Winter Intensive Revision Plan for Year 10 WJEC Further Maths | Year 10 WJEC 进阶数学：寒假强化复习计划

📚 Winter Intensive Revision Plan for Year 10 WJEC Further Maths | Year 10 WJEC 进阶数学：寒假强化复习计划

Embarking on a winter intensive revision for Year 10 WJEC Further Mathematics can be a game-changer. This subject demands a deep understanding of advanced concepts, and the holiday break offers an uninterrupted window to consolidate knowledge, tackle weak areas, and build exam confidence.

为 Year 10 WJEC 进阶数学展开寒假强化复习，可以带来转折性的提升。这门学科要求深刻理解进阶概念，而假期提供了不被打扰的时间窗口，可以巩固知识、攻克薄弱环节、建立迎考信心。

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1. Setting Goals and Building a Timetable | 设定目标与建立时间表

Before diving into revision, identify your strengths and weaknesses using a topic checklist from the WJEC specification. Set specific, measurable goals, such as mastering differentiation or improving algebraic manipulation speed.

在投入复习前，先利用 WJEC 考纲的专题清单，明确自己的强项和弱项。设定具体且可衡量的目标，例如掌握微分计算，或提高代数运算的速度。

Design a daily timetable that balances intensive study with rest. Aim for two focused sessions of 90 minutes each morning and afternoon, alternating between theory review and problem-solving practice.

设计一份兼顾密集学习与休息的每日时间表。目标是上午和下午各安排两个 90 分钟的专注时段，交替进行理论回顾和解题练习。

A sample two-week plan could involve re-teaching topics in the first week, followed by mixed exercises and timed past-paper questions in the second. Be sure to schedule short breaks and physical activity to maintain focus.

一份两周的示范计划可以在第一周重新讲授各个专题，第二周则进行混合练习和限时真题训练。务必安排短暂休息和体育锻炼，以保持专注力。

Keep a revision log to track daily progress and adjust weaker areas. Use coloured pens to highlight formulas that need extra memorisation, and place them where you can see them every day.

用复习日志追踪每日进度并调整薄弱环节。用彩色笔标出需要额外记忆的公式，并把它们贴在你每天看得到的地方。

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2. Algebra and Quadratics | 代数与二次函数

Revisit factorising techniques including common factors, grouping, and the difference of two squares: a² – b² = (a – b)(a + b). Apply these to simplify rational expressions.

重温因式分解的技巧，包括提取公因式、分组分解以及平方差公式：a² – b² = (a – b)(a + b)。将这些技巧用于化简有理式。

Master quadratic equations: ax² + bx + c = 0. Memorise the quadratic formula

x = [ -b ± √(b² – 4ac) ] / (2a)

and know how to complete the square to find the vertex of a parabola. Practice discriminant analysis to determine the nature of roots.

精通二次方程：ax² + bx + c = 0。熟记求根公式

x = [ -b ± √(b² – 4ac) ] / (2a)

并掌握配方法以确定抛物线的顶点。通过判别式分析训练来判断根的性质。

Work on simultaneous equations where one is quadratic. Use substitution to reduce to a single variable equation and always check solutions for extraneous roots.

练习一个方程为二次的联立方程组。使用代入法将其化为一元方程，并始终检验根是否为增根。

Tackle inequalities: x² – 5x + 6 > 0. Represent solutions using interval notation and on a number line, and be careful when multiplying or dividing by negative terms.

攻克不等式：x² – 5x + 6 > 0。用区间记号和在数轴上表示解集，并注意当乘以或除以负数时不等号方向的变化。

Use the sum and product of roots: for ax² + bx + c = 0, α + β = -b/a and αβ = c/a. These relationships help construct equations from given roots.

运用根与系数的关系：对于 ax² + bx + c = 0，α + β = -b/a，αβ = c/a。利用这些关系可由已知根构造方程。

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3. Functions, Graphs and Transformations | 函数、图形与变换

Understand function notation f(x), domain and range. Practice evaluating composite functions fg(x) and inverse functions f⁻¹(x), remembering that the domain of the inverse is the range of the original.

理解函数记号 f(x)、定义域和值域。练习求复合函数 fg(x) 和反函数 f⁻¹(x)，牢记反函数的定义域即原函数的值域。

Know the characteristics of common graphs: linear, quadratic, cubic, reciprocal (y = k/x), and exponential growth graphs. Use them to visualise solutions to equations.

掌握常见图形的特征：一次函数、二次函数、三次函数、反比例函数 (y = k/x) 以及指数增长图形。利用这些图形直观理解方程的解。

Apply graph transformations: y = f(x) + a (vertical translation), y = f(x + a) (horizontal translation), y = af(x) (vertical stretch), and y = f(ax) (horizontal stretch). Combine multiple transformations carefully.

运用图形变换：y = f(x) + a（垂直平移），y = f(x + a）（水平平移），y = af(x）（垂直伸缩），y = f(ax）（水平伸缩）。仔细处理多重变换的组合。

Use graph sketching to solve inequalities such as f(x) > g(x) by comparing intercepts and intersection points.

通过比较截距与交点，利用草图解决诸如 f(x) > g(x) 的不等式。

For inverse functions, reflect the graph in the line y = x. Restrict domains of non-one-to-one functions to ensure the inverse exists.

对于反函数，将图形沿直线 y = x 反射。对于非一一对应的函数，需限制定义域以确保反函数存在。

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4. Coordinate Geometry and Straight Lines | 解析几何与直线

Revise the distance between two points: d = √[(x₂ – x₁)² + (y₂ – y₁)²], and the midpoint formula: M = ((x₁ + x₂)/2, (y₁ + y₂)/2). These are essential for working with circles and perpendicular bisectors.

复习两点间距离：d = √[(x₂ – x₁)² + (y₂ – y₁)²]，以及中点公式：M = ((x₁ + x₂)/2, (y₁ + y₂)/2)。这些对于处理圆和垂直

Published by TutorHao | Year 10 进阶数学 Revision Series | aleveler.com

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