📚 Year 7 SQA Mathematics: Key Concepts Review | Year 7 SQA 数学：核心知识点梳理
Welcome to your comprehensive guide to Year 7 SQA Mathematics. This article brings together the most important topics you will encounter in S1, aligned with Scotland’s Curriculum for Excellence (CfE) Level 3. Whether you are consolidating your classroom learning or preparing for assessments, each section breaks down a key concept with clear explanations and examples. Keep this revision guide close by as you build confidence in numbers, algebra, geometry, data handling, and more.
欢迎来到 Year 7 SQA 数学全面指南。本文汇总了您在 S1 阶段将会遇到的最重要主题，与苏格兰卓越课程 (CfE) 第三级水平对齐。无论您是在巩固课堂学习，还是在为评估做准备，每个部分都以清晰的解释和示例来分解核心概念。在逐步建立对数字、代数、几何、数据处理等内容的自信心时，请随时参考这份复习指南。
1. Number Systems and Place Value | 数系与位值
At the heart of Year 7 mathematics lies a fluent understanding of whole numbers, decimals, and the place value system. You must be able to read, write, order, and round numbers up to millions and beyond, identifying the value of each digit according to its position.
Year 7 数学的核心在于对整数、小数和位值体系的熟练掌握。你需要能够读写、排序和四舍五入达到百万乃至更大的数，并根据数字的位置识别每一位的数值。
We often round numbers to the nearest 10, 100, 1000 or to a given number of decimal places. When rounding, look at the digit immediately to the right of the required place: if it is 5 or more, round up. Another key skill is partitioning numbers, for example writing 6752 as 6000 + 700 + 50 + 2.
我们经常将数字四舍五入到最接近的10、100、1000 或指定位数的小数。四舍五入时，观察目标位右边紧邻的数字：如果该数字是 5 或以上，则进位。另一个关键技能是数字拆分，例如把 6752 写作 6000 + 700 + 50 + 2。
Multiplying and dividing by powers of 10 (10, 100, 1000) shifts digits to the left or right in the place value columns. This concept directly supports later work with decimals and metric conversions, so practice moving the digits rather than just adding or removing zeros.
乘以或除以 10 的幂（10、100、1000）会使数字在位值列中向左或向右移动。这一概念直接支持后续的小数运算和公制单位换算，因此要练习移动数字位置，而不仅仅是添加或删除零。
2. Fractions, Decimals, and Percentages | 分数、小数与百分数
Year 7 learners deepen their understanding of the links between fractions, decimals, and percentages. A fraction like 3/4 can be written as the decimal 0.75 and as the percentage 75%. Recognising these equivalences without always calculating is a useful mental maths shortcut.
Year 7 学习者会加深对分数、小数和百分数之间联系的理解。像 3/4 这样的分数可以表示为小数 0.75 和百分数 75%。无需始终计算就能识别这些等价关系，是一项有用的心算技巧。
To convert a fraction to a decimal, divide the numerator by the denominator. For instance, 3/8 becomes 3 ÷ 8 = 0.375. To turn a decimal into a percentage, multiply by 100 and add the percent sign – 0.375 becomes 37.5%. Finding a percentage of an amount often involves multiplying by the fraction or decimal equivalent, and you should become comfortable with common benchmarks such as 10%, 25%, 50%, and 75%.
要将分数转换为小数，用分子除以分母。例如 3/8 变成 3 ÷ 8 = 0.375。要将小数转换为百分数，乘以 100 并添加百分号 —— 0.375 变成 37.5%。求一个数量的百分数通常涉及乘以等效的分数或小数，你应该熟练掌握像 10%、25%、50% 和 75% 这样的常见基准。
Adding and subtracting fractions require a common denominator. For varied denominators, find the lowest common multiple (LCM). Multiplying fractions is done by multiplying numerators together and denominators together. Always simplify your answers to their lowest terms.
加减分数需要通分到相同分母。对于不同的分母，找到最小公倍数 (LCM)。分数乘法是将分子相乘、分母相乘。永远要把答案化简到最简形式。
3. Negative Numbers | 负数
Working with negative numbers becomes routine in Year 7. We use them in context – temperature, bank balances, depths below sea level – and on the number line. A number line helps visualise addition and subtraction: moving right for addition, left for subtraction.
在 Year 7，与负数打交道会变得日常化。我们在温度、银行余额、海平面以下深度等情境中使用它们，并在数轴上表示。数轴有助于将加法和减法可视化：加法向右移动，减法向左移动。
When subtracting a negative number, the two minus signs become a plus. For example, 5 – (-3) = 5 + 3 = 8. Multiplying and dividing with negatives follow a simple rule: same signs give a positive result, different signs give a negative result. So (-4) × (-6) = 24, while (-4) × 6 = -24.
当减去一个负数时，两个减号变为加号。例如 5 – (-3) = 5 + 3 = 8。涉及负数的乘法和除法遵循一条简单规则：同号得正，异号得负。因此 (-4) × (-6) = 24，而 (-4) × 6 = -24。
Always be careful with the order of operations (BODMAS/BIDMAS) when negative numbers are inside brackets or paired with powers. Brackets, Orders, Division and Multiplication (left to right), Addition and Subtraction (left to right) still apply.
当负数位于括号内或与幂结合时，务必注意运算顺序 (BODMAS/BIDMAS)。括号、幂、除法和乘法（从左到右）、加法和减法（从左到右）依然适用。
4. Algebraic Expressions and Patterns | 代数表达式与规律
Algebra in Year 7 is about spotting patterns and writing simple rules using letters to stand for unknown numbers. You will learn to form expressions such as 3a + 2 or 5n – 7 from word statements and number sequences.
Year 7 的代数主要在于发现规律，并用字母代表未知数来书写简单规则。你将学会从文字描述和数列中构建如 3a + 2 或 5n – 7 这样的表达式。
Collecting like terms is a fundamental algebraic skill. Terms with the same letter part can be combined: 2x + 3y + 5x – y simplifies to 7x + 2y. You cannot combine terms with different letters or number-only terms with letter terms. Expanding a single bracket, such as 3(m + 4), uses the distributive law to give 3m + 12.
合并同类项是一项基本的代数技能。具有相同字母部分的项可以合并：2x + 3y + 5x – y 简化为 7x + 2y。你不能合并具有不同字母的项，也不能将纯数字项与含字母项合并。展开一个单项式括号，例如 3(m + 4)，应用分配律得到 3m + 12。
When working with sequences, you will be asked to find the next terms and describe the term-to-term rule, then move on to finding a position-to-term rule (the nth term). For the sequence 5, 8, 11, 14, …, the nth term is 3n + 2.
在处理数列时，你会被要求找出后续项并描述项间规则，然后进一步找到位置对项的规则（第 n 项）。对于数列 5, 8, 11, 14, …，第 n 项是 3n + 2。
5. Solving Simple Equations | 解简单方程
An equation states that two expressions are equal, and solving it means finding the value of the unknown letter that makes the statement true. Year 7 pupils work largely with one-step and two-step equations.
方程表示两个表达式相等，解方程意味着找到使等号成立的未知数的值。Year 7 学生主要处理一步和两步方程。
To keep an equation balanced, whatever operation you do to one side, you must do to the other. For x + 7 = 15, subtract 7 from both sides to get x = 8. For 4y = 28, divide both sides by 4, giving y = 7. When solving two-step equations like 2p – 3 = 9, undo the subtraction first (add 3 to both sides), then divide by 2 to find p = 6.
为了保持方程平衡，你对等式一边所做的任何运算，必须对另一边也做同样的运算。对于 x + 7 = 15，两边同时减去 7 得到 x = 8。对于 4y = 28，两边同时除以 4，得到 y = 7。在解如 2p – 3 = 9 的两步方程时，先消除减法（两边加 3），然后除以 2，求得 p = 6。
Check your solution by substituting the value back into the original equation. Always write the final answer clearly, often concluding with x = …
通过将所得数值代入原方程来检验你的解。始终清晰地写出最终答案，通常以 x = … 结尾。
6. Angles and Lines | 角与线段
Geometry in S1 introduces you to angle facts involving straight lines, points, and intersecting lines. You need to know that angles on a straight line add up to 180° and angles around a point sum to 360°.
S1 的几何会向你介绍涉及直线、点和相交线的角的事实。你需要知道直线上的角总和为 180°，围绕一个点的角总和为 360°。
Vertically opposite angles are equal when two lines cross. Recognising alternate angles and corresponding angles on parallel lines is a major step. If a pair of parallel lines is cut by a transversal, corresponding angles are equal, alternate angles are equal, and interior (co-interior) angles add up to 180°.
当两条直线交叉时，对顶角相等。识别平行线上的内错角和同位角是重要一步。如果一对平行线被一条横切线所截，同位角相等，内错角相等，同旁内角（共内角）之和为 180°。
Always use a protractor to measure and draw angles accurately. You will be expected to calculate missing angles in diagrams by applying angle facts, not by measuring them if precise numbers are given.
始终使用量角器准确地测量和绘制角。你将被要求在图表中通过应用角的事实来计算缺失的角，而不是在给定了精确数字时再去测量它们。
7. Properties of 2D Shapes | 二维图形的性质
Year 7 students classify triangles by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Equilateral triangles have three equal sides and three 60° angles. Isosceles triangles have two equal sides and two equal base angles.
Year 7 学生根据边（等边、等腰、不等边）和角（锐角、直角、钝角）对三角形进行分类。等边三角形有三条相等的边和三个 60° 的角。等腰三角形有两条相等的边和两个相等的底角。
Quadrilaterals include squares, rectangles, parallelograms, rhombuses, trapeziums, and kites. Each has specific side, angle, and diagonal properties. You should be able to identify them on a coordinate grid and use their symmetry to solve problems.
四边形包括正方形、长方形、平行四边形、菱形、梯形和风筝形。每种都有特定的边、角和对角线性质。你应该能够在坐标网格上识别它们，并利用它们的对称性来解决问题。
Lines of symmetry and rotational symmetry are important. A square has four lines of symmetry and rotational symmetry of order 4. Most quadrilaterals have an order of rotational symmetry equal to the number of times they map onto themselves in a full turn.
对称线和旋转对称很重要。正方形有4条对称线，旋转对称的阶数为4。大多数四边形的旋转对称阶数等于其在完整一周内与自身重合的次数。
8. Perimeter, Area, and Volume | 周长、面积与体积
Perimeter is the distance around the outside of a shape. For rectangles, perimeter = 2(length + width). Composite shapes require adding all side lengths, sometimes after splitting them into simpler shapes.
周长是一个图形外边界的距离。对于长方形，周长 = 2 × (长 + 宽)。复合图形需要将所有边长相加，有时需要先将它们拆分为更简单的形状。
Area measures the space inside a 2D shape. Key formulas: area of a rectangle = length × width; area of a triangle = ½ × base × height; area of a parallelogram = base × perpendicular height. Compound area problems ask you to break a shape into rectangles and triangles, calculate each area, and then sum or subtract them.
面积测量二维图形内部的空间大小。关键公式：长方形面积 = 长 × 宽；三角形面积 = ½ × 底 × 高；平行四边形面积 = 底 × 垂直高。复合面积问题要求你将图形分解为长方形和三角形，分别计算面积，然后相加或相减。
Volume of a cuboid is found by length × width × height. You will often visualise cubes and cuboids and count unit cubes. The capacity link (1 cm³ = 1 ml) also appears. Remember to use correct units – cm, cm², cm³ – and stay consistent.
长方体的体积由 长 × 宽 × 高 求得。你经常会想象立方体和长方体并计算单位立方体的数量。容量联系（1 cm³ = 1 ml）也会出现。记住使用正确的单位 —— cm、cm²、cm³ —— 并保持一致。
9. Data Handling and Averages | 数据处理与平均数
Interpreting and constructing bar charts, line graphs, pictograms, and pie charts is central to Year 7 data handling. You must be able to read scales, compare data sets, and spot trends.
解释和构建条形图、折线图、象形图和饼图是 Year 7 数据处理的核心。你必须能够读取刻度、比较数据集并发现趋势。
The three measures of average are the mean, median, and mode. The mean is found by adding all values and dividing by how many values there are. The median is the middle value when data is ordered; if there are two middle numbers, take their mean. The mode is the most frequent value.
三种平均数度量是平均数、中位数和众数。平均数是将所有数值相加并除以数值的个数。中位数是将数据排序后的中间值；如果有两个中间数，则取它们的平均数。众数是出现频率最高的值。
The range, calculated as maximum minus minimum, measures the spread of a data set. A smaller range suggests more consistency. When analysing data, comment on both an average and the range to give a fuller picture.
极差，由最大值减最小值计算得出，衡量数据集的离散程度。较小的极差表明更稳定。在分析数据时，应同时评论平均数和极差，以提供更全面的信息。
10. Probability | 概率
Probability in Year 7 is introduced as a number between 0 and 1 (or as a fraction, decimal, or percentage) that describes how likely an event is to happen. A probability of 0 means impossible; a probability of 1 means certain.
Year 7 中的概率作为一个介于 0 和 1 之间的数字（或分数、小数、百分数）引入，用来描述一个事件发生的可能性有多大。概率为 0 表示不可能；概率为 1 表示必然发生。
The probability of an event is calculated as: Number of favourable outcomes ÷ Total number of possible outcomes. When tossing a fair coin, P(head) = 1/2. Expectation is the long-run average: if you flip a coin 100 times, the expected number of heads is 50, but the actual number will vary.
事件的概率通过以下公式计算：有利结果的数量 ÷ 可能结果的总数。抛掷一枚公平硬币时，P(正面) = 1/2。期望值是长期的平均值：如果你抛一枚硬币 100 次，预期的正面次数是 50，但实际次数会有变化。
Probability scales and chance vocabulary (impossible, unlikely, even chance, likely, certain) are used to describe outcomes. You will carry out simple experiments and compare relative frequencies with theoretical probabilities, noticing that more trials bring the experimental probability closer to the theoretical one.
概率尺度和机会词汇（不可能、不太可能、均等机会、很可能、必然）用于描述结果。你将进行简单的实验，并将相对频率与理论概率进行比较，注意更多的试验会使实验概率更接近理论概率。
11. Ratio and Proportion | 比与比例
Ratio compares the sizes of two or more quantities. In a fruit bowl with 6 apples and 4 oranges, the ratio of apples to oranges is 6:4, which simplifies to 3:2. Simplifying ratios is just like simplifying fractions: divide both sides by the same number.
比用于比较两个或多个数量的大小。在一个有 6 个苹果和 4 个橙子的水果碗里，苹果与橙子的比是 6:4，化简为 3:2。化简比就像化简分数一样：两边同时除以同一个数。
Proportion problems often involve finding a missing value when one part of a ratio is known. For a paint mix where the ratio of blue to white is 1:5, if you use 3 litres of blue, you need 3 × 5 = 15 litres of white. This is sometimes called the unitary method.
比例问题常常涉及已知比的某一部分时求出缺失值。对于蓝色与白色比例为 1:5 的颜料混合物，如果你用了 3 升蓝色，那么你需要 3 × 5 = 15 升白色。这有时被称为归一法。
Map scales and scale drawings are practical applications of ratio. A scale of 1:50 000 means 1 cm on the map represents 50 000 cm (or 0.5 km) in real life. Always remember to convert units when necessary.
地图比例尺和比例图是比的实际应用。比例尺 1:50 000 意味着地图上的 1 厘米代表实际生活中的 50 000 厘米（或 0.5 公里）。始终记住在必要时进行单位换算。
12. Coordinates and Graphs | 坐标与图表
The coordinate system is extended in Year 7 to include all four quadrants. Coordinates are written as (x, y), where the x-coordinate comes first. The x-axis is horizontal; the y-axis is vertical. You will plot and read points accurately on a grid.
Year 7 的坐标系统扩展到包含所有四个象限。坐标写作 (x, y)，其中 x 坐标在前。x 轴是水平的；y 轴是垂直的。你将准确地在网格上描点和读点。
Straight-line graphs can be created from a simple rule, such as y = 2x + 1. By choosing a set of x values, calculating the corresponding y values, and plotting the points, you see that they form a straight line. Understanding that the coordinates of any point on the line satisfy the equation is foundational for later algebra.
直线图可以由简单的规则生成，例如 y = 2x + 1。通过选择一组 x 值，计算对应的 y 值，并描点，你会看到它们形成一条直线。理解线上任意点的坐标都满足该方程，是后续代数的基础。
Interpreting real-life graphs, such as distance-time graphs, is also practiced. The slope of a distance-time graph tells you about speed: a steeper slope means a faster speed, and a flat horizontal section means the object is stationary.
解释现实生活中的图表，例如距离-时间图，也是练习的内容。距离-时间图的斜率告诉你关于速度的信息：斜率越大，速度越快；一段水平的平直部分意味着物体静止。
Hint: always label axes and include a title when drawing your own graphs.
提示：在绘制自己的图表时，始终标注坐标轴并添加标题。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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