Year 11 CCEA Mathematics: Core Knowledge Checklist | Year 11 CCEA 数学：核心知识点梳理

📚 Year 11 CCEA Mathematics: Core Knowledge Checklist | Year 11 CCEA 数学：核心知识点梳理

Understanding the core topics in Year 11 CCEA Mathematics helps you build a strong foundation for your GCSE exams. This checklist highlights essential content from number, algebra, geometry, statistics and probability that you must be confident with before moving on to more advanced study. Work through each section systematically, practising with past paper questions to reinforce your skills.

掌握 Year 11 CCEA 数学的核心主题有助于为 GCSE 考试打下扎实的基础。这份清单梳理了数、代数、几何、统计与概率等必须熟练掌握的关键内容，以便顺利衔接更高阶段的学习。建议你按顺序逐一攻破，并通过真题练习巩固技能。

1. Number and Arithmetic | 数与算术

You should be able to identify different types of numbers, including natural numbers, integers, rational and irrational numbers. Understand prime numbers, multiples, factors, highest common factor (HCF) and lowest common multiple (LCM). Apply the order of operations (BIDMAS/BODMAS) correctly and work with positive and negative integers in calculations.

你应当能够辨别不同类型的数，包括自然数、整数、有理数和无理数。理解质数、倍数、因数、最大公因数 (HCF) 和最小公倍数 (LCM)。正确使用运算顺序 (BIDMAS/BODMAS)，并在计算中熟练处理正整数和负整数。

Use index notation for squares and cubes, and evaluate roots. For example, 3² = 9 and √81 = 9. Estimate answers by rounding to one significant figure. Recognise that some square roots, such as √2, are irrational and can be left in surd form unless a decimal approximation is requested.

使用平方和立方的指数表示法，并求方根。例如，3² = 9，√81 = 9。通过四舍五入到一位有效数字进行估算。识别某些平方根是无理数（如√2），除非要求小数近似值，否则保留根式形式。

2. Fractions, Decimals and Percentages | 分数、小数和百分数

Convert confidently between fractions, decimals and percentages. For instance, 3/5 = 0.6 = 60%. Add, subtract, multiply and divide fractions and mixed numbers, simplifying answers where possible. Understand terminating and recurring decimals, and be able to express a recurring decimal as a fraction in its simplest form.

在分数、小数和百分数之间熟练转换。例如，3/5 = 0.6 = 60%。会进行分数和带分数的加、减、乘、除运算，并尽可能化简结果。理解有限小数和循环小数，能将循环小数化为最简分数。

Calculate a percentage of a quantity, percentage increase or decrease, and reverse percentages to find the original amount. Apply percentage change in real-life contexts, such as discounts, VAT, and simple interest. Use multipliers efficiently, e.g. increasing by 15% means multiplying by 1.15.

计算某个量的百分数、百分比增减以及逆向百分数以求出原值。将百分比变化应用于现实情境，如折扣、增值税和单利。高效使用乘数，例如增长 15% 即乘以 1.15。

3. Ratio and Proportion | 比与比例

Express a ratio in its simplest form and divide a quantity in a given ratio. Solve direct proportion problems using unitary method or scaling. Understand the concept of constant of proportionality and use it to set up equations like y = kx. Recognise inverse proportion, where xy = k, and solve related word problems.

将比化为最简形式，并按给定比例分配数量。使用归一法或缩放法解决正比例问题。理解比例常数的概念，并用它列出方程形如 y = kx。识别反比例关系，即 xy = k，并解决相关的文字题。

Work with scale factors in maps and scale drawings. Use ratio to compare quantities, such as concentrations, speeds, and densities. Be aware of the difference between ratio and proportion when interpreting data; for example, ‘the ratio of boys to girls is 3:2’ tells you something different from ‘3 out of every 5 students are boys’.

会在图形和比例尺中使用比例因子。用比来比较数量，如浓度、速度和密度。在解读数据时注意比和比例的区别；例如“男生与女生的比是 3:2”与“每 5 名学生中有 3 名男生”表达的信息不同。

4. Algebraic Expressions and Formulae | 代数表达式与公式

Simplify algebraic expressions by collecting like terms, expanding brackets, and factorising. Master expanding a single bracket, such as 3(2x – 5) = 6x – 15, and a double bracket, e.g. (x + 4)(x – 2) = x² + 2x – 8. Factorise quadratics of the form x² + bx + c and recognise difference of two squares: a² – b² = (a + b)(a – b).

通过合并同类项、展开括号和因式分解化简代数表达式。熟练掌握展开单括号，如 3(2x – 5) = 6x – 15，以及展开双括号，如 (x + 4)(x – 2) = x² + 2x – 8。对形如 x² + bx + c 的二次式进行因式分解，并识别平方差公式：a² – b² = (a + b)(a – b)。

Substitute numbers into formulae, including those involving negative numbers and squares. Rearrange formulae to change the subject, even when the subject appears in more than one term. For example, make t the subject of v = u + at: t = (v – u)/a. Use index laws for multiplication and division of powers with the same base.

将数值代入公式，包括含有负数和平方的公式。变换公式中的主项，即使主项出现在多个项中。例如，将 v = u + at 变为以 t 为主项：t = (v – u)/a。使用同底数幂的乘除法指数法则。

5. Equations and Inequalities | 方程与不等式

Solve linear equations with one unknown, including those with brackets and fractions. Build equations from word problems, clearly defining the variable. Solve simultaneous linear equations using both elimination and substitution methods, and interpret the solution in context.

解一元一次方程，包括含有括号和分数的方程。根据文字题建立方程，清楚地定义变量。使用加减消元法和代入法解二元一次方程组，并结合实际问题解释解。

Solve quadratic equations by factorising, and where appropriate, leave solutions as fractions or decimals. Apply the quadratic formula when factorising is not straightforward. Solve linear inequalities on a number line and represent solution sets using set notation or graphic intervals. Solve simple quadratic inequalities by considering the graph’s roots.

通过因式分解解二次方程，并在适当情况下将解保留为分数或小数。当不易因式分解时，使用二次公式。在数轴上解一元一次不等式，并用集合符号或图形区间表示解集。通过考虑函数图像的根来解简单的二次不等式。

6. Graphs of Linear and Quadratic Functions | 一次函数与二次函数的图像

Plot straight-line graphs using a table of values or by identifying gradient and y-intercept from the equation y = mx + c. Find the gradient between two points and the equation of a line given two points or a point and the gradient. Understand parallel and perpendicular lines: parallel lines have the same gradient; the product of gradients of perpendicular lines is -1.

通过数值表或从方程 y = mx + c 中识别斜率和 y 截距来绘制直线图像。计算两点间的斜率，并写出已知两点或一点和斜率时的直线方程。理解平行线和垂直线：平行线斜率相等；垂直线斜率之积为 -1。

Draw and interpret quadratic graphs (parabolas) of the form y = x² + bx + c. Identify the turning point (vertex) and roots. Use graphs to solve equations, such as finding where a line intersects a curve. Recognise how the coefficient a affects the shape, and whether the parabola opens upwards (a > 0) or downwards (a < 0).

绘制和解读形如 y = x² + bx + c 的二次函数图像（抛物线）。找出顶点和根。利用图像解方程，如求直线与曲线的交点。识别系数 a 如何影响形状，抛物线何时开口向上 (a > 0) 或向下 (a < 0)。

7. Sequences | 数列

Generate terms of a sequence from an nth term rule, or deduce the nth term for linear and quadratic sequences. For a linear (arithmetic) sequence, the nth term is of the form an + b; for a quadratic sequence, it is an² + bn + c. Use the method of differences to find the quadratic nth term.

根据第 n 项规则生成数列的项，或推导一次（等差数列）和二次数列的第 n 项。等差数列通项为 an + b；二次数列通项为 an² + bn + c。用差分法求二次数列的第 n 项。

Recognise special sequences, such as triangular numbers, square numbers, and Fibonacci-type sequences. Apply sequences to real-life problems, for instance tile patterns or savings plans. Understand the difference between a term-to-term rule and a position-to-term rule, and be able to switch between them.

识别特殊数列，如三角形数、平方数和斐波那契数列。将数列应用于实际问题，如瓷砖图案或储蓄计划。理解项间递推规则与位置通项规则的区别，并能互相转换。

8. Geometry: Angles and Shapes | 几何：角与形状

Know angle facts: angles on a straight line sum to 180°, angles around a point sum to 360°, vertically opposite angles are equal. Work with angles in parallel lines: corresponding, alternate and co-interior (allied) angles. Use these to find unknown angles in diagrams and justify your reasoning.

掌握角度知识：直线上的角之和为 180°，绕一点一周的角之和为 360°，对顶角相等。运用平行线中的角：同位角、内错角和同旁内角。利用这些知识求未知角并说明理由。

Calculate interior and exterior angles of regular polygons. The sum of interior angles of an n-sided polygon is (n – 2) × 180°. Each exterior angle of a regular polygon is 360°/n. Classify triangles by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse), and know properties such as base angles of an isosceles triangle are equal.

计算正多边形的内角和外角。n 边形内角和为 (n – 2) × 180°。正多边形的每个外角为 360°/n。根据边（不等边、等腰、等边）和角（锐角、直角、钝角）对三角形分类，并掌握性质，如等腰三角形的底角相等。

9. Pythagoras and Trigonometry | 勾股定理与三角学

Apply Pythagoras’ theorem to find missing sides in right-angled triangles:
a² + b² = c² (where c is the hypotenuse).
Use the theorem to decide whether a triangle is right-angled by checking if the side lengths satisfy the equation. Solve problems involving 3D shapes by identifying right-angled triangles within them.

应用勾股定理求直角三角形的未知边：
a² + b² = c²（其中 c 为斜边）。
通过检验边长是否满足方程来判断三角形是否为直角三角形。在三维图形中识别直角三角形，解决相关问题。

Use the trigonometric ratios sine, cosine and tangent to find missing sides and angles in right-angled triangles. Remember SOH CAH TOA:
sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, tanθ = opposite/adjacent.
Calculate angles using the inverse functions sin⁻¹, cos⁻¹, tan⁻¹. Apply trigonometry to bearings and angle of elevation/depression problems.

使用三角函数比（正弦、余弦和正切）求直角三角形中缺失的边和角。记住 SOH CAH TOA：
sinθ = 对边/斜边，cosθ = 邻边/斜边，tanθ = 对边/邻边。
使用反函数 sin⁻¹、cos⁻¹、tan⁻¹ 计算角度。将三角学应用于方位角和仰角/俯角问题。

10. Perimeter, Area and Volume | 周长、面积与体积

Calculate the perimeter and area of rectangles, triangles, parallelograms, trapezia and compound shapes. Know the area of a triangle as ½ × base × height, and area of a trapezium as ½(a + b)h. Find the circumference and area of a circle using π: C = 2πr or πd, A = πr². Leave answers in terms of π unless told otherwise.

计算矩形、三角形、平行四边形、梯形和组合图形的周长与面积。记住三角形面积公式 ½ × 底 × 高，梯形面积公式 ½(a + b)h。使用 π 求圆的周长和面积：C = 2πr 或 πd，A = πr²。除非另有说明，答案可保留 π。

Work with volume and surface area of prisms, cylinders, and pyramids. Volume of a prism = area of cross-section × length. Volume of a cylinder = πr²h. Calculate the volume of a sphere (4/3 πr³) and cone (1/3 πr²h) if specified. Use standard units and convert between metric units of length, area and volume.

掌握棱柱、圆柱和棱锥的体积与表面积。棱柱体积 = 横截面积 × 长。圆柱体积 = πr²h。若指定，计算球体体积 (4/3 πr³) 和圆锥体积 (1/3 πr²h)。使用标准单位，并在长度、面积和体积的公制单位之间转换。

11. Probability | 概率

Understand that probability is a measure of the likelihood of an event occurring, with values between 0 and 1. Use the formula: P(event) = number of favourable outcomes / total number of outcomes. Work with mutually exclusive events, where P(A or B) = P(A) + P(B), and exhaustive events, where probabilities sum to 1.

理解概率是事件发生可能性的度量，取值范围在 0 和 1 之间。使用公式：P(事件) = 有利结果数 / 总结果数。运用互斥事件，P(A 或 B) = P(A) + P(B)，以及完备事件组，其概率之和为 1。

Use tree diagrams to calculate probabilities of independent and dependent events, remembering to multiply along branches and add for combined events. Construct and interpret two-way tables and Venn diagrams to solve probability problems. Apply conditional probability where appropriate, expressed as P(A|B).

使用树状图计算独立事件和相关事件的概率，沿分支相乘，合并事件时相加。构建并解读双向表和文氏图以解决概率问题。在适当情况下计算条件概率，记为 P(A|B)。

12. Statistics and Data Handling | 统计与数据处理

Collect, organise and present data using bar charts, pie charts, histograms with equal class intervals, and frequency polygons. Calculate mean, median, mode and range for discrete and continuous data. Find the mean from a frequency table using Σfx/Σf, and estimate the mean from grouped data using midpoints.

收集、整理并使用条形图、饼图、等组距直方图和频数多边形展示数据。计算离散数据和连续数据的均值、中位数、众数和极差。利用频率表使用 Σfx/Σf 求均值，并利用组中值估算分组数据的均值。

Interpret scatter graphs, draw a line of best fit and describe correlation (positive, negative or none). Understand that correlation does not imply causation. Use cumulative frequency graphs to find the median, quartiles and interquartile range. Construct box plots and use them to compare distributions.

解读散点图，画出最佳拟合线并描述相关性（正相关、负相关或无相关）。理解相关并不意味因果。使用累积频数图求中位数、四分位数和四分位距。绘制箱线图并用于比较分布。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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