📚 Maths Unit 1 Answer Key: Core Skills Checklist | 数学第1单元答案：核心技能清单
This guide reviews the most common question types in a typical Lower Secondary or IGCSE-style Unit 1 mathematics paper, with worked answers and examiner tips. Each section pairs a concise English explanation with a Chinese translation so that you can check both the method and the key vocabulary.
本指南复习典型初中或 IGCSE 风格数学第 1 单元试卷中最常见的题型，并提供详细答案和考官提示。每个小节都将简明的英文解释与中文翻译配对，帮助你同时掌握解题方法和关键术语。
1. Order of Operations | 运算顺序
ot 30. Always apply BIDMAS: Brackets first, then Indices, then Division and Multiplication from left to right, and finally Addition and Subtraction from left to right.
化简 8 + 2 × 3² 时，正确答案是 26，而不是 30。始终遵循 BIDMAS 顺序：先算括号，再算指数，然后从左到右算除法和乘法，最后从左到右算加法和减法。
Worked example: Simplify 8 + 2 × 3².
例题：化简 8 + 2 × 3²。
- Step 1: Index → 3² = 9
- Step 2: Multiplication → 2 × 9 = 18
- Step 3: Addition → 8 + 18 = 26
Answer: 26. Note that multiplication by 2 applies only to 9, not to the whole 8 + 9.
答案：26。注意乘以 2 只作用于 9，而不是整个 8 + 9。
irst, then 10 × 9 = 90. To avoid this, underline the operation you are doing in each step.
一个常见错误是严格从左到右计算，先算 8 + 2 = 10，再算 10 × 9 = 90。为避免这种情况，请在每一步中划出你正在进行的运算。
2. Negative Numbers | 负数运算
vision, two like signs give a positive result and two unlike signs give a negative result.
加上一个负数等于减去一个正数：5 + (-3) = 5 - 3 = 2。减去一个负数等于加上一个正数：5 - (-3) = 5 + 3 = 8。对于乘法和除法，同号得正，异号得负。
Example: Calculate -6 × (-4) + 10 ÷ (-2).
例题：计算 -6 × (-4) + 10 ÷ (-2)。
- -6 × (-4) = 24 because both signs are negative.
- 10 ÷ (-2) = -5 because the signs are different.
- 24 + (-5) = 24 - 5 = 19.
Final answer: 19.
最终答案：19。
ied after squaring, so -3² = -9, not 9. If you mean (-3)², you must use brackets to get 9.
在计算器中输入 -3² 时，请记住负号是在平方之后应用的，因此 -3² = -9，而不是 9。如果你想要的是 (-3)²，则必须使用括号才能得到 9。
3. Fractions, Decimals and Percentages | 分数、小数与百分数
or. To convert a decimal to a percentage, multiply by 100. For example, 3/8 = 0.375 = 37.5%. When comparing quantities, it is often easiest to express all values in the same form.
将分数转换为小数，用分子除以分母。将小数转换为百分数，乘以 100。例如，3/8 = 0.375 = 37.5%。比较数量时，通常最简单的方法是所有数值都用同一种形式表示。
Worked example: Arrange 2/5, 0.44, 41% in ascending order.
例题：将 2/5、0.44、41% 按升序排列。
- 2/5 = 0.40 = 40%
- 0.44 = 44%
- 41% = 0.41
Ascending order: 40%, 41%, 44%, so the original values are 2/5, 41%, 0.44.
升序排列：40%、41%、44%，因此原值为 2/5、41%、0.44。
ominators. First find a common denominator: 1/3 = 4/12 and 1/4 = 3/12, so the sum is 7/12.
在计算 1/3 + 1/4 这类分数加法时，不要将分母相加。先找到公分母：1/3 = 4/12，1/4 = 3/12，因此和为 7/12。
4. Simplifying Algebraic Expressions | 化简代数式
Only like terms can be combined. Like terms have exactly the same variable part, such as 3a and -5a. Coefficients are added or subtracted while the variable part stays unchanged. Terms with different powers or different variables cannot be collected.
只有同类项才可以合并。同类项具有完全相同的变量部分，例如 3a 和 -5a。系数相加或相减，变量部分保持不变。不同次数或不同变量的项不能合并。
Example: Simplify 4x + 3y - 2x + 5y - 7.
例题：化简 4x + 3y - 2x + 5y - 7。
- Combine x terms: 4x - 2x = 2x
- Combine y terms: 3y + 5y = 8y
- Constant: -7
Answer: 2x + 8y - 7.
答案：2x + 8y - 7。
Be careful with expressions such as 3x² and 2x. These are not like terms because the powers of x are different. The expression 3x² + 2x cannot be simplified further.
对于 3x² 和 2x 这样的表达式要小心。它们不是同类项，因为 x 的次数不同。表达式 3x² + 2x 不能进一步化简。
5. Solving Linear Equations | 解一元一次方程
9, subtract 4 from both sides to get 3x = 15, then divide both sides by 3 to obtain x = 5.
解一元一次方程时，对两边执行相同的运算以隔离未知数。例如，在 3x + 4 = 19 中，两边同时减去 4 得到 3x = 15，然后两边同时除以 3 得到 x = 5。
rackets should be expanded first: 2(x - 3) = 10 gives 2x - 6 = 10, then 2x = 16 and x = 8.
有括号的方程应先展开：2(x - 3) = 10 可得 2x - 6 = 10，然后 2x = 16，x = 8。
into the original equation. For x = 8, 2(8 - 3) = 2 × 5 = 10, which confirms the solution.
始终将答案代回原方程进行检验。对于 x = 8，2(8 - 3) = 2 × 5 = 10，这验证了解的正确性。
such as 5x - 3 = 2x + 9, first collect like terms: 5x - 2x = 9 + 3, so 3x = 12 and x = 4.
如果未知数出现在两边，例如 5x - 3 = 2x + 9，首先合并同类项：5x - 2x = 9 + 3，因此 3x = 12，x = 4。
6. Ratio and Proportion | 比与比例
Ratios compare parts of a whole, while proportions compare a part to the whole. To divide a quantity in a given ratio, first find the total number of parts, then find the value of one part, and finally multiply by each ratio term.
比用于比较整体中的各部分，而比例用于比较部分与整体。按给定比分配数量时，先求出总份数，再求出一份的值，最后乘以比的每一项。
Worked example: Divide £120 in the ratio 2 : 3.
例题：按 2 : 3 的比例分配 120 英镑。
- Total parts = 2 + 3 = 5
- One part = 120 ÷ 5 = 24
- First share = 2 × 24 = 48
- Second share = 3 × 24 = 72
The two amounts are £48 and £72.
两部分金额分别为 48 英镑和 72 英镑。
Ratios can be simplified in the same way as fractions. For example, 12 : 18 simplifies to 2 : 3 by dividing both sides by 6. Always express a ratio in its simplest integer form unless instructed otherwise.
比可以像分数一样化简。例如，12 : 18 两边同时除以 6 可化简为 2 : 3。除非另有说明，否则始终用最简整数比表示。
7. Perimeter, Area and Volume | 周长、面积与体积
width, triangle area A = ½ × base × height, and cuboid volume V = length × width × height.
周长是图形外轮廓的长度，面积是二维图形内部的空间，体积是三维立体内部的空间。常用公式包括：矩形面积 A = 长 × 宽，三角形面积 A = ½ × 底 × 高，长方体体积 V = 长 × 宽 × 高。
Example: A rectangle has length 8 cm and width 5 cm. Find its perimeter and area.
例题：一个矩形的长为 8 厘米，宽为 5 厘米。求它的周长和面积。
- Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm
- Area = 8 × 5 = 40 cm²
Answer: perimeter 26 cm, area 40 cm². Always include the correct units in your final answer.
答案：周长 26 厘米，面积 40 平方厘米。最终答案中一定要写明正确单位。
For compound shapes, split the shape into simpler rectangles or triangles, calculate each area separately, then add or subtract as needed. Show all working clearly
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