📚 Essential Maths Book 8i Compressed Core Revision | 《基础数学 8i》压缩核心复习
Welcome to this compressed revision guide for Essential Maths Book 8i. It brings together the key skills that Year 8 students need to master, from number operations and fractions to algebra, geometry, statistics and probability. Each section gives clear rules, worked examples and common error alerts so you can revise efficiently.
欢迎使用《基础数学 8i》压缩复习指南。本指南汇集了 Year 8 学生必须掌握的核心技能，包括数的运算、分数、代数、几何、统计与概率。每个专题都给出清晰规则、例题和常见错误提醒，帮助你高效复习。
1. Integers and Order of Operations | 整数与运算顺序
Addition and Subtraction from left to right. For example, 3 + 4 × 2 = 3 + 8 = 11, not 14.
运算顺序可用 BIDMAS 或 BODMAS 记忆：先算括号，再算指数（或乘方），然后从左到右计算乘除，最后从左到右计算加减。例如 3 + 4 × 2 = 3 + 8 = 11，而不是 14。
a negative and a positive gives a negative. Example: (−2) × (−6) = 12 but (−2) × 6 = −12.
涉及负数时，加上一个负数等于减去它的相反数：5 + (−3) = 2。两个负数相乘或相除得正，一负一正相乘或相除得负。例如 (−2) × (−6) = 12，而 (−2) × 6 = −12。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
or example, 3/4 + 1/6 = 9/12 + 2/12 = 11/12. Never add denominators: 1/2 + 1/3 is not 2/5.
分数加减时，必须先化为同分母。例如 3/4 + 1/6 = 9/12 + 2/12 = 11/12。不能直接把分子和分母分别相加：1/2 + 1/3 不等于 2/5。
iply by the reciprocal. For example, 2/3 × 5/7 = 10/21, and 2/3 ÷ 5/7 = 2/3 × 7/5 = 14/15.
分数相乘时，分子乘分子，分母乘分母；分数相除时，乘以除数的倒数。例如 2/3 × 5/7 = 10/21，2/3 ÷ 5/7 = 2/3 × 7/5 = 14/15。
convert a fraction to a percentage, multiply by 100. For instance, 3/5 = 3 ÷ 5 × 100 = 60%.
百分数是分母为 100 的分数。将分数化为百分数，可先除以分母再乘以 100。例如 3/5 = 3 ÷ 5 × 100 = 60%。
3. Ratio and Proportion | 比与比例
A ratio compares quantities in the same unit. Simplify a ratio by dividing all parts by their highest common factor. For example, 12:18 simplifies to 2:3 by dividing by 6.
比用于比较同类量。化简比时，把各项同时除以最大公因数。例如 12:18 同时除以 6，化简为 2:3。
unt in a given ratio, first find the total number of parts. For 2:3, there are 5 parts. If £60 is shared in ratio 2:3, one part is £60 ÷ 5 = £12, so the shares are £24 and £36.
按比例分配时，先求总份数。例如 2:3 共有 5 份。把 60 英镑按 2:3 分配，一份是 60 ÷ 5 = 12 英镑，因此两份为 24 英镑，三份为 36 英镑。
equal. Use cross multiplication to solve missing values, such as 3/4 = x/20 gives x = 15.
比例是一个等式，表示两个比相等。解未知项时可用交叉相乘。例如 3/4 = x/20，得 x = 15。
4. Algebraic Expressions and Equations | 代数表达式与方程
+ 4y = 2x + 6y. Expanding brackets means multiplying each term inside: 3(x + 2) = 3x + 6.
同类项是指字母部分完全相同的项，合并时只加减系数。例如 3x + 2y − x + 4y = 2x + 6y。去括号就是把括号外的数乘给括号内每一项：3(x + 2) = 3x + 6。
me operation to both sides. Solve 2x + 3 = 11 by subtracting 3, then dividing by 2: x = 4.
方程含有等号，解方程时要保持两边平衡，即两边同时进行相同运算。解 2x + 3 = 11，先两边减 3，再两边除以 2，得 x = 4。
tuting the value back into the original equation: 2(4) + 3 = 11, so the answer is correct.
得到解后，应把数值代回原方程检验：2(4) + 3 = 11，等式成立，说明答案正确。
5. Linear Graphs and Sequences | 线性图像与数列
2x + 1, choose x values, calculate y, then plot points and join them with a straight line.
坐标 (x, y) 从原点出发读取。画 y = 2x + 1 这样的线性图像时，先选若干个 x 值，算出对应的 y 值，再描点并用直线连接。
adient is the coefficient of x. In y = 2x + 1, the gradient is 2 and the y-intercept is 1.
y 轴截距是 x = 0 时的 y 值，
Published by TutorHao | Year 8 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图