📚 Essential Maths Book 8S Answers: Year 8 Core Solutions and Revision | Year 8 数学 Essential Maths Book 8S 答案解析与复习指南
Essential Maths Book 8S is a widely used Year 8 workbook that builds fluency in number, algebra, geometry, and data handling. This article summarises the main answer types, shows worked examples, and explains how to use the compressed answer set for effective revision without copying blindly.
《Essential Maths Book 8S》是 Year 8 常用的数学练习册，帮助学生在数、代数、几何和数据处理方面打牢基础。本文总结主要答案类型，给出解题范例，并说明如何有效利用精简版答案进行复习，而不是盲目抄写。
1. Understanding the Book 8S Structure | 了解 Book 8S 结构
Book 8S is organised into short exercise sets covering Number, Algebra, Shape and Space, and Handling Data. Each exercise usually begins with a worked example, then practice questions, and a summary box at the end. The answer file lists final answers in the same order, with diagrams marked clearly.
本书按短练习编排，涵盖数、代数、图形与空间、数据处理。每个练习开头通常有例题，接着是练习题，末尾有小结框。答案文件一般按相同顺序列出最终答案，图形标注清楚。
2. Integers and Order of Operations | 整数与运算顺序
tiplication, Addition and Subtraction. For example, 3 + 4 × (−2) = 3 + (−8) = −5, not −14.
Year 8 整数题常把负数与括号、乘方混合。关键规则是 BIDMAS：括号、指数、乘除、加减。例如 3 + 4 × (−2) = 3 + (−8) = −5，而不是 −14。
3 + 4 × (−2) = 3 − 8 = −5
ative numbers, (−3)² = 9 but −3² = −9 because the negative sign is not inside the bracket.
乘方时要注意，(−3)² = 9，但 −3² = −9，因为负号不在括号内。
3. Fractions, Decimals and Percentages | 分数、小数与百分数
Book 8S expects students to convert freely between 1/4, 0.25 and 25% nominators. To add 2/3 and 1/4, find the LCM of 3 and 4, which is 12: 8/12 + 3/12 = 11/12.
本书要求学生能在 1/4、0.25 和 25% 之间自由转换，并能对异分母分数进行加减。计算 2/3 + 1/4 时，先求 3 和 4 的最小公倍数 12：8/12 + 3/12 = 11/12。
2/3 + 1/4 = 8/12 + 3/12 = 11/12
Percentage increase and decrease questions often appear in the answer set. A 15% increase on £60 is found by multiplying 60 × 1.15 = 69.
百分数增减题在答案集中很常见。£60 增加 15%，用 60 × 1.15 = 69 计算。
4. Algebraic Expressions and Substitution | 代数表达式与代入
Simplifying expressions such as 5a + 3b − 2a + 7b gives 3a + 10b. The answer file shows only the final simplified form, so you must check that like terms are collected correctly.
化简如 5a + 3b − 2a + 7b 得到 3a + 10b。答案文件只显示最终化简结果，因此你要检查同类项是否合并正确。
5a + 3b − 2a + 7b = 3a + 10b
letters with given values. If a = 3 and b = −2, then 4a + 5b = 4×3 + 5×(−2) = 12 − 10 = 2.
代入题要求把字母替换为给定数值。如果 a = 3，b = −2，那么 4a + 5b = 4×3 + 5×(−2) = 12 − 10 = 2。
4a + 5b = 12 − 10 = 2
5. Linear Equations | 一元一次方程
he Book 8S answer set gives x = 5, but you need to show both steps to gain marks in class.
解如 3x + 4 = 19 的方程需要逆运算：两边先减 4，再除以 3。Book 8S 答案集给出 x = 5，但在课堂上要展示两个步骤才能得分。
3x + 4 = 19 → 3x = 15 → x = 5
n both sides, such as 5x − 2 = 2x + 7, require collecting x-terms first: 3x = 9, so x = 3.
两边都含未知数的方程如 5x − 2 = 2x + 7，要先合并 x 项：3x = 9，所以 x = 3。
6. Ratio and Proportion | 比与比例
Ratio questions often ask you to share an amount in a given ratio. To divide £72 in the ratio 2:3:4, the total number of parts is 9, so each part is £8. The shares are £16, £24, and £32.
比例题常要求按给定比例分配数量。把 £72 按 2:3:4 分配，总份数是 9，每份 £8，因此份额为 £16、£24 和 £32。
72 ÷ (2+3+4) = 8; 2×8 = 16, 3×8 = 24, 4×8 = 32
Direct proportion can be solved by finding the unit rate. If 5 pens cost £3.50, one pen costs £0.70, so 8 pens cost £5.60.
正比例可通过先求单位量解决。如果 5 支笔 £3.50，一支 £0.70，那么 8 支 £5.60。
7. Geometry: Angles and Shapes | 几何：角与图形
s. If two angles in a triangle are 65° and 47°, the third angle is 180° − 65° − 47° = 68°.
Book 8S 几何答案涉及平角、周角和三角形内角。如果三角形两个角分别是 65° 和 47°，第三个角是 180° − 65° − 47° = 68°。
180° − 65° − 47° = 68°
Alternate and corresponding angles are tested with parallel lines. When a transversal crosses parallel lines, corresponding angles are equal, and alternate interior angles are equal.
平行线中的同位角和内错角是考点。当一条截线穿过平行线时，同位角相等，内错角也相等。
8. Area, Perimeter and Volume | 面积、周长与体积
frequently. The area of a triangle with base 8 cm and height 5 cm is (8 × 5) ÷ 2 = 20 cm².
矩形、三角形和平行四边形的面积公式常考。底为 8 cm、高为 5 cm 的三角形面积是 (8 × 5) ÷ 2 = 20 cm²。
A = ½ × 8 × 5 = 20 cm²
box 4 cm by 3 cm by 5 cm has volume 60 cm³, and surface area 2(4×3 + 4×5 + 3×5) = 94 cm².
长方体体积 = 长 × 宽 × 高。一个 4 cm × 3 cm × 5 cm 的盒子体积为 60 cm³，表面积为 2(4×3 + 4×5 + 3×5) = 94 cm²。
9. Coordinates and Graphs | 坐标与图像
Plotting coordinates in all four quadrants is a core Year 8 skill. A point (−3, 4) lies in the second quadrant because x is negative and y is positive. The answer set labels axes and scale clearly.
在四个象限中绘制坐标是 Year 8 的核心技能。点 (−3, 4) 位于第二象限，因为 x 为负、y 为正。答案集清楚标注坐标轴和刻度。
Point (−3, 4): quadrant II
values. For x = 0, 1, 2, the points are (0,1), (1,3), (2,5), which lie on a straight line.
像 y = 2x + 1 这样的直线图可通过代入 x 值求得。当 x = 0、1、2 时，点为 (0,1)、(1,3)、(2,5)，它们在同一直线上。
10. Statistics and Probability | 统计与概率
sets. For 3, 7, 7, 9, 12: mean = (3+7+7+9+12) ÷ 5 = 7.6, median = 7, mode = 7, range = 9.
平均数、中位数、众数和极差从小数据集中
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