📚 Year 7 AQA Maths: Core Topics Simplified | Year 7 AQA 数学：核心知识点梳理
For Year 7 students following the AQA curriculum, mastering foundational maths skills is essential for future success. This guide breaks down the core topics into clear, manageable sections, with bilingual explanations to support learning.
对于学习 AQA 课程的七年级学生来说，掌握数学基础技能对未来的成功至关重要。本指南将核心知识点分解为清晰易掌握的部分，并提供双语解释以辅助学习。
1. Number and Place Value | 数字与位值
Whole numbers are written using digits 0–9, and the position of each digit tells us its value (units, tens, hundreds, etc.).
整数使用数字 0 到 9 书写，每个数字的位置决定了它的数值（个位、十位、百位等）。
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Units |
| 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |
numbers, round to the nearest 10, 100 or 1000, and compare using symbols >, < and =.
理解位值有助于我们给数字排序、四舍五入到最接近的十位、百位或千位，以及使用 >、< 和 = 进行比较。
2. Addition, Subtraction, Multiplication and Division | 加减乘除
Column methods allow us to add and subtract large numbers efficiently. Always line up digits by place value.
使用竖式方法可以高效地进行大数加减法。务必按位值对齐数字。
use times tables up to 12 × 12. The grid method expands numbers and multiplies each part.
乘法可以看作是重复加法，我们需要熟记 12 × 12 以内的乘法表。网格法将数字拆分后分别相乘。
Division is sharing or grouping. Short division (bus stop method) works well for dividing by a single digit.
除法是平均分配或分组。短除法（公交车站法）非常适合除以一位数。
Remember the order of operations: Brackets, Indices, Division and Multiplication (left to right), Addition and Subtraction (left to right). BIDMAS.
记住运算顺序：括号、指数、乘除（从左到右）、加减（从左到右），简称 BIDMAS。
3. Fractions, Decimals and Percentages | 分数、小数与百分数
Fractions show parts of a whole. The numerator (top) tells how many parts we have; the denominator (bottom) tells how many equal parts the whole is divided into.
分数表示整体的一部分。分子（上）表示我们有多少份，分母（下）表示整体被分成多少等份。
ue, e.g. ½ = ²⁄₄ = ⁴⁄₈. Simplify by dividing numerator and denominator by the same number.
等值分数表示相同的数值，例如 ½ = ²⁄₄ = ⁴⁄₈。通过将分子和分母除以相同的数来化简。
To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100.
要将分数转换为小数，用分子除以分母。要将小数转换为百分数，乘以 100。
Key conversions to learn: ½ = 0.5 = 50%, ¼ = 0.25 = 25%, ¾ = 0.75 = 75%, ¹⁄₁₀ = 0.1 = 10%.
需要记住的关键转换：½ = 0.5 = 50%，¼ = 0.25 = 25%，¾ = 0.75 = 75%，¹⁄₁₀ = 0.1 = 10%。
4. Ratio and Proportion | 比与比例
A ratio compares quantities. The ratio 3 : 2 means for every 3 of the first item, there are 2 of the second.
比用来比较数量。3 : 2 表示每 3 份第一个物品对应 2 份第二个物品。
Ratios can be simplified like fractions by dividing both sides by the same number.
比可以像分数一样通过两边除以相同的数来化简。
Proportion describes a part compared to the whole. If the ratio of boys to girls is 3 : 2, the proportion of boys is 3 out of 5, or ³⁄₅.
比例描述部分与整体的关系。如果男生与女生的比是 3 : 2，那么男生的比例是 5 份中的 3 份，即 ³⁄₅。
Use the unitary method to find the value of one part first, then scale up or down.
使用单位法先求出一份的值，再进行放大或缩小。
5. Algebra: Expressions and Formulae | 代数：表达式与公式
Algebra uses letters to represent unknown numbers. An expression like 3a + 2 combines numbers and letters with operations.
代数用字母表示未知数。像 3a + 2 这样的表达式将数字和字母与运算组合在一起。
We can simplify expressions by collecting like terms: 4x + 2y + x − y = 5x + y.
我们可以通过合并同类项来简化表达式：4x + 2y + x − y = 5x + y。
shows a relationship between variables, e.g. P = 2l + 2w for the perimeter of a rectangle.
公式显示了变量之间的关系，例如长方形的周长公式 P = 2l + 2w。
Substitute numbers into a formula: if l = 5 and w = 3, then P = 2 × 5 + 2 × 3 = 16.
将数字代入公式：如果 l = 5，w = 3，则 P = 2 × 5 + 2 × 3 = 16。
6. Equations and Inequalities | 方程与不等式
, e.g. x + 3 = 7. Solve by doing the inverse operation to both sides: x = 7 − 3, so x = 4.
方程表示两个表达式相等，例如 x + 3 = 7。通过对两边进行逆运算来求解：x = 7 − 3，因此 x = 4。
Always keep the equation balanced – whatever you do to one side, you must do to the other.
始终保持方程平衡——对一边做什么，对另一边也要做同样的操作。
;, ≥, ≤. The solution x > 2 means x can be any number greater than 2, but not 2 itself.
不等式使用符号 >、<、≥、≤。解 x > 2 表示 x 可以是任何大于 2 的数，但不包括 2。
Represent inequalities on a number line with open or closed circles.
用空心或实心圆点在数轴上表示不等式。
7. Sequences | 数列
A sequence is a list of numbers following a rule. In an arithmetic sequence, the difference between terms is constant.
数列是按照某种规律排列的一列数。在等差数列中，相邻两项的差是常数。
Term‑to‑term rule tells you how to get from one term to the next, e.g. add 4 each time: 3, 7, 11, 15, …
逐项规则告诉你如何从一项得到下一项，例如每次加 4：3, 7, 11, 15, …
The position‑to‑term rule (nth term) uses the position n to find any term. For the sequence 5, 10, 15, 20, … the rule is 5n.
位置到项的规则（第 n 项）使用位置 n 来求任意一项。对于数列 5, 10, 15, 20, …，规则是 5n。
Generate the first five terms using the rule: start at 2, multiply by 3 and subtract 1 each time. (First term given as 2).
使用规则生成前五项：从 2 开始，每次乘以 3 然后减去 1。（首项给定为 2）。
8. Geometry: Angles and Lines | 几何：角度与线
Angles are measured in degrees (°). A right angle is 90°, acute < 90°, obtuse between 90° and 180°, reflex > 180°.
角度以度（°）为单位。直角为 90°，锐角小于 90°，钝角在 90° 到 180° 之间，优角大于 180°。
Angles on a straight line add up to 180°. Angles around a point total 360°.
直线上的角之和为 180°。一个点周围的角之和为 360°。
Vertically opposite angles are equal. When two lines intersect, opposite angles have the same measure.
对顶角相等。当两条直线相交时，相对的角大小相等。
In parallel lines, alternate angles are equal, corresponding angles are equal, and co‑interior angles sum to 180°.
在平行线中，内错角相等，同位角相等，同旁内角互补（和为 180°）。
9. Perimeter, Area and Volume | 周长、面积与体积
around a shape. For a rectangle: P = 2(l + w). Add all side lengths for irregular shapes.
周长是图形一周的长度。对于长方形：P = 2(l + w)。不规则图形需将所有边长相加。
easures the surface inside a shape. Rectangle: A = l × w. Triangle: A = ½ × base × height.
面积衡量图形内部表面的大小。长方形：A = l × w。三角形：A = ½ × 底 × 高。
Units: area is in square units (cm², m²). Volume is in cubic units (cm³, m³).
单位：面积用平方单位（厘米²，米²）。体积用立方单位（厘米³，米³）。
of a cuboid: V = length × width × height. Count cubes to find volume of irregular solids.
长方体体积：V = 长 × 宽 × 高。数小立方体个数来求不规则立体的体积。
10. Coordinates and Graphs | 坐标与图表
Coordinates are written as (x, y). The x‑axis is horizontal, the y‑axis is vertical. The origin is (0, 0).
坐标写作 (x, y)。x 轴是水平的，y 轴是垂直的。原点为 (0, 0)。
Plot points by moving along the x‑axis first, then up the y‑axis. 'Along the corridor, up the stairs.'
描点时先沿 x 轴移动，再沿 y 轴向上移动。“先走过走廊，再上楼梯。”
Straight‑ from equations like y = 2x + 1. Create a table of values, plot points, then draw the line.
由方程如 y = 2x + 1 绘制的直线图。先列数值表，描点，然后连线。
The gradient tells us how steep the line is. The intercept is where the line crosses the y‑axis.
斜率表示直线的陡峭程度。截距是直线与 y 轴相交的点。
11. Statistics | 统计
Data can be collected, organised and displayed. Tally charts and frequency tables help count occurrences.
数据可以被收集、整理和展示。计数表和频数表帮助记录出现次数。
Bar charts show discrete data with gaps between bars. The height of each bar represents the frequency.
条形图用于显示离散数据，条形之间有空隙。每条的高度代表频数。
Pictograms use symbols to represent a number of items. A key explains the scale.
象形图使用符号来表示若干项目。图例解释比例。
The mean is the average: sum of values divided by the number of values. The median is the middle value when ordered. The mode is the most frequent value.
平均数（均值）是将所有数值之和除以数值的个数。中位数是将数据排序后位于中间的值。众数是出现最频繁的值。
12. Probability | 概率
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain).
概率衡量事件发生的可能性，范围从 0（不可能）到 1（必定发生）。
obability of an event = number of favourable outcomes / total number of possible outcomes.
事件概率 = 有利结果的数量 / 所有可能结果的总数。
Probabilities can be written as fractions, decimals or percentages. The probability of rolling a 3 on a fair dice is ¹⁄₆.
概率可以写成分数、小数或百分数。掷一枚均匀骰子得到 3 的概率是 ¹⁄₆。
The probabilities of all possible outcomes add up to 1. If the probability of rain is 0.3, the probability it does not rain is 0.7.
所有可能结果的概率之和为 1。如果下雨的概率是 0.3，那么不下雨的概率是 0.7。
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