📚 Year 10 Eduqas Maths: Summer Bridging and Revision Guide | Year 10 Eduqas 数学：暑期预习与衔接课程
Summer gives you a valuable window to solidify the skills you developed in Year 9 and to build confidence for the GCSE course ahead. This bridging guide covers the essential topics from number, algebra, geometry, statistics and probability, helping you hit the ground running when you return to school.
暑假为你提供了一个宝贵的机会，可以巩固九年级所学的技能，并为接下来的GCSE课程树立信心。这份衔接指南涵盖了数、代数、几何、统计和概率等核心主题，帮助你在返校后迅速进入学习状态。
1. Introduction: Why a Summer Bridging Course? | 引言：为什么需要暑期衔接课程？
The transition from Key Stage 3 to GCSE mathematics can feel challenging. The Eduqas specifications build on earlier work but require a deeper understanding of concepts and the ability to apply them to multi-step problems.
从关键阶段3过渡到GCSE数学可能会让人感到有些吃力。Eduqas的课程大纲建立在之前学习的基础之上，但要求你对概念有更深入的理解，并能将其应用到多步骤的问题中。
A summer bridging programme allows you to revisit areas where you felt less confident and to preview the style of questions you will meet in Year 10. Spending just 20–30 minutes a day on focused practice can make a significant difference.
暑期衔接计划能让你重温那些不太自信的领域，并提前熟悉十年级会遇到的题型。每天只需花20–30分钟进行有针对性的练习，就能带来显著的变化。
In this guide, we have selected the most important Year 9 topics and introduced the key ideas you will need for the first term of Year 10. Work through the sections, try the examples and keep a notebook of any questions you find tricky.
在本指南中，我们挑选了最重要的九年级课题，并介绍了十年级第一学期所需要的关键概念。你可以逐节学习，尝试例题，并将感到困难的问题记录在笔记本上。
2. Number Skills: Fractions, Decimals and Percentages | 数字技能：分数、小数和百分数
Being fluent with fractions, decimals and percentages is essential across almost every GCSE topic. You should be able to convert between them quickly and perform all four operations.
熟练掌握分数、小数和百分数几乎对每一个GCSE课题都至关重要。你需要能够快速在它们之间进行转换，并完成所有的四则运算。
Recall that ½ = 0.5 = 50%, ¼ = 0.25 = 25%, and ¾ = 0.75 = 75% For repeating decimals, use dots to indicate the recurring digits; for example, 1/3 = 0.3̇.
请记住：½ = 0.5 = 50%，¼ = 0.25 = 25%，¾ = 0.75 = 75%。将任意分数转换为小数，只需用分子除以分母。对于循环小数，用点号表示循环节；例如 1/3 = 0.3̇。
Adding and subtracting fractions requires a common denominator:
- Find the least common multiple of the denominators. | 找到分母的最小公倍数。
- Rewrite each fraction with this denominator. | 用该分母重新书写每一个分数。
- Add or subtract the numerators and keep the denominator. | 将分子相加或相减，分母不变。
To multiply fractions, multiply the numerators together and multiply the denominators together. To divide by a fraction, multiply by its reciprocal.
分数相乘时，将分子与分子相乘、分母与分母相乘。除以一个分数时，则乘以其倒数。
Example: (2/3) ÷ (4/5) = 2/3 × 5/4 = 10/12 = 5/6
Percentage increase and decrease are also vital. To increase £80 by 15%, multiply by 1.15 to get £92. To decrease £120 by 30%, multiply by 0.70 to get £84.
百分数的增加和减少同样重要。将80英镑增加15%，乘以1.15得到92英镑。将120英镑减少30%，乘以0.70得到84英镑。
3. Algebraic Foundations: Expressions and Simplifying | 代数基础：表达式与化简
Algebra is the language of mathematics. You need to be comfortable collecting like terms, expanding brackets and using index laws.
代数是数学的语言。你需要熟练地合并同类项、展开括号以及运用指数运算法则。
Like terms have exactly the same variable part. For example, 3a and 5a are like, but 3a and 3a² are not. Simplify 4x + 2y − 3x + 5y to x + 7y.
同类项具有完全相同的字母部分。例如，3a 和 5a 是同类项，但 3a 和 3a² 则不是。将 4x + 2y − 3x + 5y 化简为 x + 7y。
(2x − 5) = 6x − 15. Expand and simplify 2(3x + 1) + 3(x − 4) = 6x + 2 + 3x − 12 = 9x − 10.
展开一个括号时，将括号外的项乘以括号内的每一项。例如，3(2x − 5) = 6x − 15。展开并化简 2(3x + 1) + 3(x − 4) = 6x + 2 + 3x − 12 = 9x − 10。
The index laws are especially important:
- xᵐ × xⁿ = xᵐ⁺ⁿ | 同底数幂相乘，底数不变，指数相加。
- xᵐ ÷ xⁿ = xᵐ⁻ⁿ | 同底数幂相除，底数不变，指数相减。
- (xᵐ)ⁿ = xᵐ×ⁿ | 幂的乘方，底数不变，指数相乘。
- x⁰ = 1 (for any non-zero x) | 任何非零数的0次方等于1。
Make sure you can apply these both forwards and backwards, as you will need them when solving equations and rearranging formulas.
请确保你能够正向和逆向运用这些法则，因为在解方程和变换公式时都会用到它们。
4. Equations and Inequalities | 方程与不等式
Solving linear equations is one of the most fundamental skills in GCSE mathematics. The aim is to isolate the unknown on one side of the equation by performing the same operation on both sides.
解一次方程是GCSE数学中最基本的技能之一。目标是通过在方程两边同时进行相同的运算，将未知数单独移到方程的一边。
Solve: 5y + 7 = 2y − 8
de by 3: y = −5. Always check your answer by substituting back into the original equation.
两边同时减去 2y：3y + 7 = −8。再两边同时减去 7：3y = −15。除以3：y = −5。务必通过代入原方程来检验答案是否正确。
Now extend this to inequalities. The rules are almost identical, except: if you multiply or divide both sides by a negative number, you must reverse the direction of the inequality sign.
现在将这一方法扩展到不等式。解不等式的规则几乎完全相同，但有一个例外：当你将两边同时乘以或除以一个负数时，必须反转不等号的方向。
solution on a number line with an open circle for < or >, and a closed circle for ≤ or ≥.
例如，−2x > 6，两边除以 −2，得到 x < −3。在数轴上表示解集时，< 或 > 用空心圆圈，≤ 或 ≥ 用实心圆点。
5. Coordinates and Linear Graphs | 坐标系与线性图像
You should already be able to plot points in all four quadrants, using the form (x, y). Year 10 moves quickly onto understanding the equation of a straight line and interpreting its gradient and y-intercept.
你应该已经能够在四个象限中绘制坐标点，形式为 (x, y)。到了十年级，学习进度会很快，需要你进一步理解直线方程，并解读其斜率和 y 轴截距。
nts the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis).
直线的一般方程为 y = mx + c，其中 m 表示斜率（倾斜程度），c 是 y 轴截距（直线与 y 轴的交点）。
) / (x₂ − x₁). A positive gradient slopes upwards, a negative gradient slopes downwards. Horizontal lines have gradient 0; vertical lines have undefined gradient.
要计算两点 (x₁, y₁) 和 (x₂, y₂) 之间的斜率，可用公式 m = (y₂ − y₁) / (x₂ − x₁)。正斜率向上倾斜，负斜率向下倾斜。水平线的斜率为0；垂直线的斜率无定义。
= −1, 0, 1, 2, calculate the y-values, plot the points and join them with a straight line.
通过列出数值表来练习根据方程画直线。对于 y = 2x − 1，选取 x = −1, 0, 1, 2，计算出对应的 y 值，描点并用直线连接起来。
6. Ratio, Proportion and Rates of Change | 比率、比例与变化率
Ratio questions appear regularly on the Eduqas papers, often in contexts such as sharing money, mixing ingredients or comparing sizes. Always write ratios in their simplest form and keep the order consistent.
在Eduqas的试卷中，比率问题经常出现，常见的情境包括分配金钱、混合食材或比较大小。务必用最简形式书写比率，并保持顺序一致。
e a quantity in a given ratio by finding the total number of parts. For example, to divide £72 in the ratio 3 : 5, total parts = 8, so one part = £9. The shares are 3 × £9 = £27 and 5 × £9 = £45.
按给定比率分配数量时，先求出总份数。例如，按 3 : 5 的比例分配72英镑，总份数 = 8，一份 = 9英镑。因此分配额为 3 × 9 = 27英镑 和 5 × 9 = 45英镑。
Proportion describes how two quantities change together. If two quantities are directly proportional, their ratio stays constant. If y is inversely proportional to x, then their product is constant. You will study these in more depth in Year 10.
比例描述了两个量是如何一同变化的。如果两个量成正比，则它们的比值保持不变。如果 y 与 x 成反比，则它们的乘积恒定。十年级你将更深入地学习这些内容。
Rates of change link to gradient ideas. Common examples are speed (distance ÷ time), density (mass ÷ volume) and unit pricing. Master converting between compound units such as km/h to m/s.
变化率与斜率的概念相联系。常见的例子有速度（距离÷时间）、密度（质量÷体积）和单价。要熟练掌握复合单位之间的换算，比如 km/h 与 m/s 之间的转换。
7. Geometry: Angles and Properties of Shapes | 几何：角与图形的性质
A secure knowledge of angle facts makes geometry problems much easier. Ensure you can recall and apply these rules without hesitation:
牢固掌握各种角的性质能让几何问题变得简单许多。请确保你能毫不犹豫地回想并运用以下规则：
- Angles on a straight line sum to 180°. | 直线上的角之和为180°。
- Angles around a point sum to 360°. | 绕一点一周的角之和为360°。
- Vertically opposite angles are equal. | 对顶角相等。
- Angles in a triangle sum to 180°. | 三角形的内角和为180°。
- Angles in a quadrilateral sum to 360°. | 四边形的内角和为360°。
Parallel lines introduce corresponding angles, alternate angles and co-interior (allied) angles. When a pair of parallel lines is cut by a transversal, corresponding angles are equal, alternate angles are equal, and co-interior angles sum to 180°.
平行线会带来同位角、内错角以及同旁内角。当一对平行线被一条截线切割时，同位角相等，内错角相等，同旁内角之和为180°。
°. The sum of exterior angles for any convex polygon is always 360°. These properties are essential for solving multi-step problems in Year 10.
在多边形中，n 边形内角和为 (n − 2) × 180°。任何凸多边形的外角和始终为360°。这些性质是十年级解决多步骤几何问题的基础。
8. Perimeter, Area and Volume | 周长、面积与体积
erence C of a circle with radius r is given by C = 2πr, or C = πd where d is the diameter.
你需要熟练计算直线图形周长和圆的周长。半径为 r 的圆的周长 C 由 C = 2πr 或 C = πd 给出，其中 d 为直径。
ase × perpendicular height) and trapezia (A = ½(a + b)h). The area of a circle is A = πr².
在面积方面，要熟记矩形的面积公式（A = 长 × 宽）、三角形的面积公式（A = ½ × 底 × 高）、平行四边形的面积公式（A = 底 × 垂直高度）以及梯形的面积公式（A = ½(a + b)h）。圆的面积为 A = πr²。
For compound shapes, divide the shape into simpler shapes, calculate each area separately and then add or subtract as needed. Label your working clearly.
对于组合图形，将其分割成简单图形，分别计算每一部分的面积，然后根据需要相加或相减。书写过程时要清晰地标注每一步。
linders give V = πr²h. You will meet spheres, pyramids and cones later in the GCSE course.
棱柱的体积：体积 = 横截面积 × 长度。长方体的体积 V = 长×宽×高，圆柱体的体积 V = πr²h。球体、棱锥和圆锥的体积将在GCSE课程的后期出现。
9. Statistics: Averages and Charts | 统计：平均数与图表
Data handling skills are tested both in the calculator and non-calculator papers. Know your three measures of average — mean, median and mode — and the measure of spread, the range.
数据处理技能在计算器与非计算器试卷中都会考查。你需要掌握三种平均数——平均数（均值）、中位数和众数——以及衡量离散程度的极差。
The mean is found by adding all values and dividing by the number of values. The median is the middle value when the data are ordered. The mode is the most frequent value. The range is the largest value minus the smallest.
平均数是将所有数值相加后除以数值的个数。中位数是将数据排序后位于中间的值。众数是出现频率最高的值。极差则是最大值减去最小值。
You must also be able to read and construct charts: bar charts, pie charts, line graphs and scatter graphs. Scatter graphs show the relationship between two variables; if the points tend to follow a straight line, we say there is correlation.
你还必须能够阅读并绘制图表：条形图、饼图、折线图和散点图。散点图展示两个变量之间的关系；如果数据点大致沿着一条直线分布，我们就说存在相关性。
tegory = (frequency / total frequency) × 360°. Label each sector clearly or provide a key.
绘制饼图时请记住，每个类别的扇形角度 = (频数 ÷ 总频数) × 360°。要清晰地标注每个扇形或提供图例。
10. Probability Basics | 概率基础
Probability is a measure of how likely an event is to happen, written as a fraction, decimal or percentage between 0 (impossible) and 1 (certain).
概率是衡量一个事件发生可能性大小的尺度，可以用分数、小数或百分数表示，其值介于0（不可能事件）和1（必然事件）之间。
provided all outcomes are equally likely. For a fair six-sided die, P(rolling a 4) = 1/6.
概率 = （有利结果的数量）÷（所有可能结果的总数），前提是所有结果发生的可能性相等。对于一个均匀的六面骰子，掷出4点的概率为 1/6。
1 − the probability that it does happen. For example, P(not rolling a 4) = 1 − 1/6 = 5/6.
一个事件不发生的概率等于1减去该事件发生的概率。例如，P(没有掷出4) = 1 − 1/6 = 5/6。
You will also meet sample space diagrams and simple tree diagrams. A tree diagram helps you list the outcomes of two or more events. Multiply along the branches to find combined probabilities, and add the final probabilities when more than one branch leads to the desired outcome.
你还会接触到样本空间图和简单的树状图。树状图能帮助你列出两个或更多事件的所有结果。沿分支相乘以得到组合概率，当有多条分支导向同一结果时，则将各条分支的末端概率相加。
Always check that the probabilities on a tree diagram sum to 1 at each set of branches.
请始终检查树状图中每一组分叉上的概率之和是否为1。
11. Effective Revision and Practice Strategies | 高效复习与练习策略
Simply reading notes is not an effective way to learn mathematics. Active practice, where you solve problems and then check your answers, builds fluency and confidence.
仅仅是阅读笔记并不是学习数学的有效方法。主动练习，也就是动手解题然后核对答案，才能培养熟练度和自信心。
Create a weekly plan that mixes topics. For example, Monday – number, Tuesday – algebra, Wednesday – geometry, Thursday – data, Friday – mixed practice. Use past paper questions from the Eduqas website to check your understanding under exam-style conditions.
你可以制定一个每周计划，将不同的课题穿插安排。例如：星期一——数字，星期二——代数，星期三——几何，星期四——数据处理，星期五——综合练习。利用Eduqas官网上的历年真题，在模拟考试的条件下检验自己的理解程度。
When you make a mistake, do not just look at the answer. Write out a correct solution step by step and add a short note explaining what went wrong. This helps your brain build the correct pathways.
当你做错题时，不要只看答案。要逐步写出正确的解答过程，并添加简短的笔记解释错误的原因。这样能帮助你的大脑建立起正确的思维通路。
Keep a 'formula book' where you record all the key formulas, angle facts and conversions. Review it regularly and test yourself without looking. Being able to recall formulas quickly is essential for the non-calculator paper.
准备一本‘公式手册’，记录所有关键的公式、角的性质以及单位换算。定期复习并尝试在不看手册的情况下进行自测。能够快速地回想公式，对非计算器试卷至关重要。
12. Looking Ahead: Key Year 10 Topics | 展望：十年级重点课题
The Year 10 Eduqas scheme of work builds directly on these foundations. Topics you can expect to encounter early on include:
十年级的Eduqas教学计划直接建立在这些基础之上。你将在学期初接触到的一些课题包括：
- Solving quadratic equations by factorising, completing the square, and using the quadratic formula. | 通过因式分解、配方法和求根公式来解二次方程。
- Trigonometry in right-angled triangles: using sine, cosine and tangent ratios (SOH CAH TOA). | 直角三角形中的三角学：运用正弦、余弦和正切比（SOH CAH TOA）。
- Simultaneous equations, both linear and linear/quadratic pairs. | 联立方程，包括一次联立方程以及一次与二次联立方程。
- Further work on vectors, including vector geometry. | 更深层的向量知识，包括向量几何。
- More advanced probability, including conditional probability and Venn diagrams. | 更高级的概率，包括条件概率和韦恩图。
- Circles – theorems involving angles, chords and tangents. | 圆 —— 涉及角、弦和切线的定理。
Don't worry if some of these titles look unfamiliar. The important thing is that you arrive in September with solid number, algebra and angle skills. That strong base will make the new material far easier to understand.
如果你觉得其中一些名词看起来陌生，不用担心。关键是你在九月份开学时能拥有扎实的数字、代数和角的技能。一旦有了这个坚实的基础，新知识就会变得容易理解得多。
Use this summer not to race ahead, but to build depth and accuracy. If you finish the bridging activities feeling confident with fractions, linear equations and basic trigonometry, you will be in an excellent position to succeed in Year 10 and beyond.
利用这个暑假，不是为了超前赶进度，而是为了加深理解和提高准确性。如果你在完成衔接活动后，能对分数、一次方程和基本的三角学充满信心，那么你就已经处于非常有利的位置，能够在十年级乃至以后的课程中取得成功。
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图