📚 Essential Maths 8H Homework Book Compressed | Year 8 数学精华练习册核心要点
The Essential Maths 8H Homework Book is a widely used practice resource for Year 8 students following the English mathematics curriculum. This compressed revision guide pulls together the core topics, key formulas, and common exam-style skills so you can review efficiently and build confidence before assessments.
《Essential Maths 8H Homework Book》是 Year 8 学生广泛使用的数学练习资源。这份压缩版复习指南汇总了核心主题、关键公式和常见考试型技能，帮助你高效复习并在评估前建立信心。
1. Number and Place Value | 数与位值
Year 8 extends place value to large numbers and decimal places. You must be able to round to a given number of decimal places, identify significant figures, and order positive and negative numbers correctly.
Year 8 将位值概念扩展到大数和小数位。你必须能够按要求的小数位进行四舍五入、识别有效数字，并正确排列正数和负数。
= 2² × 3 × 5. This supports finding the highest common factor and lowest common multiple.
质因数分解是一项关键技能：将一个数写成质数的乘积，例如 60 = 2² × 3 × 5。这有助于求最大公因数和最小公倍数。
Directed numbers also appear in multi-step calculations. Use a number line mentally for addition and subtraction of negatives, and remember the sign rules for multiplication and division.
正负数也出现在多步运算中。在加减负数时可以借助数轴进行思考，并记住乘法和除法中的符号规则。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
onvert fluently between fractions, decimals and percentages. For example, ⅜ = 0.375 = 37.5%. Memorising common equivalents saves time in homework and tests.
你应该在分数、小数和百分数之间熟练转换。例如，⅜ = 0.375 = 37.5%。记住常见等值关系可以在作业和测试中节省时间。
Operations with mixed numbers require converting to improper fractions and finding common denominators. For addition, rewrite each fraction with the same denominator before adding the numerators.
带分数的运算需要先转化为假分数并找到公分母。做加法时，先以相同的分母重写每个分数，再对分子相加。
Percentage problems include finding a percentage of an amount, percentage increase and decrease, and reverse percentages. Always identify the original amount before applying a multiplier.
百分数问题包括求一个数量的百分数、百分数增减和逆运算。在应用乘数之前，一定要先确定原始数量。
3. Ratio and Proportion | 比与比例
A ratio compares the sizes of two or more parts, while proportion compares a part to the whole. Simplify ratios by dividing all terms by their common factor, just like simplifying fractions.
比用于比较两个或多个部分的大小，而比例则比较部分与整体。化简比的方法与化简分数类似，将所有项除以公因数。
Dividing a quantity in a given ratio involves finding the total number of parts, then multiplying the value of one part by each ratio term. Direct proportion problems often use the unitary method or a scale factor.
按给定比分配数量需要先求出总份数，再用一份的值乘以比中的每一项。正比例问题通常使用单位法或比例因子来求解。
4. Algebra Basics | 代数基础
efficients while keeping the variable part unchanged. For example, 5a + 3b - 2a = 3a + 3b.
合并同类项的方法是加减系数而保持变量部分不变。例如，5a + 3b - 2a = 3a + 3b。
Index laws for multiplication and division are essential. The key rules include am × an = am+n and am ÷ an = am-n.
指数的乘法和除法法则非常重要。关键规则包括 am × an = am+n 和 am ÷ an = am-n。
ab + ac. Factorising is the reverse process, where you take out the highest common factor.
展开单项括号使用分配律：a(b + c) = ab + ac。因式分解则是相反的过程，即提取最大公因式。
5. Linear Equations | 一元一次方程
step. For example, to solve 3x + 5 = 20, first subtract 5, then divide by 3, giving x = 5.
解一元一次方程时要逐步使用逆运算。例如，解 3x + 5 = 20，先减去 5，再除以 3，得到 x = 5。
When the unknown appears on both sides, collect the variable terms on one side first. Then use inverse operations as usual and check your answer by substituting it back into the original equation.
当未知数出现在等式两边时，先把含变量项移到同一边。然后照常使用逆运算，并把答案代回原方程进行检验。
Always write each step on a new line in homework. Neat working reduces sign errors and makes it easier to spot mistakes.
在作业中每一步都要另起一行书写。整洁的过程能减少符号错误，也更容易发现失误。
6. Sequences and Graphs | 数列与图像
Linear sequences can be described by the nth term. For example, the nth term 3n + 2 generates the sequence 5, 8, 11, 14, and so on.
等差数列可以用第 n 项来表示。例如，第 n 项 3n + 2 生成的数列为 5、8、11、14，依此类推。
irs, and join them with a ruler. The equation y = mx + c has gradient m and y-intercept c.
绘制直线图像时，先建立 x 和 y 的数值表，描出坐标点，再用直尺连接。方程 y = mx + c 中，m 是斜率，c 是 y 轴截距。
Reading graphs accurately means checking the scale on both axes. Do not assume one square equals one unit unless the axes are labelled that way.
准确读取图像时要注意两轴的刻度。除非坐标轴明确标注一小格等于一个单位，否则不要自行假设。
7. Angles and Shapes | 角与图形
Use basic angle facts: angles on a straight line sum to 180°, angles around a point sum to 360°, and vertically opposite angles are equal.
掌握基本角度事实：直线上的角和为 180°，一点周围的角和为 360°，对顶角相等。
In triangles, the interior angles sum to 180°. An exterior angle of a triangle equals the sum of the two opposite interior angles, which is useful for multi-step angle problems.
三角形内角和为 180°。三角形的一个外角等于两个不相邻内角之和，这在多步角度问题中非常有用。
o find the sum of interior angles. A quadrilateral is 2 triangles, giving 2 × 180° = 360°.
对于多边形，可以将图形分割成三角形来求内角和。四边形可以分成 2 个三角形，因此内角和为 2 × 180° = 360°。
8. Area and Perimeter | 面积与周长
ngle, A = length × width and P = 2(length + width). For a triangle, A = ½ × base × height.
掌握常见二维图形的公式。矩形：A = 长 × 宽，P = 2 × (长 + 宽)。三角形：A = ½ × 底 × 高。
llelogram, A = base × perpendicular height. For a trapezium, the area formula is given by:
平行四边形：A = 底 × 垂直高。梯形的面积公式为：
A = ½(a + b)h
where a and b are the parallel sides and h is the perpendicular height.
其中 a 和 b 是两条平行边，h 是垂直高。
r². Use the π button on a calculator unless the question asks for an answer in terms of π.
对于圆，周长为 C = πd，面积为 A = πr²。除非题目要求用 π 表示答案，否则在计算器上使用 π 键。
9. Transformations and Symmetry | 变换与对称
Describe transformations precisely, including the type, direction, size and centre. For translations, use a vector such as (3, -2), meaning 3 units right and 2 units down.
描述变换时要准确，包括类型、方向、大小和中心。平移使用向量，如 (3, -2)，表示向右 3 个单位、向下 2 个单位。
Rotations require a centre, angle and direction, for example a 90° clockwise rotation about (0, 0). Reflections need a mirror line, and enlargements need a scale factor and centre.
旋转需要说明中心、角度和方向，例如绕 (0, 0) 顺时针旋转 90°。反射需要对称轴，放大需要比例因子和中心。
Line symmetry means a shape can be folded along a line so both halves match. Rotational symmetry is the number of times a shape fits onto itself in a full turn.
线对称是指一个图形可以沿某条直线折叠后两边完全重合。旋转对称则是指图形在一整圈旋转中与自身重合的次数。
10. Statistics and Probability | 统计与概率
Calculate mean, median, mode and range from lists and frequency tables. The mean is the total of all values divided by the number of values; the range is the largest minus the smallest.
从列表和频数表计算平均数、中位数、众数和极差。平均数等于所有数值的总和除以数值的个数；极差等于最大值减最小值。
From a frequency table, multiply each value by its frequency before summing. The median is the middle value when data are ordered, and the mode is the most frequent value.
在频数表中，先将每个数值乘以它的频数再求和。将数据排序后，中位数是中间的值，众数是出现次数最多的值。
The probability of an event is found by:
事件的概率用以下公式计算：
P(event) = number of favourable outcomes ÷ total number of outcomes
Probabilities always lie between 0 and 1, and the probabilities of all possible outcomes add up to 1.
概率始终在 0 到 1 之间，所有可能结果的概率之和为 1。
11. Homework Strategy and Common Errors | 作业策略与常见错误
Set a fixed time and place for mathematics homework. Attempt every question, show full working, and mark your answers using the back of the book or a separate answer sheet before seeking help.
为数学作业设定固定的时间和地点。尝试每一道题，写出完整过程，并在寻求帮助之前使用书后答案或单独的答案页进行批改。
Common errors include sign mistakes in directed numbers, confusing area with perimeter, forgetting units, and misreading graph scales. Circle or underline key words in word problems to avoid careless slips.
常见错误包括正负数符号错误、混淆面积与周长、忘记单位以及误读图表的刻度。在应用题中圈出或划出关键词可以避免粗心失误。
A compressed revision session should focus on worked examples and your weakest topics. Redo only the questions you got wrong, then try a new question on the same skill to check understanding.
压缩复习应聚焦于例题和你最薄弱的主题。只重做你做错的题目，然后尝试一道同技能的新题来检验理解程度。
12. Exam-Style Practice | 考试型练习
Use past paper style questions under timed conditions. For multi-step problems, break the task into small steps and write down what you are calculating at each stage.
在限时条件下练习真题型题目。对于多步骤问题，将任务分解成小步骤，并写出每一步在计算什么。
Check units, rounding and whether your answer is reasonable in the context of the question. If a question asks for money, give two decimal places unless stated otherwise.
检查单位、舍入以及答案在题目情境中是否合理。如果题目涉及货币，除非另有说明，答案应保留两位小数。
Show working even when a calculator is allowed. Method marks are often awarded for correct substitution and process, so a clear layout can improve your final grade.
即使允许使用计算器，也要展示解题过程。正确的代入和步骤通常可以得到方法分，因此清晰的书写能提高最终成绩。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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