📚 Mastering Year 8 Maths: Essential Maths Book 8C Core Review | 掌握八年级数学：Essential Maths Book 8C 核心复习
Welcome to the TutorHao Year 8 Maths revision guide based on Essential Maths Book 8C. This article condenses the most important topics from the book into a clear, bilingual summary. You will revisit number skills, algebra, geometry, and statistics with worked examples and exam-style reminders.
欢迎阅读 TutorHao 根据《Essential Maths Book 8C》编写的八年级数学复习指南。本文将该书最重要的主题浓缩为清晰的中英双语总结。您将重新回顾数字技能、代数、几何和统计，并配有例题和考试提示。
1. Number Skills and Place Value | 数字技能与位值
large numbers, identify the value of each digit, and use index notation such as 10² = 100.
在 Book 8C 中，数字部分从位值、10 的幂和负数排序开始。你必须能够读写大数、识别每个数字的值，并使用指数符号，例如 10² = 100。
10² = 100, 10³ = 1000, 10⁰ = 1
For negative numbers, remember that the further left a number is on the number line, the smaller it is. So −7 < −2 because −7 lies to the left of −2.
对于负数，请记住在数轴上越靠左的数字越小。因此 −7 < −2，因为 −7 位于 −2 的左侧。
When rounding to a given number of decimal places, look at the next digit. If it is 5 or more, round up. For example, 3.146 rounded to 2 decimal places is 3.15.
当四舍五入到指定小数位时，查看下一位数字。如果是 5 或更大，则向上进位。例如，3.146 四舍五入到两位小数是 3.15。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
nvert fluently between fractions, decimals and percentages. Key facts include ½ = 0.5 = 50%, ¼ = 0.25 = 25% and ¾ = 0.75 = 75%.
你需要熟练地在分数、小数和百分比之间进行转换。关键事实包括 ½ = 0.5 = 50%、¼ = 0.25 = 25% 和 ¾ = 0.75 = 75%。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/3 | 0.333... | 33⅓% |
ract fractions, first find a common denominator. For example, 2/3 + 1/6 = 4/6 + 1/6 = 5/6.
要加减分数，首先要找到公分母。例如，2/3 + 1/6 = 4/6 + 1/6 = 5/6。
2/3 + 1/6 = 4/6 + 1/6 = 5/6
To multiply fractions, multiply the numerators and multiply the denominators. To divide by a fraction, multiply by its reciprocal.
要乘以分数，将分子相乘并将分母相乘。要除以一个分数，乘以其倒数。
3. Ratio and Proportion | 比与比例
A ratio compares quantities. Always simplify a ratio by dividing all parts by their highest common factor. For example, 12:18 simplifies to 2:3.
比用于比较数量。始终通过将所有部分除以它们的最大公因数来简化比。例如，12:18 简化为 2:3。
To divide a quantity in a given ratio, first add the parts. For example, divide £60 in the ratio 2:3. The total parts are 2 + 3 = 5, so one part is £60 ÷ 5 = £12. The shares are 2 × £12 = £24 and 3 × £12 = £36.
要按给定比例分配数量，首先将各部分相加。例如，按 2:3 分配 60 英镑。总份数为 2 + 3 = 5，因此一份为 60 ÷ 5 = 12 英镑。份额分别为 2 × 12 = 24 英镑和 3 × 12 = 36 英镑。
2:3 → 2 + 3 = 5 parts → £60 ÷ 5 = £12 per part
ty Direct proportion means that as one quantity increases, the other increases at the same rate. Use the unitary method: if 5 pens cost £2, then one pen costs £2 ÷ 5 = £0.40, so 20 pens cost 20 × £0.40 = £8.
正比例意味着当一个量增加时，另一个量以相同的速率增加。使用单位法：如果 5 支笔花费 2 英镑，那么一支笔花费 2 ÷ 5 = 0.40 英镑，因此 20 支笔花费 20 × 0.40 = 8 英镑。
4. Algebraic Expressions and Formulae | 代数表达式与公式
e letter combinations can be added or subtracted. For example, 3a + 2b − a + 5b = 2a + 7b.
在代数中，你要合并同类项。具有相同字母组合的项可以相加或相减。例如，3a + 2b − a + 5b = 2a + 7b。
3a + 2b − a + 5b = 2a + 7b
m inside. For example, 3(x + 2) = 3x + 6. To factorise, do the reverse: 4x + 8 = 4(x + 2).
要展开括号，将外面的项乘以里面的每一项。例如，3(x + 2) = 3x + 6。要因式分解，则反向操作：4x + 8 = 4(x + 2)。
on means replacing letters with numbers. If a = 3 and b = 5, then 2a + b = 2 × 3 + 5 = 11.
代入意味着用数字替换字母。如果 a = 3 且 b = 5，则 2a + b = 2 × 3 + 5 = 11。
5. Solving Linear Equations | 解一元一次方程
4x − 3 = 9. Add 3 to both sides to get 4x = 12, then divide both sides by 4 to get x = 3.
要解一元一次方程，使用平衡法：对方程两边进行相同的运算。例如，解 4x − 3 = 9。两边加 3 得到 4x = 12，然后两边除以 4 得到 x = 3。
4x − 3 = 9 → 4x = 12 → x = 3
s, expand them first. For example, 2(x − 5) = 6 becomes 2x − 10 = 6, so 2x = 16 and x = 8.
如果方程包含括号，请先展开它们。例如，2(x − 5) = 6 变为 2x − 10 = 6，因此 2x = 16，x = 8。
Always check your answer by substituting it back into the original equation.
始终通过将答案代回原方程来检验。
6. Sequences, Functions and Graphs | 数列、函数与图像
A sequence is a list of numbers following a rule. The nth term of a linear sequence is often written as an + b, where a is the common difference.
数列是按照规则排列的一组数字。线性数列的第 n 项通常写作 an + b，其中 a 是公差。
has a common difference of 3, so the nth term is 3n + 1. Check: when n = 1, 3 × 1 + 1 = 4.
例如，数列 4、7、10、13... 的公差为 3，因此第 n 项为 3n + 1。检验：当 n = 1 时，3 × 1 + 1 = 4。
Sequence: 4, 7, 10, 13 → nth term = 3n + 1
oose x-values, calculate y-values, and plot the points. The points lie on a straight line.
坐标写作 (x, y)。要绘制线性图像，例如 y = 2x + 1，选择 x 值，计算 y 值，然后描点。这些点位于一条直线上。
7. Angles and Polygons | 角与多边形
Angles on a straight line add up to 180°, and angles around a point add up to 360°. Vertically opposite angles are equal.
直线上的角之和为 180°，围绕一个点的角之和为 360°。对顶角相等。
The interior angles of a triangle add up to 180°, and the interior angles of a quadrilateral add up to 360°.
三角形的内角之和为 180°，四边形的内角之和为 360°。
s (n − 2) × 180°. For example, a hexagon has 6 sides, so the sum is (6 − 2) × 180° = 720°.
对于任何有 n 条边的多边形，内角之和为 (n − 2) × 180°。例如，六边形有 6 条边，因此内角之和为 (6 − 2) × 180° = 720°。
Interior angle sum = (n − 2) × 180°
The exterior angles of any polygon add up to 360°. In a regular polygon, each exterior angle equals 360° ÷ n.
任何多边形的外角之和为 360°。在正多边形中，每个外角等于 360° ÷ n。
8. Perimeter, Area and Volume | 周长、面积与体积
around a shape. For a rectangle, perimeter P = 2(l + w), where l is length and w is width.
周长是围绕一个形状的距离。对于矩形，周长 P = 2(l + w)，其中 l 是长，w 是宽。
am A = base × height, trapezium A = ½ × (a + b) × h, where a and b are the parallel sides.
你必须掌握的面积公式：矩形 A = 长 × 宽，三角形 A = ½ × 底 × 高，平行四边形 A = 底 × 高，梯形 A = ½ × (a + b) × h，其中 a 和 b 是平行边。
A(triangle) = ½ × b × h, A(trapezium) = ½ × (a + b) × h
V = length × width × height. Compound shapes can be split into rectangles or known shapes.
体积测量三维形状内部的空间。对于长方体，体积 V = 长 × 宽 × 高。组合图形可以分割成矩形或已知形状。
9. Transformations and Symmetry | 变换与对称
Transformations include reflection, rotation, translation and enlargement. Always describe a transformation fully: for rotation give the centre, angle and direction; for enlargement give the centre and scale factor.
变换包括反射、旋转、平移和放大。始终完整描述变换：旋转需给出中心、角度和方向；放大需给出中心和比例因子。
A reflection flips a shape over a mirror line. A rotation turns a shape about a fixed point. A translation slides a shape by a vector, and an enlargement changes its size.
反射使图形沿镜像线翻转。旋转使图形绕固定点转动。平移使图形按向量滑动，放大则改变其大小。
A shape has line symmetry if it can be folded so both halves match. Rotational symmetry is the number of times a shape fits onto itself in one full turn.
如果一个图形可以折叠使两半重合，则它具有线对称。旋转对称是图形在完整旋转一周中与自身重合的次数。
10. Statistics and Probability | 统计与概率
For a data set, the mean is the sum of values divided by the number of values. The median is the middle value when data are ordered. The mode is the most frequent value, and the range is the largest value minus the smallest.
对于一组数据，平均数等于数值之和除以数值个数。中位数是数据排序后的中间值。众数是出现最频繁的值，极差是最大值减最小值。
Mean = sum of values ÷ number of values
) and 1 (certain). Probability = number of favourable outcomes ÷ total number of outcomes.
概率衡量事件发生的可能性。它始终介于 0（不可能）和 1（必然）之间。概率 = 有利结果数 ÷ 总结果数。
For example, if a bag has 3 red and 5 blue marbles, the probability of picking a red marble is 3/8.
例如，如果一个袋子里有 3 个红色和 5 个蓝色弹珠，则取出红色弹珠的概率是 3/8。
P(red) = 3/8 = 0.375 = 37.5%
Published by TutorHao | Maths Revision Series | aleveler.com
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