📚 Year 7 SQA Maths Formula Quick Reference Guide | 七年级 SQA 数学公式速查手册
This quick reference guide covers the essential mathematical formulas and theorems that every Year 7 student following the SQA curriculum needs to know. Whether you are revising for an end-of-topic test or preparing for assessments, these bite-sized summaries will help you recall key methods for perimeter, area, volume, angles, averages, and more. Each formula is presented in a clear, bilingual format so you can build confidence in both English and mathematical Chinese terminology.
这份速查手册涵盖了每一位 SQA 课程七年级学生都必须掌握的基本数学公式和定理。无论你是在为期末测验复习，还是在备战评估，这些简洁的归纳都能帮你快速回忆周长、面积、体积、角度、平均值等关键计算方法。每条公式都以清晰的中英对照形式呈现，让你同时熟悉英文和数学中文术语，从而建立信心。
1. Perimeter and Area of Squares and Rectangles | 正方形和长方形的周长与面积
The perimeter is the total distance around the edge of a shape. For a rectangle, add the length and width together, then multiply by 2. For a square, multiply the side length by 4. The area measures the surface inside the shape: for a rectangle, multiply length by width; for a square, side × side.
周长是图形边缘的总长度。长方形周长：将长和宽相加，再乘以 2。正方形周长：边长 × 4。面积测量图形内部的表面大小：长方形面积 = 长 × 宽；正方形面积 = 边长 × 边长。
Perimeter of a rectangle = 2(l + w) Area of a rectangle = l × w
长方形周长 = 2(长 + 宽) 长方形面积 = 长 × 宽
Perimeter of a square = 4s Area of a square = s²
正方形周长 = 4 × 边长 正方形面积 = 边长²
2. Area of a Triangle | 三角形的面积
To find the area of any triangle, you need the base length and the perpendicular height (the height at a right angle to the base). The formula is half the base multiplied by the height. Remember that the height must be the vertical measurement, not the slanting side unless the triangle is right-angled.
要计算任意三角形的面积，你需要底边长度和垂直高度（与底边成直角的高度）。公式为底乘高除以二。请记住，高度必须是垂直距离，而不是斜边长度，除非该三角形是直角三角形。
Area of a triangle = ½ × base × height
三角形面积 = ½ × 底 × 高
3. Area of a Parallelogram | 平行四边形的面积
A parallelogram is a four-sided shape with opposite sides parallel. Its area is calculated by multiplying the base length by the vertical height (not the slant height). The vertical height is the perpendicular distance between the base and the opposite side.
平行四边形是一种对边平行的四边形。其面积的计算方法为底边长乘以垂直高度（而非斜边高）。垂直高度是指底边与其对边之间的垂直距离。
Area of a parallelogram = base × vertical height
平行四边形面积 = 底 × 垂直高
4. Area of a Circle | 圆的面积
The area of a circle uses the radius (the distance from the centre to the edge) and the constant π (pi), which is approximately 3.14. The formula is pi times the square of the radius. If you are given the diameter, remember to halve it to find the radius before squaring.
圆的面积要用半径（圆心到圆周的距离）和常数 π（圆周率）进行计算，π 约等于 3.14。公式为 π 乘以半径的平方。如果已知直径，请记住先将其除以 2 得到半径，再计算平方。
Area of a circle = π × r² (where r = radius)
圆的面积 = π × 半径² (r = 半径)
5. Circumference of a Circle | 圆的周长
The circumference is the distance all the way round the circle. There are two common formulas: one using the radius (2 × π × r) and one using the diameter (π × d). Use whichever is easier with the information given in the question.
周长是绕圆一周的长度。常见公式有两种：一种用半径（2 × π × r），另一种用直径（π × d）。根据题目给出的已知条件，选择更方便的公式即可。
Circumference = 2 × π × r or Circumference = π × d
圆的周长 = 2 × π × 半径 或 圆的周长 = π × 直径
6. Volume of a Cuboid | 长方体的体积
Volume measures the space inside a 3D shape. For a cuboid (a box-shaped solid), multiply the length, width, and height. The answer is always in cubic units (e.g., cm³). Make sure all three dimensions are in the same unit before multiplying.
体积用于测量三维图形内部的空间大小。对于长方体（盒状立体），将长、宽、高相乘即可。答案单位始终为立方单位（如 cm³）。相乘前请确保三个维度的单位一致。
Volume of a cuboid = length × width × height
长方体体积 = 长 × 宽 × 高
7. Angles on a Straight Line and Around a Point | 平角与周角
Angles on a straight line always add up to 180 degrees. Angles around a single point add up to 360 degrees. These rules help you find missing angles in intersecting lines and diagrams without needing to measure them.
直线上的角之和始终为 180 度。围绕一个点的所有角之和为 360 度。利用这些规则，你无需测量即可求出相交直线和图形中未知角的大小。
Angles on a straight line sum to 180° Angles around a point sum to 360°
直线上的角之和 = 180° 绕点一周的角之和 = 360°
8. Mean, Median, Mode, and Range | 平均数、中位数、众数和范围
These four terms summarise sets of data. The mean is found by adding all values and dividing by how many there are. The median is the middle value when the data is sorted in order. The mode is the value that appears most often. The range is the difference between the largest and smallest values.
这四个术语用于概括一组数据。平均数（均值）是将所有数值相加后除以数据个数。中位数是将数据按顺序排列后位于中间的数。众数是出现次数最多的数值。范围（极差）是最大值与最小值之差。
Mean = (sum of values) ÷ (number of values)
平均数 = (数值总和) ÷ (数值个数)
Range = largest value − smallest value
范围 = 最大值 − 最小值
9. Speed, Distance, Time | 速度、距离、时间
The relationship between speed, distance, and time is often remembered as the formula triangle. Distance travelled equals speed multiplied by time. Rearrange it to find speed (distance ÷ time) or time (distance ÷ speed). Always check the units of measurement before doing calculations.
速度、距离和时间之间的关系常通过“公式三角形”来记忆。行驶距离等于速度乘以时间。可根据需要变形公式：求速度用距离除以时间，求时间用距离除以速度。计算前务必检查测量单位是否统一。
Distance = Speed × Time
距离 = 速度 × 时间
Speed = Distance ÷ Time Time = Distance ÷ Speed
速度 = 距离 ÷ 时间 时间 = 距离 ÷ 速度
10. Percentage Change | 百分比变化
Percentage change compares the difference between an old value and a new value relative to the original amount. First, work out the actual change (increase or decrease), then divide by the original quantity, and finally multiply by 100 to get the percentage. This formula is used to describe discounts, profits, and growth.
百分比变化用于比较新旧数值之间的差异占原始量的比例。先算出实际变化量（增加或减少），再除以原值，最后乘以 100 得到百分比。这个公式常用于描述折扣、利润和增长。
Percentage change = (change ÷ original amount) × 100%
百分比变化 = (变化值 ÷ 原始量) × 100%
11. Simple Algebraic Substitution and Simplifying | 简单的代数代入与化简
Algebra uses letters (often x, y, a, b) to stand for unknown numbers. Substitution means replacing a letter with a known number and calculating the result. Simplifying an expression involves collecting like terms (terms with the same letter or number part). For example, 3a + 2a simplifies to 5a, while a × a is written as a².
代数用字母（通常为 x、y、a、b）表示未知数。代入是指用已知的数字替换字母，再计算出结果。化简表达式则需要合并同类项（含有相同字母或数字部分的项）。例如，3a + 2a 可化简为 5a，而 a × a 写作 a²。
When a = 4, the expression 3a + 2 = 3(4) + 2 = 14
当 a = 4 时，表达式 3a + 2 = 3×4 + 2 = 14
12. Units and Conversion Reminders | 单位与换算提醒
Always check that lengths are in the same unit before applying area or volume formulas. Common metric conversions include 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m. For mass, 1 kg = 1000 g. For capacity, 1 litre = 1000 ml. Remember that 1 m² = 10,000 cm², not 100 cm², because area uses squared units.
在应用面积或体积公式之前，务必检查长度单位是否统一。常用的公制换算包括：1 cm = 10 mm，1 m = 100 cm，1 km = 1000 m。质量方面，1 kg = 1000 g。容量方面，1 升 = 1000 毫升。请牢记 1 m² = 10,000 cm²，而不是 100 cm²，因为面积单位涉及平方。
Length: 1 m = 100 cm Area: 1 m² = 100 cm × 100 cm = 10,000 cm²
长度：1 米 = 100 厘米 面积：1 平方米 = 100 厘米 × 100 厘米 = 10,000 平方厘米
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