📚 GCSE WJEC Maths: End-of-Term Revision Checklist | GCSE WJEC 数学：期末复习提纲
The GCSE WJEC Mathematics specification demands a strong grasp of core mathematical concepts, problem-solving skills, and the ability to apply knowledge in real-world contexts. This end-of-term revision checklist highlights the essential topics you should focus on to ensure you are fully prepared for your assessments. Use this guide to structure your revision and identify any areas needing more practice.
GCSE WJEC 数学大纲要求牢固掌握核心数学概念、解决问题的能力以及在现实情境中应用知识的能力。这份期末复习提纲突出了你应该重点关注的关键主题，以确保你为评估做好充分准备。使用本指南来组织你的复习，并找出需要更多练习的薄弱环节。
1. Number and Calculation | 数与计算
Review arithmetic with integers, decimals and negative numbers; always follow the order of operations (BIDMAS/BODMAS).
复习整数、小数和负数的算术运算；始终遵循运算顺序（BIDMAS/BODMAS）。
Know how to round numbers to a given number of decimal places or significant figures, and understand upper and lower bounds.
知道如何将数字四舍五入到指定的小数位数或有效数字，并理解上界和下界。
Work confidently with powers (indices) and roots, including squares, cubes, and fractional/negative indices such as 2⁻³ and 16½.
熟练运用幂（指数）和方根，包括平方、立方以及分数/负指数，如 2⁻³ 和 16½。
rs and standard form (A × 10ⁿ) and perform calculations in standard form using index laws.
在普通数字与标准形式（A × 10ⁿ）之间进行转换，并利用指数法则进行标准形式的计算。
Use estimation strategies to check the reasonableness of your answers, especially in multi-step problems.
使用估算策略检查答案的合理性，尤其是在多步骤问题中。
Apply knowledge of multiples, factors, primes, HCF and LCM to solve problems; remember to use prime factorisation where helpful.
运用倍数、因数、质数、最大公因数和最小公倍数解决问题；如有帮助，使用质因数分解。
2. Fractions, Decimals, and Percentages | 分数、小数和百分比
Add, subtract, multiply and divide fractions and mixed numbers; simplify your answers and cancel common factors before multiplying.
对分数和带分数进行加减乘除运算；化简结果并在乘法前约去公因数。
ractions, decimals and percentages, and recognise common equivalents like ⅛ = 0.125 = 12.5%.
在分数、小数和百分比之间流畅转换，并识别常见等价关系，如 ⅛ = 0.125 = 12.5%。
Find a fraction or a percentage of an amount, and increase or decrease an amount by a given percentage; use multiplier methods for compound changes.
求某数量的几分之几或百分之几，并按给定百分比增加或减少数量；对于复合变化使用乘数法。
Calculate percentage profit, loss, and original values after a percentage change, including reverse percentages.
计算百分比利润、亏损以及百分比变化后的原始值，包括反向百分比。
Order fractions, decimals and percentages by converting them into the same form; place them on a number line.
通过将分数、小数和百分比转换为同一种形式来排序；将它们放置在数轴上。
Work with one quantity as a percentage of another and solve problems involving repeated percentage change, such as compound interest and depreciation.
计算一个数量占另一个数量的百分比，并解决涉及重复百分比变化的问题，如复利和贬值。
3. Ratio and Proportion | 比与比例
Express ratios in their simplest form and divide a quantity into two or more parts according to a given ratio.
以最简形式表示比，并按给定比将一个数量分成两部分或多部分。
Solve problems involving direct proportion, including recipes, scale drawings and best buys; use the unitary method to find the value of a single item.
解决涉及正比例的问题，包括食谱、比例图和最佳购买；使用归一法求单项的价值。
Recognise and work with indirect (inverse) proportion, understanding that as one quantity increases the other decreases at the same rate.
识别并处理反比例，理解当一个量增加时另一个量以相同速率减少。
Convert between ratios, fractions and percentages in context, and interpret ratio-based information in exam-style questions.
在具体情境中在比、分数和百分比之间转换，并在考试题型中解读基于比的信息。
Use scale factors for lengths, areas and volumes of similar shapes; understand that if the length scale factor is k, the area scale factor is k² and volume is k³.
对相似图形使用长度、面积和体积的比例因子；理解如果长度比例因子为 k，则面积比例因子为 k²，体积为 k³。
Apply ratio concepts to mixture problems and map scales, and always check that ratios are in the same units.
将比的概念应用于混合物问题和地图比例尺，并始终检查比的单位是否一致。
4. Algebraic Expressions | 代数表达式
ing like terms and using the laws of indices: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ.
通过合并同类项和使用指数法则化简代数表达式：aᵐ × aⁿ = aᵐ⁺ⁿ，aᵐ ÷ aⁿ = aᵐ⁻ⁿ，(aᵐ)ⁿ = aᵐⁿ。
Expand brackets, including single, double and triple brackets; for (x + a)(x + b) remember FOIL and simplify.
展开括号，包括单重、双重和三重括号；对于 (x + a)(x + b)，记住先用 FOIL 再化简。
Factorise expressions by taking out common factors, and factorise quadratics of the form x² + bx + c and ax² + bx + c (Higher).
通过提取公因式分解表达式，并对形如 x² + bx + c 和 ax² + bx + c 的二次式进行因式分解（高级内容）。
Use algebraic identities, difference of two squares a² – b² = (a+b)(a–b), and factorise completions for Higher tier.
使用代数恒等式、平方差公式 a² – b² = (a+b)(a–b)，以及高级内容中的完全配方。
Substitute positive and negative numbers into expressions and formulae, and evaluate them step by step.
将正数和负数代入表达式和公式，并逐步求值。
Change the subject of a formula, including formulae where the subject appears on both sides or involves powers and roots.
改变公式的主项，包括主项出现在两边或涉及幂和方根的公式。
5. Equations and Inequalities | 方程与不等式
Solve linear equations with unknowns on one or both sides, including those with brackets and fractional coefficients.
解未知数在一侧或两侧的线性方程，包括含有括号和分数系数的方程。
Set up and solve equations from word problems, translating real-life situations into algebraic language.
根据文字题建立并求解方程，将现实情境转化为代数语言。
y factorising, by completing the square (Higher), and by using the quadratic formula x = [–b ± √b² – 4ac]/2a (Higher).
通过因式分解、配方法（高级）和二次公式 x = [–b ± √b² – 4ac]/2a（高级）解二次方程。
Solve simultaneous equations both graphically and algebraically; for two linear equations use elimination or substitution.
通过图象法和代数法解联立方程；对于两个线性方程，使用消元法或代入法。
Represent inequalities on a number line using open and closed circles, and solve linear inequalities; remember to flip the sign when multiplying or dividing by a negative.
用空心圈和实心圈在数轴上表示不等式，并解线性不等式；记住当乘以或除以负数时，不等号方向要改变。
Find integer solutions to inequalities and represent regions defined by linear inequalities on graphs by shading the unwanted region.
求不等式的整数解，并通过阴影表示出线性不等式定义的区域。
6. Graphs and Functions | 图表与函数
ret straight-line graphs in the form y = mx + c, identifying gradient m and y-intercept c.
绘制并解读形如 y = mx + c 的直线图，识别斜率 m 和 y 轴截距 c。
Find the equation of a line given two points, or given a point and the gradient; calculate the gradient of perpendicular lines (negative reciprocal).
已知两点或一点和斜率，求直线方程；计算垂直线的斜率（负倒数）。
Draw and interpret quadratic, cubic, reciprocal and exponential graphs; recognise their shapes and key features such as turning points and asymptotes.
绘制并解读二次、三次、反比例和指数函数图象；识别它们的形状和关键特征，如转折点和渐近线。
Understand function notation f(x) and evaluate functions; for f(x) = x² – 3, find f(2) and solve f(x) = 0.
理解函数表示法 f(x) 并求函数值；对于 f(x) = x² – 3，求 f(2) 并解方程 f(x) = 0。
Use graphs to solve equations, such as reading off intersections to solve simultaneous equations or finding roots of a quadratic.
利用图象解方程，例如通过读取交点解联立方程或求二次方程的根。
Interpret distance–time and velocity–time graphs; gradient gives speed or acceleration, and area under a velocity–time graph gives distance (Higher).
解读距离-时间图和速度-时间图；斜率表示速度或加速度，速度-时间图下的面积表示距离（高级）。
7. Sequences | 数列
Identify and generate linear (arithmetic) sequences, finding the nth term in the form an + b.
识别并生成线性（算术）数列，求出形如 an + b 的第 n 项。
Continue number and pattern sequences, spot term-to-term rules and describe them in words.
延续数字和图案数列，发现逐项规则并用词语描述。
Recognise and use quadratic sequences (Higher); find the nth term of a quadratic sequence where the second difference is constant.
识别并使用二次数列（高级）；求第二差为常数的二次数列的第 n 项。
Use sequences to solve applied problems, such as matchstick patterns and tile arrangements.
使用数列解决应用问题，如火柴棍图案和瓷砖排列。
Distinguish between arithmetic sequences and other sequences like geometric or Fibonacci-type sequences.
区分算术数列和其他数列，如等比数列或斐波那契型数列。
Determine whether a given term is in a sequence by using the nth term formula and solving equations.
通过使用第 n 项公式并解方程，判断给定项是否在数列中。
8. Geometry: Angles and Shapes | 几何：角与形状
Recall and apply angle facts: angles on a straight line sum to 180°, at a point 360°, vertically opposite angles are equal, and angles in a triangle sum to 180°.
回忆并应用角度知识：直线上的角之和为 180°，一点周角为 360°，对顶角相等，三角形内角之和为 180°。
Calculate interior and exterior angles of regular polygons; use the formulas (n–2) × 180°/n and 360°/n.
计算正多边形的内角和外角；使用公式 (n–2) × 180°/n 和 360°/n。
Apply properties of parallel lines: corresponding angles, alternate angles and co-interior (supplementary) angles are key.
应用平行线性质：同位角、内错角和同旁内角（互补）是关键。
Use Pythagoras' missing sides in right-angled triangles and apply it to 2D problems including coordinates.
使用勾股定理 a² + b² = c² 求直角三角形中的缺失边长，并将其应用于包括坐标在内的二维问题。
Learn the properties of special quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, kite) and their diagonals.
学习特殊四边形（正方形、矩形、平行四边形、菱形、梯形、筝形）的性质及其对角线。
Understand and use the geometric names of parts of a circle: radius, diameter, chord, tangent, arc, sector and segment.
理解并使用圆各部分的几何名称：半径、直径、弦、切线、弧、扇形和弓形。
9. Perimeter, Area, and Volume | 周长、面积与体积
Calculate the perimeter and area of squares, rectangles, triangles, parallelograms and trapeziums using standard formulas.
使用标准公式计算正方形、矩形、三角形、平行四边形和梯形的周长和面积。
ircles; area = πr², circumference = 2πr or πd. Leave answers in terms of π when specified.
求圆的面积和周长；面积 = πr²，周长 = 2πr 或 πd。当要求时，答案保留 π。
Work out the area of compound shapes by splitting them into simpler shapes; be careful with units.
通过将复合图形分解为更简单的图形来计算面积；注意单位。
ers, pyramids, cones and spheres; learn the volume of a pyramid as ⅓ × base area × height.
计算直棱柱、圆柱、棱锥、圆锥和球的表面积和体积；记住棱锥体积为 ⅓ × 底面积 × 高。
c units of length, area and volume; understand that 1 cm² = 100 mm², 1 m³ = 1,000,000 cm³.
在长度、面积和体积的公制单位之间进行换算；理解 1 cm² = 100 mm²，1 m³ = 1,000,000 cm³。
Use similarity to relate lengths, areas and volumes; for similar solids, the volume scale factor is the cube of the linear scale factor.
使用相似关系联系长度、面积和体积；对于相似立体，体积比例因子是线性比例因子的立方。
10. Pythagoras and Trigonometry | 勾股定理与三角学
Master Pythagoras' theorem in right-angled triangles, including finding the hypotenuse or a shorter side; use it to check if a triangle is right-angled.
熟练掌握直角三角形中的勾股定理，包括求斜边或短边；用它来检验三角形是否为直角三角形。
, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent to find missing sides and angles.
应用三角比 sin θ = 对边/斜边，cos θ = 邻边/斜边，tan θ = 对边/邻边 求缺失的边和角。
Use the sine rule a/sin A = b/sin B = c/sin C and cosine rule a² = b² + c² – 2bc cos A for non-right-angled triangles (Higher).
对非直角三角形使用正弦定理 a/sin A = b/sin B = c/sin C 和余弦定理 a² = b² + c² – 2bc cos A（高级）。
Know exact trigonometric values for key angles: sin 30° = ½, sin 45° = √2/2, sin 60° = √3/2, and similarly for cos and tan.
知道关键角的精确三角值：sin 30° = ½，sin 45° = √2/2，sin 60° = √3/2，余弦和正切同理。
Solve problems involving angles of elevation and depression, bearings, and trigonometry in 3D contexts.
解决涉及仰角、俯角、方位角以及三维情境中的三角学问题。
= sin x, y = cos x and y = tan x for 0° ≤ x ≤ 360°, and solve simple equations using them.
绘制并解读在 0° ≤ x ≤ 360° 范围内的三角函数图象 y = sin x、y = cos x 和 y = tan x，并利用它们解简单方程。
11. Statistics | 统计
Present data using appropriate diagrams: bar charts, pie charts, frequency polygons, scatter graphs, stem-and-leaf diagrams, and cumulative frequency graphs (Higher).
使用恰当的图表呈现数据：条形图、饼图、频数多边形、散点图、茎叶图以及累积频数图（高级）。
Calculate and interpret averages: mean, median, mode, and range; choose the most appropriate average for a given dataset.
计算和解读平均数：均值、中位数、众数和极差；为给定的数据集选择最合适的平均数。
Find the mean from a frequency table, both ungrouped and grouped; for grouped data, use midpoints.
从非分组和分组频数表中求均值；对于分组数据，使用组中值。
Draw and use cumulative frequency curves to find medians, quartiles and interquartile range, and construct box plots.
绘制并使用累积频数曲线来求中位数、四分位数和四分位距，并构建箱线图。
Interpret scatter diagrams and describe correlation (positive, negative, none); draw a line of best fit and use it to make predictions.
解读散点图并描述相关关系（正相关、负相关、无相关）；画出最佳拟合线并用其进行预测。
Understand and compare distributions using statistical measures; comment on averages and spread when comparing two sets of data.
理解并使用统计指标比较分布；在比较两组数据时，对平均数和离散程度进行评述。
12. Probability | 概率
Use the probability scale from 0 (impossible) to 1 (certain); write probabilities as fractions, decimals or percentages.
使用从 0（不可能）到 1（必然）的概率尺度；将概率写成分数、小数或百分比。
ingle event: P(event) = number of favourable outcomes / total number of possible outcomes.
计算单个事件的概率：P(事件) = 有利结果数 / 可能结果总数。
Estimate probabilities from experimental data using relative frequency; understand that more trials lead to a more reliable estimate.
使用相对频率从实验数据中估计概率；理解试验次数越多估计越可靠。
Work with combined events using sample space diagrams, two-way tables and systematic listing to ensure all outcomes are counted.
使用样本空间图、双向表和系统化列出所有结果的方式处理组合事件。
P(A) × P(B) for independent events, P(A or B) = P(A) + P(B) for mutually exclusive events.
使用“AND”和“OR”规则：对于独立事件，P(A 且 B) = P(A) × P(B)；对于互斥事件，P(A 或 B) = P(A) + P(B)。
Complete and use tree diagrams for independent and dependent events; understand conditional probability and its notation for Higher tier.
完成并使用独立和相依事件的树状图；理解条件概率及其在高级中的表示法。
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