Year 8 SQA Mathematics: Core Knowledge Review | Year 8 SQA 数学：核心知识点梳理

📚 Year 8 SQA Mathematics: Core Knowledge Review | Year 8 SQA 数学：核心知识点梳理

Welcome to this comprehensive review of Year 8 SQA Mathematics. This article consolidates the key topics you will encounter in the Scottish Curriculum for Excellence at S2 level. Mastering these fundamentals will build a strong foundation for further study. We cover number systems, algebra, geometry, data handling, and more.

欢迎阅读这篇Year 8 SQA数学全面梳理文章。本文整合了苏格兰卓越课程S2阶段的核心知识点，掌握这些基础将为后续学习打下坚实的根基。我们将涵盖数系、代数、几何、数据处理等。

---

1. Number Types and Operations | 数的类型与运算

In Year 8, you will work with a range of number types: positive and negative integers, decimals, and the four operations. It is essential to apply the order of operations correctly. Remember BIDMAS: Brackets, Indices, Division, Multiplication, Addition, Subtraction. For example, 3 + 4 × 2 = 3 + 8 = 11, not 14. You also need to be confident in long multiplication and division, and use place value to round numbers to a given number of decimal places or significant figures.

在Year 8，你将接触一系列数类型：正整数和负整数、小数以及四则运算。正确应用运算顺序至关重要。记住BIDMAS：括号、指数、除法、乘法、加法、减法。例如，3 + 4 × 2 = 3 + 8 = 11，而不是14。你还需要熟练掌握长乘法和长除法，并利用位值将数字四舍五入到指定的小数位或有效数字。

You will also encounter square numbers (e.g., 5² = 25), cube numbers (e.g., 4³ = 64), and their roots. Estimating square roots between two integers is a useful skill.

你还会遇到平方数（例如5² = 25）、立方数（例如4³ = 64）及其根。估算一个平方根在两个整数之间是一项有用的技能。

---

2. Fractions, Decimals and Percentages | 分数、小数与百分数

Converting between fractions, decimals and percentages is a fundamental skill. For instance, ½ = 0.5 = 50%. You should be able to simplify fractions by dividing the numerator and denominator by their highest common factor. Perform all four operations with fractions: to add or subtract, find a common denominator; to multiply, multiply numerators and denominators; to divide, multiply by the reciprocal.

分数、小数和百分数之间的转换是一项基本技能。例如，½ = 0.5 = 50%。你应该能够通过分子和分母除以它们的最大公因数来化简分数。进行分数的四则运算：加减时，寻找公分母；乘法时，分子分母分别相乘；除法时，乘以倒数。

Percentage calculations include finding a percentage of a quantity, and expressing one number as a percentage of another. You will also solve problems involving percentage increase and decrease, such as adding 15% tax to a price.

百分数计算包括求一个数量的百分之几，以及将一个数表示为另一个数的百分之几。你还将解决涉及百分比增减的问题，例如在价格上加15%的税。

---

3. Algebraic Expressions and Equations | 代数表达式与方程

Algebra uses letters to stand for unknown numbers. In Year 8, you will simplify expressions by collecting like terms: 4x + 2y – x + 5y = 3x + 7y. You will multiply a single term across a bracket, such as 3(2n – 4) = 6n – 12, and factorise expressions like 10a + 15 = 5(2a + 3).

代数使用字母代表未知数。在Year 8，你将通过合并同类项来化简表达式：4x + 2y – x + 5y = 3x + 7y。你会将单项式乘以括号，例如 3(2n – 4) = 6n – 12，并对表达式进行因式分解，如 10a + 15 = 5(2a + 3)。

Solving equations involves finding the value of the unknown. Use inverse operations: for x + 5 = 12, subtract 5; for 3x = 18, divide by 3; for 2x + 1 = 11, subtract 1 then divide by 2. Always check your solution by substituting back.

解方程涉及求出未知数的值。使用逆运算：对于 x + 5 = 12，减去5；对于 3x = 18，除以3；对于 2x + 1 = 11，先减1再除以2。始终通过代回原方程检验你的解。

---

4. Ratio and Proportion | 比与比例

A ratio compares two or more quantities. Write ratios in their simplest form, just like fractions. For example, 8:12 simplifies to 2:3. To divide £40 in the ratio 3:5, you split it into 3+5=8 parts, each worth £5, so £15 and £25.

比用来比较两个或多个数量。把比写成最简形式，就像分数一样。例如，8:12简化为2:3。将40英镑按3:5分配，分成3+5=8份，每份5英镑，因此得到15英镑和25英镑。

Direct proportion means as one quantity increases, the other increases at the same rate. Use the unitary method: if 5 pens cost £3.50, one pen costs £0.70, so 8 pens cost £5.60. You will also use ratio to interpret scale drawings and find actual distances.

正比例意味着一个量增加，另一个量以相同速率增加。使用单一单位法：如果5支笔花费3.50英镑，一支笔花费0.70英镑，那么8支笔花费5.60英镑。你还会用比来解读比例图并求实际距离。

---

5. Angles and Polygons | 角与多边形

Angle basics: you can measure angles with a protractor in degrees (°). Key facts: angles on a straight line add to 180°, angles around a point add to 360°, and vertically opposite angles (formed by intersecting lines) are equal. Use these to find missing angles without measuring.

角度基础：你可以用量角器以度(°)为单位测量角度。关键知识：直线上的角之和为180°，一点周围的角之和为360°，对顶角（由相交线形成）相等。运用这些知识无需测量即可求出缺失的角。

Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). The sum of interior angles in any triangle is 180°. For quadrilaterals, the sum is 360°. Regular polygons have equal sides and equal interior angles. The exterior angle of a regular n-sided polygon is 360°/n.

三角形可按边分类（等边、等腰、不等边）和按角分类（锐角、直角、钝角）。任何三角形的内角和都是180°。四边形的内角和为360°。正多边形有相等的边和相等的内角。正n边形的外角为360°/n。

---

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

Perimeter is the total distance around a shape. For a circle, the perimeter is called the circumference.

周长是围绕形状的总距离。对于圆，周长被称为圆周。

C = πd or C = 2πr (π ≈ 3.14)

Area measures the surface. Key formulas: area of rectangle = length × width; area of triangle = ½ × base × height; area of parallelogram = base × perpendicular height. You should also find the area of compound shapes by splitting them into simpler shapes.

面积测量表面。关键公式：矩形面积 = 长 × 宽；三角形面积 = ½ × 底 × 高；平行四边形面积 = 底 × 垂直高。你还应该通过将组合形状分割成简单形状来求面积。

Volume is the space a 3D object occupies. For cubes and cuboids:

Published by TutorHao | Year 8 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）