📚 Essential Maths Book 7 Compressed Question Types Explained | 核心数学第七册精要题型解析
Essential Maths Book 7 is a widely used resource in Key Stage 3 that distills the Year 7 curriculum into focused practice. This article breaks down the most common question types found in its compressed format, covering number operations, fractions, algebra, geometry, and data handling. Each section provides a clear approach to tackling problems, helping students build confidence and fluency.
《核心数学第七册》是英国关键阶段3广泛使用的精要练习册，它将七年级课程浓缩为针对性训练。本文解析其中最常见的题型，涵盖数字运算、分数、代数、几何和数据处理。每个部分都给出清晰的解题方法，帮助学生建立信心和熟练度。
1. Place Value and Ordering | 位值与排序题型
Questions often ask you to write numbers in words or digits up to millions, or to identify the value of a underlined digit. For example, in 4 307 256 the digit 3 represents 300 000.
这类问题常要求你用文字或数字写出百万以内的数，或指出下划线数字的位值。例如在 4 307 256 中，数字 3 代表 300 000。
Ordering integers and decimals from smallest to largest is another key skill. Remember to align decimal points and compare digits column by column from the left.
整数和小数的排序也是关键技能。记得对齐小数点，从左到右逐列比较数字。
2. Addition and Subtraction with Whole Numbers | 整数加减法题型
Column addition and subtraction underpin many Book 7 exercises. Watch out for regrouping when a column sum exceeds 9, or when you need to borrow from a higher place value.
竖式加减法是第七册许多练习的基础。当一列之和超过9时要注意进位，需要从高位借位时要格外小心。
Word problems often involve real‑life contexts like money or distances. Always show your working clearly to avoid careless mistakes.
应用题常涉及金钱或距离等现实情境。务必将解题步骤写清楚，避免粗心出错。
3. Multiplication and Division Strategies | 乘法与除法策略题型
Mental multiplication by 10, 100, 1000 appears frequently. The rule is simple: move the digits to the left by the number of zeros. 45 × 100 = 4500.
心算乘10、100、1000的题目频繁出现。规则很简单：有多少个零就把数字向左移动多少位。45 × 100 = 4500。
Long multiplication and short division with remainders are also tested. Express remainders as whole numbers, fractions, or decimals as directed. For instance, 73 ÷ 4 = 18 r 1 or 18 ¼ or 18.25.
长乘法和有余数的短除法也是考查点。按要求将余数写成整数、分数或小数。例如 73 ÷ 4 = 18 余 1，或 18 ¼，或 18.25。
4. Factors, Multiples and Primes | 因数、倍数与质数题型
Find all factors of a number, such as factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Remember that 1 and the number itself are always factors.
找出一个数的所有因数，比如36的因数：1, 2, 3, 4, 6, 9, 12, 18, 36。记住1和它本身总是因数。
Prime numbers up to 100 are essential to memorise — 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Prime factorisation expresses a number as a product of primes, e.g. 60 = 2² × 3 × 5.
100以内的质数必须记住——2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97。质因数分解是将一个数表示为质数的乘积，例如 60 = 2² × 3 × 5。
5. Fractions – Equivalent, Simplifying and Comparing | 分数——等价、化简与比较题型
Simplifying fractions means dividing numerator and denominator by the same whole number until the fraction is in its simplest form. 8/12 simplifies to 2/3 (divide by 4).
化简分数是指用同一个整数同除分子和分母，直到分数成为最简形式。8/12 化简为 2/3（同除以4）。
To compare fractions like 3/4 and 5/6, find a common denominator (12): 3/4 = 9/12, 5/6 = 10/12, so 5/6 is larger. Converting between mixed numbers and improper fractions is another regular exercise.
比较分数如 3/4 和 5/6 时，先找到公分母（12）：3/4 = 9/12，5/6 = 10/12，所以 5/6 更大。带分数与假分数之间的互化也是常见练习。
6. Decimals and Percentages | 小数与百分数题型
Rounding decimals to 1 or 2 decimal places is a core skill. For 3.678 to 2 d.p., look at the third decimal (8), so round up to 3.68.
将小数四舍五入到一位或两位小数是核心技能。将 3.678 精确到两位小数，看第三位小数（8），因此进位得 3.68。
Converting between fractions, decimals and percentages: 1/4 = 0.25 = 25%. Finding a percentage of an amount, e.g. 30% of £240 = 0.30 × 240 = £72, is a frequently assessed problem-solving type.
分数、小数和百分数之间的互化：1/4 = 0.25 = 25%。求一个量的百分之几，例如 240 英镑的 30% = 0.30 × 240 = 72 英镑，是常考的应用题型。
7. Introduction to Algebra | 代数入门题型
Writing expressions from words: ‘5 more than a number n’ becomes n + 5. Substituting values into formulae, such as find 3a + 2b when a = 4 and b = 5 → 3×4 + 2×5 = 12 + 10 = 22.
由文字写出表达式：“比一个数 n 多5”写成 n + 5。代入数值到公式中，比如求当 a=4, b=5 时 3a+2b 的值 → 3×4+2×5=12+10=22。
Collecting like terms simplifies expressions: 4x + 2y – x + 3y = 3x + 5y. Remember you can only combine terms with exactly the same variable part.
合并同类项可以化简表达式：4x + 2y – x + 3y = 3x + 5y。记住只能合并变量部分完全相同的项。
8. Simple Equations | 简单方程题型
One‑step equations like x + 7 = 15 are solved by doing the inverse operation on both sides: x = 15 – 7, so x = 8. Two‑step equations combine two operations, e.g. 3y – 4 = 11. First add 4: 3y = 15, then divide by 3: y = 5.
像 x + 7 = 15 这样的一步方程，可在两边进行逆运算求解：x = 15 – 7，得 x = 8。两步方程结合了两种运算，例如 3y – 4 = 11。先加4：3y = 15，再除以3：y = 5。
Always check your answer by substituting it back into the original equation. This habit reduces errors in exam conditions.
答完题后务必将答案代回原方程检验。这个习惯能减少考试中的错误。
9. Geometry – Angles and Shapes | 几何——角与图形题型
Measuring angles with a protractor and classifying them (acute, right, obtuse, reflex) appear in many Book 7 tasks. A right angle is exactly 90°; an acute angle is less than 90°.
用量角器测量角度并分类（锐角、直角、钝角、优角）出现在第七册的许多练习中。直角恰好是90°；锐角小于90°。
Angle facts on a straight line (sum to 180°) and around a point (sum to 360°) are used to find missing angles. If one angle on a straight line is 65°, the other is 180° – 65° = 115°.
直线上的角之和为180°，一点周围的角之和为360°，这些角的基本性质可用来求未知角。若直线上一个角为65°，则另一角为180° – 65° = 115°。
10. Perimeter and Area | 周长与面积题型
Perimeter of a rectangle is found by adding all sides or using 2(length + width). For a rectangle 8 cm by 5 cm, perimeter = 2 × (8+5) = 26 cm.
长方形的周长可通过将所有边长相加或使用 2×(长+宽) 求得。对一个长8厘米、宽5厘米的长方形，周长 = 2×(8+5) = 26 厘米。
Area of a rectangle = length × width; area of a triangle = ½ × base × height. Composite shapes may require splitting into known figures. A square of side 6 cm has area 36 cm².
长方形的面积 = 长 × 宽；三角形的面积 = ½ × 底 × 高。组合图形可能需要分割为已知图形。边长为6厘米的正方形面积为36平方厘米。
11. Data Handling and Graphs | 数据处理与图表题型
Reading and interpreting bar charts, pictograms and line graphs is a key skill. Pay attention to the scale on each axis and what each symbol or bar represents.
阅读和解释条形图、象形图和折线图是一项关键技能。要注意每个轴的刻度以及每个符号或条形所代表的数量。
Finding the mode (most frequent), median (middle value when ordered), mean (sum ÷ count) and range (largest – smallest) from a list of numbers is standard. For 3, 7, 7, 2, 5: mean = (3+7+7+2+5) ÷ 5 = 4.8; mode = 7; median = 5; range = 7 – 2 = 5.
从一组数字中找出众数（出现最频繁的）、中位数（按序排列后的中间值）、平均数（总和÷个数）和极差（最大减最小）是标准题型。对于 3, 7, 7, 2, 5：平均数 = (3+7+7+2+5)÷5 = 4.8；众数 = 7；中位数 = 5；极差 = 7–2 = 5。
12. Real‑Life Problem Solving | 实际生活应用题题型
Word problems require translating a situation into a mathematical calculation. Key words like ‘altogether’ hint at addition, ‘how many more’ suggests subtraction, ‘each’ or ‘per’ points to multiplication or division.
应用题需要将情境转化为数学计算。像“总共”暗示加法，“多多少”暗示减法，“每个”或“每”则指向乘法或除法。
Multi‑step problems often involve money, measures or time. Break them down into simple steps and check each calculation. For example, buying 3 pens at £1.25 each and a notebook for £2.50: total = 3×1.25 + 2.50 = 3.75 + 2.50 = £6.25.
多步骤问题常涉及金钱、度量或时间。把它们分解成简单步骤并检查每一步计算。例如，买3支笔每支1.25英镑和一本笔记本2.50英镑：总花费 = 3×1.25 + 2.50 = 3.75 + 2.50 = 6.25 英镑。
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