IGCSE Mathematics 100 Practice Questions | G-1 练习册 100

📚 IGCSE Mathematics 100 Practice Questions | G-1 练习册 100

This workbook is a concise revision tool built around 100 exam-style questions. It covers the key strands of the IGCSE Mathematics syllabus: number, algebra, geometry, trigonometry, statistics, and probability. Working through the entire set will sharpen your computational fluency, reinforce conceptual understanding, and build the confidence needed for the final exam.

这本练习册以100道考试风格的题目为核心，是一份精炼的复习工具。它涵盖IGCSE数学教学大纲的主要模块：数、代数、几何、三角学、统计与概率。完整刷完这100题，能够提升计算熟练度、深化概念理解，并为最终考试建立信心。

1. Overview of the Workbook | 练习册概览

Each question has been selected to target a specific skill or exam technique. You will find a balanced mix of short calculation questions, multi-step problem-solving tasks, and interpretation questions based on real-life contexts. The questions are arranged by topic so you can practise systematically.

每道题都经过精选，旨在对应一项具体技能或考试技巧。你会看到简短计算题、多步解题任务和基于实际情境的题意理解题的均衡搭配。题目按主题分类，方便你有条不紊地进行练习。

The distribution of questions across topics is shown below. Use this table to plan your revision time.

各主题的题目分布如下表所示。可根据此表规划复习时间。

Topic	Number of Questions
Number	15
Algebra	25
Geometry	20
Trigonometry	10
Statistics	20
Probability	10
Total	100

2. Number and Arithmetic | 数与算术

The number section tests your ability to work with integers, fractions, decimals, percentages, ratios, powers, roots, and standard form. A typical question may ask you to evaluate an expression involving negative indices or to convert between fractions and decimals.

数模块考查整数、分数、小数、百分数、比、幂、根和标准形式的运用能力。典型题目要求计算含负指数的表达式，或在分数与小数之间进行转换。

For example, you might be asked to work out:

例如，你可能会被要求计算：

2⁻³ × √16 = 1/8 × 4 = 1/2

Remember that a negative index means the reciprocal of the positive power: 2⁻³ = 1/2³ = 1/8. Also, √16 = 4, so the product is 1/2. When using standard form, a number such as 4500 is written as 4.5 × 10³, and 0.0062 as 6.2 × 10⁻³.

请记住：负指数表示正指数之倒数：2⁻³ = 1/2³ = 1/8。同时√16 = 4，因此乘积为1/2。使用标准形式时，4500应写作4.5 × 10³，而0.0062写作6.2 × 10⁻³。

A common error is to treat 2⁻³ as −8. In fact, 2⁻³ = 1/(2 × 2 × 2) = 1/8. Always write down the fraction before simplifying.

常见错误是将2⁻³误认为−8。实际上2⁻³ = 1/(2 × 2 × 2) = 1/8。写下分数再化简，不要跳步。

3. Algebra | 代数

Algebra is the largest section in the workbook. Questions cover simplifying expressions, expanding brackets, factorising, solving linear and quadratic equations, rearranging formulas, sequences, inequalities, and coordinate geometry.

代数是练习册中占比最大的模块。题目包括化简表达式、展开括号、因式分解、解一次与二次方程、重排公式、数列、不等式和坐标几何。

One typical quadratic equation is:

一个典型的二次方程为：

x² − 5x + 6 = 0

Factorising the left-hand side gives (x − 2)(x − 3) = 0. Therefore, x = 2 or x = 3. Always check your solution by substituting back into the original equation.

因式分解左边得(x − 2)(x − 3) = 0。因此x = 2或x = 3。务必把解代回原方程检查。

For simultaneous equations, use substitution or elimination. For example:

对于联立方程，可用代入法或消元法。例如：

y = 2x + 1, x + y = 10

Substitute y = 2x + 1 into the second equation: x + (2x + 1) = 10, so 3x + 1 = 10, giving 3x = 9, hence x = 3 and y = 7.

将y = 2x + 1代入第二个方程：x + (2x + 1) = 10，即3x + 1 = 10，得3x = 9，所以x = 3，y = 7。

4. Geometry and Mensuration | 几何与测量

Geometry questions require knowledge of angle properties, triangle congruence and similarity, circle theorems, and perimeter, area, and volume of common shapes. You should be able to state the formula for the area of a circle, the circumference of a circle, and the surface area of a cylinder.

几何题需要掌握角的性质、三角形全等与相似、圆定理，以及常见图形的周长、面积和体积。你应当能熟练写出圆的面积公式、圆的周长公式和圆柱的表面积公式。

The area of a circle is A = πr², and the circumference is C = 2πr. For a sphere of radius r, the volume is V = (4/3)πr³. To avoid errors, keep π in your calculation until the final step, then round sensibly.

圆面积公式为A = πr²，周长公式为C = 2πr。对于半径为r的球体，体积为V = (4/3)πr³。为避免误差，π应先保留在计算中，最后再合理取近似值。

Example: A cylinder has a radius of 5 cm and a height of 10 cm. Its curved surface area is 2πrh = 2 × π × 5 × 10 = 100π ≈ 314 cm². If you are asked for the total surface area, add the two circular ends: 2πr² + 2πrh = 50π + 100π = 150π ≈ 471 cm².

例：一个圆柱的半径为5 cm，高为10 cm。其侧面积为2πrh = 2 × π × 5 × 10 = 100π ≈ 314 cm²。若要求总表面积，要加上两个圆形底面：2πr² + 2πrh = 50π + 100π = 150π ≈ 471 cm²。

Remember that when two triangles are similar, corresponding sides are in the same ratio. If the scale factor is k, the area scale factor is k² and the volume scale factor is k³.

记住两个三角形相似时，对应边长成比例。若相似比为k，则面积比为k²，体积比为k³。

5. Trigonometry | 三角学

Trigonometry at IGCSE mainly concerns right-angled triangles. You must know the three basic ratios:

IGCSE三角学主要涉及直角三角形。你必须掌握三个基本比值：

sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent

Use the acronym SOH-CAH-TOA to remember them. You should recall the exact values for angles 30°, 45°, and 60°.

可用英文缩写SOH-CAH-TOA帮助记忆。你还应记住30°、45°和60°角的精确值。

Angle	sin	cos	tan
30°	1/2	√3/2	1/√3
45°	√2/2	√2/2	1
60°	√3/2	1/2	√3

For non-right-angled triangles, you may need the sine rule or cosine rule. These are given in the formula sheet in many exams, but you must know when to apply them.

对于非直角三角形，可能需要正弦定理或余弦定理。许多考试会给公式表，但你必须知道何时使用它们。

6. Statistics and Probability | 统计与概率

The statistics questions involve calculating the mean, median, mode, and range of a data set. You should also be able to read frequency tables, bar charts, pie charts, and cumulative frequency graphs.

统计题涉及计算数据集的平均数、中位数、众数和极差。你还应能读懂频数表、条形图、饼图和累积频数图。

For the mean of a set of values, use the formula:

一组数据的平均值用以下公式：

mean = sum of values / number of values

Probability questions ask for the chance of an event happening. The probability of an event is always between 0 and 1. For independent events A and B, the probability that both occur is P(A and B) = P(A) × P(B).

概率题询问事件发生的可能性。事件概率总在0与1之间。对于独立事件A与B，两者同时发生的概率为P(A且B) = P(A) × P(B)。

Example: If you roll a fair six-sided die, the probability of rolling a 6 is 1/6. The probability of rolling a 6 twice in a row is (1/6) × (1/6) = 1/36.

例如：掷一枚均匀六面骰子，得到6的概率是1/6。连续两次得到6的概率为(1/6) × (1/6) = 1/36。

When using tree diagrams, multiply probabilities along the branches and add probabilities for different routes to the same outcome.

使用树状图时，沿分支相乘概率，再将通向同一结果的不同路径概率相加。

7. Problem Solving Strategies | 解题策略

Many questions in the workbook are presented in context. A structured approach helps you deal with them efficiently. Follow these four steps for every problem.

练习册中许多题目以情境形式呈现。采用结构化方法能帮助你高效解题。对每道题都遵守以下四个步骤。

Read the question carefully and underline all given data. Identify what you are asked to find.

仔细读题，划出所有已知数据，明确要求什么。
Choose the appropriate method or formula. Relate the problem to a similar question you have seen before.

选择合适的方法或公式，把题目与以前见过的类似题联系起来。
Carry out the calculation, showing every step. Keep units in your working.

分步计算，展示每一步，并在过程中保留单位。
Check your answer. Does it make sense? Round to an appropriate degree of accuracy if required.

检查答案：结果是否合理？如需要，按要求精确到适当位数。

8. Common Mistakes to Avoid | 常见错误

Certain errors appear again and again in IGCSE mathematics exams. Being aware of them will help you avoid losing easy marks.

某些错误在IGCSE数学考试中反复出现。了解这些错误有助于你避免丢掉容易的分数。

Sign errors: When expanding brackets, remember to multiply every term inside the bracket by the factor outside, including the signs. For example, -(x − 3) = -x + 3.

符号错误：展开括号时，要用括号外的因式乘以括号内每一项，包括符号。例如-(x − 3) = -x + 3。
Forgetting unit conversion: In geometry, if lengths are in metres and areas are in square metres, do not mix centimetres and metres without converting.

忘记单位换算：几何中长度以米为单位、面积以平方米为单位时，不要在没有换算的情况下混用厘米和米。
Rounding too early: Do not round intermediate answers. Keep full accuracy until the final answer.

过早取近似值：不要在中间步骤就四舍五入。保持完整精度，直到最后答案。
Misreading the scale on a graph: When reading from a graph, always check the axes and the intervals between grid lines.

读图时看错刻度：从图上读取数据时，务必检查坐标轴以及网格线之间的间隔。

9. Practice Regimen | 练习方法

To get the most from the 100-question workbook, plan a regular practice schedule. Rather than finishing all questions in one session, spread the work across several days.

为充分利用这100题，请规划规律的练习计划。不要一次性全部完成，而是分散在数天内进行。

A suggested schedule is:

一个建议计划是：

Day	Questions	Time
1	1-20	40 min
2	21-40	40 min
3	41-60	40 min
4	61-80	40 min
5	81-100	40 min

After completing each day’s set, mark your answers and record the topics where you lost marks. Spend at least 10 minutes reviewing your mistakes. On day 6, attempt the questions you previously got wrong.

每天完成后批改答案，并记录失分的主题。至少花10分钟复习错误。第6天，重新做之前做错的题目。

10. Self-Assessment and Review | 自我评估与复习

Use a mark scheme or a friend to check your answers. For each question, give yourself full, partial, or zero marks. This will give you an accurate picture of your strengths and weaknesses.

使用评分标准或请同学帮忙批改。每道题给自己评满分、部分分或零分。这能让你准确了解自己的强项和弱项。

A useful review technique is to create a one-page error log. Write down:

一个有效的复习技巧是制作一页错误记录。写下：

The question number and topic.

题号和主题。
The mistake you made.

你犯的错误。
The correct method.

正确的方法。
A similar practice question for future revision.

一道相似的练习题，供将来复习使用。

By tracking your progress across the 100 questions, you will see consistent improvement. Revisit the workbook every weekend until the exam. Aim to reduce the time you spend on each question while maintaining accuracy.

通过跟踪这100题的完成情况，你会看到持续进步。每周都重温练习册，直到考试。目标是在保持准确率的同时，缩短每道题的用时。

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IGCSE Mathematics 100 Practice Questions | G-1 练习册 100