📚 Year 10 WJEC Maths: Summer Prep & Bridging Course | WJEC 10年级数学：暑期预习与衔接课程
Moving from Year 9 into Year 10 marks a significant step in your WJEC Mathematics journey. The summer break is the perfect time to consolidate your existing skills and get a head start on the new topics you will meet. This bridging guide highlights the essential concepts, from number work to algebra and geometry, and provides a clear pathway to build confidence before the term begins.
从9年级升入10年级是WJEC数学学习的重要转折点。暑假是巩固已有知识、提前接触新课题的最佳时机。这份衔接指南聚焦从数字运算到代数与几何的核心概念，并为你铺设一条清晰的路径，帮助你在新学期开始前建立自信。
1. Understanding the WJEC Year 10 Maths Curriculum | 理解WJEC 10年级数学课程
In Year 10, the WJEC course deepens your understanding of the four main areas: Number, Algebra, Geometry & Measure, and Statistics & Probability. You will begin preparing for the GCSE Mathematics – Numeracy and GCSE Mathematics qualifications, which both test application and reasoning. The summer is an excellent time to familiarise yourself with the specification and identify the topics that carry the most weight.
10年级的WJEC课程将深化你对四大板块的理解：数字、代数、几何与测量，以及统计与概率。你将开始为GCSE数学—数理应用和GCSE数学两个资格做准备，它们都着重考查应用与推理。暑假正是熟悉大纲、找出权重最高主题的好机会。
WJEC places a strong emphasis on problem-solving in real-world contexts. You will encounter questions about budgeting, interpreting bills, and using measures in practical situations. Knowing this helps you see why your summer prep should mix pure skills with everyday applications.
WJEC高度重视真实情境中的问题解决。你会遇到与预算、账单解读和实际测量相关的题目。明白这一点有助于理解为什么暑期预习应当将纯技能与日常应用结合起来。
2. Building Strong Number Skills | 夯实数字运算技能
Before tackling advanced algebra, make sure you can work fluently with integers, decimals, and negative numbers. Practise adding, subtracting, multiplying, and dividing without a calculator, especially when dealing with larger numbers or money. In WJEC exams, method marks are often awarded even if the final answer is incorrect.
在挑战进阶代数之前，请确保你能熟练处理整数、小数和负数。练习在不使用计算器的情况下进行加减乘除，尤其是处理较大数字或涉及钱款时。在WJEC考试中，即便最终答案有误，方法分通常也能拿到。
A solid grasp of place value and rounding is equally important. Be able to round to a given number of decimal places or significant figures, and know how to estimate answers to check calculator results. Typical exam problems ask you to estimate the cost of a shopping basket or the area of a room.
牢固掌握位值和近似值同样重要。要能够按要求将数字舍入到指定的小数位数或有效数字，并知道如何估算答案以检查计算器结果。典型的考题会让你估算购物篮的总价或房间的面积。
Example: 456.728 rounded to 2 decimal places → 456.73
示例：456.728 舍入到 2 位小数 → 456.73
3. Fractions, Decimals and Percentages | 分数、小数与百分比
The ability to move confidently between fractions, decimals and percentages is a core WJEC requirement. During the summer, revise how to convert a fraction like 3/5 to a decimal (0.6) and a percentage (60%), and practise ordering mixed lists of these forms.
在分数、小数和百分比之间自如转换是WJEC的核心要求。暑假期间，复习如何将像 3/5 这样的分数转换为小数（0.6）和百分比（60%），并练习给这些形式混合的数值排序。
You should also revisit fraction arithmetic: addition, subtraction, multiplication, and division. Remember that adding fractions requires a common denominator, while multiplying means multiplying numerators and denominators directly. Apply these to word problems involving recipes or discounts.
你还应该重温分数的四则运算：加减乘除。记住，加减分数需要通分，而乘法则直接将分子和分母分别相乘。将这些技能应用到涉及食谱或折扣的文字题中。
Percentages beyond 100% and repeated percentage change (like compound interest) often appear in Year 10. Use the multiplier method: a 15% increase uses a multiplier of 1.15, and a decrease of 15% uses 0.85. Practise calculating VAT, sale prices, and profit.
超过100%的百分比以及重复百分比变化（如复利）经常出现在10年级。使用乘数法：增长15%就用1.15这个乘数，减少15%就用0.85。练习计算增值税、折后价和利润。
Increase £240 by 15% → £240 × 1.15 = £276
将240英镑增加15% → 240 × 1.15 = 276英镑
4. Algebra: Expressions, Substitution and Simplifying | 代数：表达式、代入与化简
Algebra forms the backbone of the Year 10 syllabus. Start by reviewing how to write expressions using letters, and how to substitute values into simple formulae. For instance, if a = 3 and b = 5, evaluate 2a + b. This skill is tested regularly, often hidden inside geometry or statistics questions.
代数是10年级教学大纲的支柱。先复习如何用字母表示表达式，以及如何将数值代入简单公式。例如，若 a = 3，b = 5，求 2a + b 的值。这项技能经常被考查，常常隐藏在几何或统计题中。
Collecting like terms is the next essential step. Be able to simplify expressions such as 4x + 3y – 2x + 5y to 2x + 8y. Understanding that x and x² are not like terms is a common pitfall. Use colour or underlining to group similar terms when practising.
合并同类项是下一步的关键。要能化简诸如 4x + 3y – 2x + 5y 得到 2x + 8y 这样的表达式。明白 x 和 x² 不是同类项是一个常见的易错点。练习时可用颜色或下划线将同类项分组。
Expanding single brackets is also part of the bridging work. Use the distributive law: 3(2x + 4) = 6x + 12. Similarly, factorising by taking out the highest common factor, such as turning 5x + 15 into 5(x + 3), will be heavily used in Year 10 equation solving.
展开单项括号也是衔接学习的一部分。运用分配律：3(2x + 4) = 6x + 12。类似地，通过提取最大公因数进行因式分解，例如将 5x + 15 化为 5(x + 3)，将在10年级的方程求解中大量使用。
5. Solving Equations and Inequalities | 解方程与解不等式
Year 10 students are expected to solve linear equations quickly and accurately. An equation like 5x – 7 = 2x + 8 requires you to collect x terms on one side and numbers on the other. Always perform the same operation on both sides to maintain balance.
10年级的学生需要快速准确地把方程解出来。对于像 5x – 7 = 2x + 8 这样的方程，你需要将含 x 的项移到一边，数字移到另一边。解题时始终对等式两边执行相同的运算，以保持平衡。
5x – 7 = 2x + 8 → 5x – 2x = 8 + 7 → 3x = 15 → x = 5
5x – 7 = 2x + 8 → 5x – 2x = 8 + 7 → 3x = 15 → x = 5
Inequalities follow similar rules but remember to flip the inequality sign when multiplying or dividing by a negative number. For example, –2x < 10 becomes x > –5. Representing inequalities on a number line with open and closed circles is a common exam task.
不等式的解法与方程类似，但要记住：当乘或除以一个负数时，需要反转不等号。例如，–2x < 10 变成 x > –5。在数轴上用空心圈和实心圈表示不等式是常见的考题。
6. Sequences and the nth Term | 数列与第 n 项
Sequences are a visual and logical part of algebra. You will work with arithmetic sequences where the difference between terms is constant. The nth term formula for a linear sequence like 4, 9, 14, 19, … is 5n – 1. Learn to find this by noting the common difference and the zero term.
数列是代数中视觉和逻辑性较强的部分。你将学习等差数列，即相邻两项之差恒定的数列。像 4, 9, 14, 19 这样的线性数列的第 n 项公式是 5n – 1。学会通过找出公差和第零项来得到这个公式。
WJEC also introduces non-linear sequences, such as square numbers or triangle numbers, and may ask you to continue a pattern or describe the rule in words. Summer preparation can include recognising patterns like n², n² + 1 or 2ⁿ.
WJEC还会引入非线性数列，如平方数或三角形数，并可能要求你接着写几项或用文字描述规律。暑期预习可以包括识别像 n²、n² + 1 或 2ⁿ 这样的模式。
Applying the nth term to find whether a large number belongs to a sequence is another key skill. If a job can be done in 103 days and the pattern follows 3, 7, 11, …, check if 103 fits by setting 4n – 1 = 103. Solving gives n = 26, so day 103 is included.
运用第 n 项判断一个较大的数是否属于某个数列也是一项关键技能。如果一项工作需要103天完成，且进度遵循3, 7, 11……的规律，要判断103是否符合，可设 4n – 1 = 103。解得 n = 26，因此第103天被包含在内。
7. Ratio, Proportion and Rates | 比、比例与速率
Ratio problems are a major feature of WJEC Numeracy papers. You need to be confident sharing an amount in a given ratio, such as dividing £300 in the ratio 2:3:5. Add the parts (2+3+5=10), then find the value of one part (£30) before multiplying.
比例题是WJEC数理应用试卷的重要特色。你需要熟练掌握按给定比例分配一个量的方法，例如按 2:3:5 分配300英镑。先将比的前项相加（2+3+5=10），再算出一份的价值（30英镑），然后分别相乘。
Best buy and exchange rate questions are common. To find the best value, calculate the unit price (e.g. price per 100 ml or per 1 kg). Clear labelling of working is essential to secure method marks, even if arithmetic slips occur.
最佳购卖和汇率问题也很常见。为找到最划算的选择，需计算单价（例如每100毫升或每公斤的价格）。清晰标注解题步骤对拿到方法分至关重要，即使计算上出现失误。
Direct proportion involves using the formula y = kx. If 5 pens cost £3.75, then 8 pens cost: first find k = 3.75 ÷ 5 = 0.75, then y = 0.75 × 8 = £6.00. Recognising this structure will help in science and finance contexts as well.
正比例关系则会用到公式 y = kx。如果5支笔售价3.75英镑，那么8支笔的价格为：先求 k = 3.75 ÷ 5 = 0.75，然后 y = 0.75 × 8 = 6.00英镑。识别这种结构对科学和金融背景的题目也很有帮助。
8. Angles, Polygons and Symmetry | 角、多边形与对称
Geometry in Year 10 builds on angle facts met in earlier years. You must be secure with the sum of angles on a straight line (180°), around a point (360°), and in a triangle (180°). These are the building blocks for solving more complex diagrams.
10年级的几何建立在之前学过的角度知识之上。你必须牢固掌握一条直线上各角之和（180°）、绕一点一周各角之和（360°）以及三角形内角之和（180°）。这些是解决更复杂图形的基础。
Polygon work includes calculating interior and exterior angles. The exterior angles of any convex polygon always sum to 360°. For a regular polygon, each exterior angle is 360° ÷ n, where n is the number of sides. The interior angle is simply 180° – exterior angle.
多边形的学习包括计算内角和外角。任何凸多边形的外角和总是360°。对于正多边形，每个外角等于 360° ÷ n，其中 n 为边数。内角则等于 180° – 外角。
Regular octagon: exterior angle = 360° ÷ 8 = 45°, interior angle = 135°.
正八边形：外角 = 360° ÷ 8 = 45°，内角 = 135°。
Transformations – reflection, rotation, translation and enlargement – need both precise drawing and accurate description. When describing a rotation, specify centre, angle, and direction. For an enlargement, give the centre and the scale factor. Use tracing paper to practise.
图形变换——反射、旋转、平移和缩放——既需要精确绘制，也需要准确描述。在描述旋转时，要指明旋转中心、角度和方向。描述缩放时，则需给出中心和比例因子。练习时可以使用描图纸。
9. Perimeter, Area and Volume | 周长、面积与体积
By Year 10, you are expected to calculate areas of rectangles, triangles, parallelograms and trapeziums without hesitation. Learn and recall the formula for the area of a trapezium: ½(a + b)h, where a and b are the parallel sides and h is the perpendicular height. WJEC formula sheets will be provided, but knowing how to apply the formula is key.
到10年级，你应该能不假思索地计算矩形、三角形、平行四边形和梯形的面积。记住并复述梯形的面积公式：½(a + b)h，其中 a 和 b 为平行边，h 为垂直高。WJEC会提供公式表，但关键在于懂得如何运用公式。
Area of compound shapes often involves splitting the shape into rectangles and triangles, then adding or subtracting areas. Be careful with units: converting between mm², cm² and m² can be tricky. 1 m² = 10,000 cm², not 100 cm².
组合图形的面积常常需要将图形拆分为矩形和三角形，然后相加或相减面积。注意单位的转换：mm²、cm² 和 m² 之间的换算很容易出错。1 m² = 10,000 cm²，而不是 100 cm²。
Volume of prisms and cylinders is an extension of area. Volume = area of cross-section × length. For a cylinder, this becomes πr²h. Practise giving answers in terms of π and as decimals, and be ready to convert between volume and capacity (1 cm³ = 1 ml, 1000 cm³ = 1 litre).
棱柱和圆柱的体积是面积概念的延伸。体积 = 横截面积 × 长度。对于圆柱，公式为 πr²h。练习用 π 表示答案以及给出小数值，并做好体积与容积之间的转换（1 cm³ = 1 ml，1000 cm³ = 1 升）。
10. Statistics: Charts and Averages | 统计：图表与平均数
Data handling remains prominent in Year 10. You will draw and interpret bar charts, pie charts, line graphs and stem-and-leaf diagrams. A common WJEC task is to complete a pie chart given a frequency table. You must calculate the angle for each sector: (frequency ÷ total) × 360°.
数据处理在10年级仍然相当重要。你将绘制和解读条形图、饼图、折线图和茎叶图。WJEC常见的题目是给出一张频数表，要求完成一幅饼图。你必须计算每个扇形的角度：（频数 ÷ 总数）× 360°。
The mean, median, mode and range are used to summarise data. For grouped data, the mean is an estimate using midpoints: Σ(fx) ÷ Σf. The modal class is the group with the highest frequency, and the median can be found from a cumulative frequency graph or by interpolation.
平均数、中位数、众数和极差用于概括数据。对于分组数据，使用组中点估算平均数：Σ(fx) ÷ Σf。众数组是频数最高的组，而中位数可以通过累积频数图或插值法找到。
Scatter graphs and correlation are introduced thoroughly. Draw a line of best fit and use it to make predictions. Understand that correlation does not imply causation, a nuance that often appears in WJEC reasoning questions.
散点图与相关性被详细引入。画出一条最佳拟合线并用它进行预测。要理解相关性并不意味着因果关系，这一细微之处常出现在WJEC的推理题中。
11. Introduction to Probability | 概率入门
Probability in Year 10 moves beyond simple event probability. You will learn to use probability trees for independent events, such as flipping a coin twice or picking sweets without replacement. The key rule: probabilities on each set of branches must sum to 1.
10年级的概率学习超越了单一事件的概率。你将学习对独立事件使用概率树，例如抛掷硬币两次或不放回地抽取糖果。关键规则是：每组树枝上的概率之和必须为1。
The probability of two independent events both happening is found by multiplying along the branches. For rolling a 6 on a fair dice and then tossing heads on a coin, the probability is (1/6) × (1/2) = 1/12. Build these trees step by step and label every branch clearly.
两个独立事件同时发生的概率通过将树枝上的概率相乘得到。如果抛掷一个均匀骰子得到6点，然后掷硬币得到正面，概率为 (1/6) × (1/2) = 1/12。逐步构建这些树形图，并清楚地标出每根树枝。
Expected frequency is another useful idea: multiply the probability by the number of trials. If the probability of rain is 0.3 and we consider 20 days, we expect rain on 6 days. This connects probability back to real-world decision making.
期望频数是另一个有用的概念：用概率乘以试验次数。如果降雨概率为0.3，我们考虑20天，那么预计有6天降雨。这就把概率和现实决策联系了起来。
12. Designing Your Summer Study Plan | 设计你的暑期学习计划
A little structure goes a long way. Divide your summer weeks into three phases: revision of Year 9 fundamentals, bridging activities that blend old and new, and a final week of previewing the first Year 10 topics. Aim for 20-30 minutes of maths on most days rather than cramming.
有条理的安排能事半功倍。把暑假划分为三个阶段：复习9年级基础知识，进行新旧知识融合的衔接活动，最后一周预览10年级开篇主题。多数日子每天花20-30分钟学习数学，而不是临时突击。
Use WJEC specimen papers and BBC Bitesize materials aligned to WJEC. Keep a notebook for common mistakes, and practice showing full working, just as you will in exams. Pair up with a friend and quiz each other on key facts like angle rules or area formulas.
使用WJEC样卷和BB C Bitesize上与WJEC配套的资料。准备一个笔记本记录常见错误，并练习像考试中那样写出完整步骤。找个伙伴，互相考问关键知识点，比如角度定理或面积公式。
Finally, remember that mathematics is a skill that develops through consistent practice and reflection. Celebrate small wins, and do not rush the process. A steady summer routine will make your Year 10 start far smoother and more rewarding.
最后，请记住数学是通过持续练习和反思来进步的技能。为每一个小成就喝彩，不要急于求成。一个稳健的暑期作息会让你的10年级开局顺利得多，收获也多得多。
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