📚 Year 9 SQA Mathematics: Key Formulas & Theorems | 九年级SQA数学关键公式定理
This quick reference handbook compiles the essential formulas and theorems for Year 9 SQA Mathematics. It is designed to help you review key concepts across number, algebra, geometry, measurement, and statistics quickly and effectively. Each section presents the most important rules and formulas paired with clear examples, making revision straightforward and efficient.
本速查手册汇编了九年级 SQA 数学的关键公式和定理，旨在帮助你快速有效地复习数、代数、几何、测量和统计等核心概念。每个小节都呈现最重要的规则和公式，并配有清晰的示例，让复习变得简单高效。
1. Number & Fractions | 数与分数
Equivalent fractions represent the same value. You can create equivalent fractions by multiplying or dividing the numerator and denominator by the same non-zero number. For example, ½ = 2/4 = 3/6.
等值分数表示相同的数值，可以将分子和分母同时乘以或除以同一个非零数来得到等值分数。例如 ½ = 2/4 = 3/6。
To add or subtract fractions, first find a common denominator. Multiply fractions by multiplying numerators together and denominators together. To divide by a fraction, multiply by its reciprocal.
分数的加减法需要先通分找到公分母。分数乘法直接将分子相乘、分母相乘。分数除法则是乘以除数的倒数。
a/b + c/d = (ad + bc)/bd a/b × c/d = ac/bd a/b ÷ c/d = a/b × d/c = ad/bc
2. Percentages & Ratios | 百分数与比例
A percentage expresses a number as a fraction of 100. To find a percentage of an amount, multiply the amount by the percentage divided by 100. Percentage change = (change ÷ original) × 100%.
百分数表示一个数占 100 的几分之几。求一个数量的百分之几，用该数量乘以百分数除以 100。百分比变化 = (变化量 ÷ 原值) × 100%。
Ratios compare two or more quantities. Simplify ratios by dividing all parts by their greatest common factor. Sharing in a given ratio involves dividing the total into equal parts based on the sum of the ratio terms.
比例用于比较两个或多个量。化简比例需将所有项除以它们的最大公因数。按比例分配时，先把总量按比例项之和分成若干份。
Ratio a : b simplified: divide by HCF(a, b)
3. Algebraic Expressions & Simplifying | 代数表达式与化简
Like terms have exactly the same variable parts. Simplify by collecting like terms. For instance, 3x + 5y − 2x + y = x + 6y.
同类项具有完全相同的字母部分。化简时合并同类项，例如 3x + 5y − 2x + y = x + 6y。
To expand brackets, multiply the term outside by each term inside. a(b + c) = ab + ac. Double brackets expand using FOIL: (a + b)(c + d) = ac + ad + bc + bd.
展开括号时，将括号外的项乘以括号内的每一项。a(b + c) = ab + ac。双括号展开可用乘法分配律：(a + b)(c + d) = ac + ad + bc + bd。
Factorising is the reverse of expanding. Look for the highest common factor (HCF) of all terms and place it outside the brackets. For example, 4x + 6 = 2(2x + 3).
因式分解是展开的逆运算。找出所有项的最高公因式(HCF)并将其放在括号外。例如 4x + 6 = 2(2x + 3)。
4. Solving Equations & Inequalities | 解方程与不等式
To solve linear equations, isolate the variable using inverse operations. Always do the same to both sides to keep the equation balanced. Example: 2x + 3 = 11 → 2x = 8 → x = 4.
解一元一次方程时，通过逆运算隔离变量。必须对方程两边同时进行相同的运算以保持平衡。例如 2x + 3 = 11 → 2x = 8 → x = 4。
When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign. For example, −2x > 6 becomes x < −3.
解不等式时，若两边同时乘或除以一个负数，不等号方向要改变。例如 −2x > 6 变为 x < −3。
If a < b then a + c < b + c but if c < 0, ac > bc
5. Coordinates & Linear Graphs | 坐标与直线图
The equation of a straight line is y = mx + c, where m is the gradient (slope) and c is the y-intercept. The gradient is calculated as rise over run: m = (y₂ − y₁)/(x₂ − x₁).
直线方程为 y = mx + c，其中 m 是斜率，c 是 y 轴截距。斜率通过垂升比水平距离计算：m = (y₂ − y₁)/(x₂ − x₁)。
To plot a linear graph, find at least two points that satisfy the equation, plot them, and draw a straight line through them. Parallel lines have the same gradient.
绘制直线图时，至少找出满足方程的两个点，描点并用直线连接。平行线具有相同的斜率。
6. Angles & Lines | 角与直线
Vertically opposite angles are equal. Angles on a straight line sum to 180°. Angles around a point sum to 360°.
对顶角相等。平角上的角度总和为 180°。绕一点一周的角度总和为 360°。
When parallel lines are cut by a transversal, alternate angles are equal, corresponding angles are equal, and co-interior (allied) angles sum to 180°.
当平行线被一条截线所截时，内错角相等，同位角相等，同旁内角互补（和为 180°）。
7. Triangles & Polygons | 三角形与多边形
The sum of interior angles of a triangle is always 180°. An exterior angle of a triangle equals the sum of the two opposite interior angles.
三角形内角和总是 180°。三角形的一个外角等于与它不相邻的两个内角之和。
For any polygon with n sides, the sum of interior angles = (n − 2) × 180°. The sum of exterior angles of any convex polygon is 360°.
对于任意 n 边形，内角和 = (n − 2) × 180°。任何凸多边形的外角和都是 360°。
Sum of interior angles = (n − 2) × 180°
8. Perimeter & Area | 周长与面积
Perimeter is the total distance around a shape. For a rectangle, P = 2l + 2w. For a circle, the circumference is C = πd = 2πr.
周长是图形一周的长度。长方形周长 P = 2l + 2w。圆的周长 C = πd = 2πr。
Key area formulas:
重要面积公式：
Rectangle: A = lw Triangle: A = ½ bh Parallelogram: A = bh
Trapezium: A = ½ (a + b)h Circle: A = πr²
For compound shapes, split the shape into simpler parts, calculate each area, and then add or subtract as appropriate.
对于组合图形，可将其分割为简单部分，分别计算面积，然后相加或相减。
9. Volume & Surface Area | 体积与表面积
Volume of a cuboid: V = length × width × height. Volume of a prism: V = area of cross-section × length. For a cylinder, V = πr²h.
长方体体积：V = 长 ×
Published by TutorHao | Year 9 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导