Winter Break Intensive Revision Plan for Year 12 WJEC Mathematics

📚 Winter Break Intensive Revision Plan for Year 12 WJEC Mathematics | 寒假强化复习计划

Year 12 is a critical time for building the foundations of A level Mathematics. With mock exams approaching and the AS papers on the horizon, the winter break offers a valuable opportunity to consolidate your learning and address any weaknesses. This intensive revision plan is designed specifically for WJEC students, covering Unit 1: Pure Mathematics A and Unit 2: Applied Mathematics A (Statistics and Mechanics). It provides a structured two‑week schedule, topic‑by‑topic guidance, and exam technique tips to help you return to school feeling confident and in control.

12年级是为A level数学打下基础的关键时期。随着模拟考试临近和AS正式考试日益迫近，寒假提供了一个宝贵的机会来巩固所学并弥补薄弱环节。这份强化复习计划专为WJEC考生设计，覆盖第一单元：纯数学A和第二单元：应用数学A（统计与力学）。它将为你提供一个结构化的两周时间表、逐专题指导以及应试技巧，帮助你在返校时充满信心，游刃有余。

1. Assess Your Current Understanding | 评估你当前的掌握水平

Before diving into revision, take a diagnostic test using a recent WJEC past paper or topic tests. Mark your work honestly against the mark scheme and record your scores by topic: algebra, coordinate geometry, calculus, statistics, and mechanics. This will highlight precisely where you are losing marks and which areas need the most urgent attention.

在开始复习之前，先用一份近期的WJEC往年真题或专题测试进行一次诊断性自测。诚实对照评分标准批改，并按专题记录分数：代数、坐标几何、微积分、统计和力学。这样能精确地显示出你在哪里丢分，哪些领域最需要紧急关注。

Create a simple strengths and weaknesses table. For each topic, rate your confidence on a scale of 1–5. Be ruthless: if you cannot explain a concept clearly without notes, it is a weakness. This self‑assessment will inform how you allocate time in the revision timetable.

制作一个简单的强项和弱项表格。对每个专题，用1–5分给自己的信心评分。对自己诚实：如果无法在不看笔记的情况下清晰地解释一个概念，那它就是弱项。这份自我评估将指导你在复习时间表中如何分配时间。

2. Create a Realistic Revision Timetable | 制定一份切实可行的复习时间表

The winter break typically lasts two to three weeks. Aim for 3–4 hours of focused study each weekday, leaving weekends lighter for rest and consolidation. Divide each day into three 50‑minute sessions with short breaks in between, mirroring the concentration required in an exam. Assign specific topics to each session, alternating between pure and applied to maintain variety.

寒假通常持续两到三周。目标是每个工作日集中学习3–4小时，周末安排轻松一些，以便休息和巩固。将每天分成三个50分钟的学习时段，中间安排短暂休息，这能模拟考试所需的专注度。为每个时段分配具体专题，并在纯数和应用数学之间交替进行，以保持新鲜感。

A sample day could be: Session 1 — Differentiation from first principles; Session 2 — Binomial distribution and hypothesis testing; Session 3 — Mixed practice from past papers. Write your timetable out and place it where you will see it every morning. Treat it as a contract with yourself.

一天的示例可以是：时段1——从第一性原理求导；时段2——二项分布与假设检验；时段3——真题混合练习。把时间表写下来，放在每天早晨都能看到的地方。把它看作与自己签订的契约。

3. Master Pure Mathematics: Algebra and Functions | 掌握纯数学：代数与函数

WJEC Unit 1 places a heavy emphasis on algebraic manipulation. Ensure you can confidently factorise quadratics, cubics, and expressions involving the difference of two squares. Revise completing the square and the quadratic formula:

WJEC第一单元非常重视代数运算。确保你能自信地对二次三项式、三次式以及平方差形式的表达式进行因式分解。复习配方法和二次公式：

x = [ –b ± √(b² – 4ac) ] / (2a)

Move on to the discriminant and its link to the number of real roots. Practice sketching quadratic graphs, labelling the vertex and intercepts, and solving quadratic inequalities using a sign diagram. For functions, be clear on domain, range, composite functions fg(x), and inverse functions f⁻¹(x). WJEC often asks you to find the inverse and state its domain.

接下来复习判别式及其与实根个数的联系。练习绘制二次函数图像，标出顶点和截距，并利用符号图解法求解二次不等式。关于函数，要明确定义域、值域、复合函数fg(x)以及反函数f⁻¹(x)。WJEC经常要求求出反函数并说明其定义域。

4. Master Pure Mathematics: Coordinate Geometry and Sequences | 掌握纯数学：坐标几何与数列

The straight line remains a key topic. Know how to find the gradient between two points, the equation y – y₁ = m(x – x₁), and conditions for parallel and perpendicular lines. Apply these to geometric problems, such as finding the perpendicular bisector of a chord of a circle. For circles, memorise the standard form (x – a)² + (y – b)² = r², and be ready to complete the square to find the centre and radius.

直线仍然是核心专题。掌握如何求两点间斜率、方程 y – y₁ = m(x – x₁)，以及平行和垂直的条件。将这些知识应用于几何问题，比如求圆弦的垂直平分线。对于圆，熟记标准形式 (x – a)² + (y – b)² = r²，并准备好通过配方法求圆心和半径。

Sequences introduced in Year 12 include arithmetic progressions. The nth term is uₙ = a + (n – 1)d and the sum to n terms is Sₙ = n/2 [2a + (n – 1)d] or n/2 (a + l). Use sigma notation Σ confidently. You may also meet recurrence relationships of the form uₙ₊₁ = f(uₙ); practice generating terms and analysing long‑term behaviour.

12年级引入的数列包括等差数列。第n项为 uₙ = a + (n – 1)d，前n项和为 Sₙ = n/2 [2a + (n – 1)d] 或 n/2 (a + l)。熟练使用求和符号Σ。你可能还会遇到形如 uₙ₊₁ = f(uₙ) 的递推关系，练习生成项并分析长期趋势。

5. Master Pure Mathematics: Trigonometry | 掌握纯数学：三角学

Start by ensuring you can use exact trigonometric values for 0°, 30°, 45°, 60°, 90° without a calculator. Sketch the sine, cosine, and tangent graphs, noting their periodic nature and key points. WJEC frequently tests solving trigonometric equations within a given interval, such as sin θ = 0.5 for 0° ≤ θ ≤ 360°. Use the CAST diagram or graph method to find all solutions.

首先要确保自己能在没有计算器的情况下写出0°、30°、45°、60°、90°的精确三角函数值。绘制正弦、余弦和正切函数的图像，注意它们的周期性和关键点。WJEC经常考查在给定区间内求解三角方程，例如在0° ≤ θ ≤ 360°内求解 sin θ = 0.5。使用CAST图或图像法求出所有解。

Trigonometric identities are essential. Know that tan θ = sin θ / cos θ and sin²θ + cos²θ = 1. Be prepared to use these to solve more complex equations or to prove simple identities. Always show clear, logical steps in your working.

三角恒等式至关重要。牢记 tan θ = sin θ / cos θ 以及 sin²θ + cos²θ = 1。准备好利用这些恒等式求解更复杂的方程或证明简单的恒等式。解题过程中始终要展示清晰、逻辑的步骤。

6. Master Pure Mathematics: Differentiation and Integration | 掌握纯数学：微分与积分

Calculus is a large part of Unit 1. Begin by revising differentiation from first principles for simple polynomials — WJEC has asked for this method directly. Then drill the power rule: if f(x) = xⁿ, then f'(x) = nxⁿ⁻¹. Practice differentiating sums and multiples, and finding equations of tangents and normals.

微积分在第一单元中占很大比重。首先复习从第一性原理求简单多项式的导数——WJEC曾直接要求过这种方法。然后大量练习幂函数求导法则：若 f(x) = xⁿ，则 f'(x) = nxⁿ⁻¹。练习对和与倍数求导，以及求切线和法线的方程。

For integration, treat it as the reverse of differentiation. The indefinite integral of xⁿ is xⁿ⁺¹/(n+1) + c, for n ≠ –1. Learn to find the constant of integration c when given a point on the curve. Definite integration and area under a curve are also examined; always discuss whether the area is above or below the x‑axis to avoid sign errors.

对于积分，把它看作微分的逆运算。xⁿ的不定积分为 xⁿ⁺¹/(n+1) + c，其中 n ≠ –1。学会在已知曲线上一点时求出积分常数c。定积分和曲线下的面积也会考查；解题时一定要讨论面积在x轴上方还是下方，以避免符号错误。

7. Conquer Applied Mathematics: Statistics | 攻克应用数学：统计学

The statistics section of WJEC Unit 2 covers probability, discrete random variables, the binomial distribution, and an introduction to hypothesis testing. Revise basic probability laws: P(A’) = 1 – P(A) and the addition rule P(A ∪ B) = P(A) + P(B) – P(A ∩ B). Make sure you are comfortable with Venn diagrams and tree diagrams.

WJEC第二单元的统计学部分涵盖概率、离散随机变量、二项分布以及假设检验的入门知识。复习基本概率法则：P(A’) = 1 – P(A) 以及加法法则 P(A ∪ B) = P(A) + P(B) – P(A ∩ B)。确保自己能够熟练使用维恩图和树形图。

The binomial distribution X ~ B(n, p) is a major topic. The probability formula is:

二项分布 X ~ B(n, p) 是一个重要专题。其概率公式为：

P(X = r) = ⁿCᵣ pʳ (1 – p)ⁿ⁻ʳ

You must be able to calculate probabilities using this formula, a calculator, or the tables provided by WJEC. Hypothesis testing for a binomial distribution involves stating the null and alternative hypotheses, finding the critical region or p‑value, and writing a conclusion in the context of the problem. Always define the test statistic clearly.

你必须能够使用该公式、计算器或WJEC提供的表格计算概率。二项分布的假设检验包括陈述原假设和备择假设、找出临界区域或p值，并结合问题背景写出结论。始终清晰地定义检验统计量。

8. Conquer Applied Mathematics: Mechanics | 攻克应用数学：力学

Mechanics requires a clear physical understanding of the situation. Start by mastering the SUVAT equations for constant acceleration in a straight line:

力学要求对物理情景有清晰的理解。首先掌握匀加速直线运动的SUVAT方程：

v = u + at
s = ut + ½at²
s = ½(u + v)t
v² = u² + 2as
s = vt – ½at²

where u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement. Learn to choose the correct equation by listing the known quantities and identifying the one you need to find. Practice problems involving vertical motion under gravity, taking g = 9.8 ms⁻² and deciding on a consistent positive direction.

其中u为初速度，v为末速度，a为加速度，t为时间，s为位移。学会通过列出已知量并确定需要求解的量来选择正确的方程。练习涉及重力作用下的竖直运动问题，取 g = 9.8 ms⁻²，并确定一个一致的正方向。

Newton’s laws form the basis of force problems. Draw clear force diagrams showing weight, normal reaction, tension, and friction. Use F = ma to form equations of motion. For problems on inclined planes, resolve the weight into components parallel and perpendicular to the plane. The maximum frictional force is F ≤ μR, where μ is the coefficient of friction and R is the normal reaction.

牛顿定律是力问题的基础。绘制清晰的受力图，显示出重力、法向反力、拉力和摩擦力。使用 F = ma 建立运动方程。对于斜面问题，将重力分解为平行和垂直于斜面的分量。最大摩擦力为 F ≤ μR，其中μ为摩擦系数，R为法向反力。

9. Past Paper Practice and Exam Technique | 真题练习与应试技巧

After covering the content, devote at least one quarter of your revision time to full past papers. WJEC papers follow a predictable structure. For Unit 1, expect around 8–10 questions testing a mix of topics, with calculus often dominating the later questions. For Unit 2, statistics and mechanics are separated into distinct sections, each worth roughly half the marks.

在完成内容复习后，将至少四分之一的复习时间用于完整的真题练习。WJEC试卷结构可预测。第一单元通常有8–10道题，混合考查各专题，微积分往往在后面的题目中占主导。第二单元中，统计和力学分为不同的部分，各占约一半分数。

When marking your work, use the official mark scheme to understand how marks are awarded. Pay attention to method marks (M1), accuracy marks (A1), and answer marks (B1). In mechanics, you must state the physical principle you are using to earn method marks. In statistics, all probability conclusions must be written in context. Time management is critical: allocate roughly one minute per mark, and do not spend 15 minutes on a 4‑mark factorisation.

在批改作业时，利用官方评分标准来理解分数是如何分配的。注意方法分（M1）、准确性分（A1）和答案分（B1）。在力学中，你必须陈述所使用的物理原理才能获得方法分。在统计中，所有概率结论必须结合背景书写。时间管理至关重要：大致按每分钟做一分的题目来分配时间，不要在一道4分的因式分解上花费15分钟。

10. Common Mistakes and How to Avoid Them | 常见错误及如何避免

A frequent error is forgetting the constant of integration +c. Always write +c immediately when you integrate an indefinite integral, and then use the given conditions to find its value. In mechanics, confusion over the positive direction leads to sign errors; draw an arrow to define positive direction at the start of every problem and stick to it.

一个常见错误是忘记积分常数+c。在进行不定积分时，务必立即写出+c，然后利用给定条件求出它的值。在力学中，混淆正方向会导致符号错误；在每一道题开始时画一个箭头定义正方向，并始终坚持它。

In algebra, a slip often occurs when expanding brackets with a negative sign outside. Use brackets carefully: –(x – 3) = –x + 3, not –x – 3. In hypothesis testing, students sometimes write ‘accept H₀’ instead of ‘do not reject H₀’; you must understand that lack of evidence against H₀ does not prove it true. Always write a final sentence referring back to the original claim.

在代数中，当括号外有负号时展开容易出错。小心使用括号：–(x – 3) = –x + 3，而不是 –x – 3。在假设检验中，学生有时会写成“接受H₀”而不是“不拒绝H₀”；必须理解缺乏反对H₀的证据并不能证明它正确。始终写一句最终陈述，回扣原始声明。

Finally, calculator misuse costs marks. Ensure your calculator is in degree mode for trigonometry unless radians are specified. Know how to calculate binomial coefficients efficiently and how to use the statistical functions to find probabilities without manual calculation errors.

最后，计算器使用不当也会丢分。除非题目指定弧度，否则确保计算器处于角度模式。了解如何高效计算二项式系数，以及如何使用统计功能求解概率，避免手工计算错误。

11. Mock Exam Simulation | 模拟考试实战演练

In the final two days of your winter revision, set up a full mock exam at home. Find a new practice paper, ideally one you have not seen, and complete it under timed conditions with no interruptions. For Unit 1, allow 2 hours 30 minutes; for Unit 2, allow 1 hour 45 minutes. Sit at a clear desk and resist the urge to check notes.

在寒假复习的最后两天，在家里安排一次完整的模拟考试。找一份新的练习卷，最好是你没见过的，并在计时且无干扰的条件下完成。第一单元计时2小时30分钟，第二单元1小时45分钟。坐在整洁的书桌前，克制住查看笔记的冲动。

After finishing, mark the paper and analyse every error. Categorise them as knowledge gaps (you did not know the method), careless slips, or misinterpretation of the question. This final diagnosis will give you a precise list of errors to eliminate before the real exam.

完成后，批改试卷并分析每一个错误。将它们归类为知识漏洞（不知道方法）、粗心失误或对题目的误解。这最后的诊断将为你提供一份精确的错误清单，以便在真正考试前消除它们。

12. Final Tips and Revision Resources | 最后提示与复习资源

Consistency beats cramming. Use active recall methods: after studying a topic, close the book and write down everything you remember. Teach a difficult concept aloud to an imaginary audience — this reveals gaps in your understanding instantly. Use flashcards for exact trig values, differentiation rules, and SUVAT equations.

持续巩固胜过临阵磨枪。使用主动回忆法：学完一个专题后，合上书，写下你记住的所有内容。对着想象中的听众大声讲解一个困难的概念——这会立刻揭示出你理解上的漏洞。使用抽认卡记忆精确三角函数值、微分法则和SUVAT方程。

The WJEC website provides past papers, mark schemes, and the detailed specification. Use the specification as a checklist to ensure you have covered every point. Other helpful resources include the WJEC endorsed textbooks and online platforms offering video tutorials on specific topics.

WJEC官网提供了往年真题、评分标准以及详细的教学大纲。将大纲用作检查清单，确保你已覆盖每一个知识点。其他有用的资源包括WJEC认可的教科书以及提供具体专题视频讲解的在线平台。

Published by TutorHao | Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Winter Break Intensive Revision Plan for Year 12 WJEC Mathematics | 寒假强化复习计划