Year 10 Cambridge Mathematics: Core Topics Review | Year 10 Cambridge 数学：核心知识点梳理

📚 Year 10 Cambridge Mathematics: Core Topics Review | Year 10 Cambridge 数学：核心知识点梳理

This revision guide provides a comprehensive overview of the core topics covered in Year 10 Cambridge Mathematics, including number, algebra, geometry, trigonometry, statistics and probability. Each section highlights key concepts and formulas to help you consolidate your understanding and prepare for assessments.

这篇复习指南全面梳理了 Year 10 剑桥数学的核心知识点，涵盖数字、代数、几何、三角学、统计与概率。每个部分重点突出关键概念和公式，帮助你巩固理解，为考试做好准备。

1. Number and Operations | 数与运算

You need to be confident working with integers, fractions, decimals and percentages, and converting between them. Operations include addition, subtraction, multiplication and division, respecting the order of operations (BODMAS/BIDMAS).

你需要熟练掌握整数、分数、小数和百分数的运算及其相互转换。运算包括加减乘除，并遵循运算顺序（括号、乘方、乘除、加减）。

Standard form (scientific notation) is used to represent very large or small numbers: a × 10ⁿ where 1 ≤ a < 10 and n is an integer. For example, 45,000 = 4.5 × 10⁴ and 0.00032 = 3.2 × 10⁻⁴.

标准形式（科学记数法）用于表示极大或极小的数：a × 10ⁿ，其中 1 ≤ a < 10，n 是整数。例如，45,000 = 4.5 × 10⁴，0.00032 = 3.2 × 10⁻⁴。

Ratio and proportion problems often involve sharing quantities in a given ratio or solving direct and inverse proportion. Use the unitary method or algebraic equations to find unknown values.

比率与比例问题常涉及按给定比例分配数量，或解决正比例与反比例问题。用单位法或代数方程求未知值。

Estimation and rounding to a given number of significant figures or decimal places are essential skills. Always check the reasonableness of your answers.

估算和舍入到给定有效数字或小数位数是必备技能。务必检查答案的合理性。

2. Algebra Basics | 代数基础

Simplify expressions by collecting like terms: 3x + 2y – x + 5y = 2x + 7y. Use the distributive law to expand brackets: a(b + c) = ab + ac, and double brackets: (x + 3)(x – 2) = x² + x – 6.

通过合并同类项化简表达式：3x + 2y – x + 5y = 2x + 7y。利用分配律展开括号：a(b + c) = ab + ac，以及双括号：(x + 3)(x – 2) = x² + x – 6。

Factorising is the reverse of expanding. Common techniques include taking out a common factor, e.g., 6x² + 9x = 3x(2x + 3), and factorising quadratic trinomials such as x² + 5x + 6 = (x + 2)(x + 3). Recognise the difference of two squares: a² – b² = (a + b)(a – b).

因式分解是展开的逆运算。常用方法包括提取公因式，例如 6x² + 9x = 3x(2x + 3)，以及分解二次三项式，如 x² + 5x + 6 = (x + 2)(x + 3)。识别平方差公式：a² – b² = (a + b)(a – b)。

Manipulate algebraic fractions by finding a common denominator and simplifying. Remember to factorise numerators and denominators before cancelling.

通过寻找公分母并化简来处理代数分式。取消前记得对分子和分母进行因式分解。

Use index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, and a⁻ⁿ = 1/aⁿ. Understand fractional and negative indices.

运用指数定律：aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)

Published by TutorHao | Year 10 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）