation	Result
1	Subtract 15 from both sides	x = 17
2	Check: 17 + 15 = 32	✓

4. Check Your Answer | 验算检查

After solving, always plug the answer back into the original problem. For equations, substitute x into the left-hand side and verify it equals the right-hand side. Also consider whether the answer makes sense in the context of the question, especially for word problems about length, money, or time.

求解之后，务必将答案代回原题验证。对于方程，把 x 代入左边，确认它等于右边。同时考虑答案在题目语境中是否合理，尤其是涉及长度、金钱或时间的实际应用题。

Check: If the answer were 18, then 18 + 15 = 33 ≠ 32, so 18 is wrong.

5. Tackle Multiple-Choice Questions | 攻克选择题

In multiple-choice questions, read every option before deciding. Use the process of elimination to remove obviously incorrect answers. If you are stuck, substitute the options into the problem to see which one satisfies the condition.

做选择题时，先阅读所有选项，再用排除法去掉明显错误的答案。如果卡住了，可以把各个选项代入题目，看哪一个满足条件。

Try rough estimation before doing exact calculation.

先进行粗略估算，再做精确计算。
Be careful with signs and units; exam setters often include traps.

注意正负号和单位，出题者常设置陷阱。

6. Manage Your Time | 时间管理

Allocate time according to the marks for each question. In an IGCSE paper, a two-mark question should not take ten minutes. A good rule is: use about one minute per mark for the first attempt, then return to harder questions later if time remains.

根据题目的分值分配时间。在 IGCSE 试卷中，一道 2 分题不应该耗时 10 分钟。一个实用的规则是：初次答题时，大约每分钟做 1 分值的题目，之后若有剩余时间再回头处理难题。

Marks	Suggested Time
1 mark	1 minute
2 marks	2–3 minutes
5 marks	5–7 minutes

7. Common Problem Types | 常见题型

Learn to recognize the structure of typical exam problems. The most common IGCSE types include: percentages and profit/loss, ratios and proportions, area and perimeter, linear equations, simultaneous equations, and probability. Each type has a signature method.

学习识别典型考题的结构。IGCSE 最常见的题型包括：百分比与盈亏、比与比例、面积与周长、线性方程、联立方程和概率。每种题型都有其标志性的解法。

Percentages: Convert the percentage to a decimal and multiply.

百分比：将百分数化成小数再相乘。
Ratios: Divide the total by the sum of ratio parts.

比：用总量除以比值的各部分之和。
Area: Identify the shape and apply the correct formula.

面积：识别图形并套用对应公式。

8. Practice with Sample Questions | 真题演练

Now let us apply these strategies to a few sample questions. Work through them before reading the solutions.

现在让我们用这些策略来练习几个例题。请先自己作答，再阅读解答。

Sample 1: A shop increases a price of $40 by 15%. Find the new price.

例题 1：一家商店将 40 美元的价格上调 15%。求新价格。

Increase = 15% × 40 = 0.15 × 40 = 6

New price = 40 + 6 = 46

Sample 2: Solve the equation 3x − 5 = 16.

例题 2：解方程 3x − 5 = 16。

3x − 5 = 16 → 3x = 21 → x = 7

9. Avoid Common Mistakes | 避免常见错误

Avoid losing marks carelessly. Do not forget to change the sign when moving terms across the equals sign. Be careful with the order of operations: brackets first, then indices, then multiplication and division, then addition and subtraction (BIDMAS). Write everything down instead of doing steps mentally.

避免因粗心而丢分。移项到等号另一边时不要忘记变号。注意运算顺序：先括号，再指数，然后乘除，最后加减（BIDMAS）。把步骤写下来，不要凭空心算。

Always include units in your final answer when the question uses them.

当题目带有单位时，最终答案务必写上单位。
Do not round too early; keep full precision until the last step.

不要过早四舍五入，直到最后一步再取精确值。

5 + 3 × 2 = 5 + 6 = 11, not 16.

10. Build Exam Confidence | 建立考试信心

Confidence comes from preparation. Review past papers, practice timed exercises, and make sure you understand your mistakes. Before the exam, sleep well and prepare your calculator and geometry tools. During the exam, keep calm: begin with questions you can solve quickly, then move to harder ones.

信心来自充分的准备。复习历年真题，进行限时训练，并确保理解自己的错误。考试前保证睡眠充足，准备好计算器和绘图工具。考试中保持冷静：先做能快速解决的问题，再处理难题。

Remember that every mark counts. Even when you cannot fully solve a problem, write down any relevant formulas or partial steps; they may earn you marks. Stay positive and trust your training.

记住每一分都很重要。即使不能完全解出一道题，写下相关的公式或部分步骤也可能帮你得分。保持积极心态，相信自己的训练。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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Math Problem Solving: Test Prep | 数学解题：考试准备