📚 Year 8 Essential Maths Book 8: Core Topics | Year 8 数学核心考点精讲
This article is a focused revision guide for Year 8 students using Essential Maths Book 8. It summarises the most important topics in Number, Algebra, Geometry, Statistics and Probability, with worked examples and key formulae.
本文是使用《Essential Maths Book 8》的 Year 8 学生专用复习指南，总结数字、代数、几何、统计与概率中最核心的知识点，并提供例题与关键公式。
1. Number Sense and Place Value | 数感与位值
Year 8 students need to be confident with large numbers and decimals. Place value tells us the value of each digit based on its position. For example, in 3 456.78, the digit 3 means 3 thousands, 4 means 4 hundreds, 5 means 5 tens, 6 means 6 ones, 7 means 7 tenths and 8 means 8 hundredths.
Year 8 学生需要熟练处理大数与小数。位值表示每个数字根据其位置所代表的值。例如在 3 456.78 中，数字 3 表示 3 个千，4 表示 4 个百，5 表示 5 个十，6 表示 6 个一，7 表示 7 个十分之一，8 表示 8 个百分之一。
Rounding and estimation are key skills. To round 27 486 to the nearest thousand, look at the hundreds digit (4): since it is less than 5, round down to 27 000.
四舍五入与估算也是关键技能。将 27 486 四舍五入到最接近的千位时，看百位数字（4）：因为小于 5，因此向下舍入到 27 000。
ge or small numbers. For example, 56 000 = 5.6 × 10⁴. This makes comparing numbers easier.
对非常大或非常小的数引入科学计数法。例如 56 000 = 5.6 × 10⁴。这样可以更容易比较数字的大小。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
decimals and percentages is essential. A fraction like 3/4 means 3 ÷ 4 = 0.75, which is 75%. To convert a percentage to a fraction, write it over 100 and simplify: 40% = 40/100 = 2/5.
分数、小数与百分比之间的转换是基本技能。分数 3/4 表示 3 ÷ 4 = 0.75，即 75%。把百分比转换为分数时，先写成百分之几并化简：40% = 40/100 = 2/5。
/3 + 1/4, the common denominator is 12: 2/3 = 8/12 and 1/4 = 3/12, so 8/12 + 3/12 = 11/12.
分数相加时，先找到公分母。例如 2/3 + 1/4，公分母为 12：2/3 = 8/12，1/4 = 3/12，因此 8/12 + 3/12 = 11/12。
6/35. To divide by a fraction, multiply by its reciprocal: 2/5 ÷ 3/7 = 2/5 × 7/3 = 14/15.
分数相乘时，分子与分母分别相乘：2/5 × 3/7 = 6/35。除以一个分数等于乘以它的倒数：2/5 ÷ 3/7 = 2/5 × 7/3 = 14/15。
| Fraction | Decimal | Percentage |
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
3. Negative Numbers and Order of Operations | 负数与运算顺序
5 + (−3) = 5 − 3 = 2. Subtracting a negative is the same as adding: 5 − (−3) = 5 + 3 = 8.
负数出现在温度、银行余额和坐标中。加上一个负数等于减去它的绝对值：5 + (−3) = 5 − 3 = 2。减去一个负数等于加上它的绝对值：5 − (−3) = 5 + 3 = 8。
24 and (−12) ÷ (−3) = 4. When signs are different, the result is negative: (−4) × 6 = −24.
两个负数相乘或相除，结果为正：(−4) × (−6) = 24，(−12) ÷ (−3) = 4。当符号不同时，结果为负：(−4) × 6 = −24。
For mixed calculations, follow BIDMAS/BODMAS: Brackets, Indices, Division/Multiplication, Addition/Subtraction. In 2 +
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