Year 7 CAIE Maths: Quick Vocabulary Memorisation Guide | Year 7 CAIE 数学：词汇术语速记指南

📚 Year 7 CAIE Maths: Quick Vocabulary Memorisation Guide | Year 7 CAIE 数学：词汇术语速记指南

Welcome to this quick guide designed to help Year 7 students master key mathematical vocabulary for the CAIE curriculum. Learning the language of maths is just as important as solving problems. This article covers essential terms across number, algebra, geometry, and data handling, and offers simple memory tricks to make them stick.

欢迎阅读这本为Year 7学生设计的速记指南，旨在帮助掌握CAIE数学课程的关键词汇。学习数学语言与解题同样重要。本文涵盖数字、代数、几何和数据处理等领域的核心术语，并提供简单的记忆技巧，让它们根深蒂固。

1. Number Types | 认识数字类型

Integer: An integer is any whole number that can be positive, negative, or zero. Integers have no fractional or decimal part. Think of ‘integer’ as a word related to ‘entire’ or ‘whole’.

整数：整数是任意完整的数，可以是正数、负数或零。整数没有小数或分数部分。记住‘整’字代表完整，不零碎。

Whole number: Whole numbers start from 0 and go up by ones: 0, 1, 2, 3, … They do not include negatives.

自然数（或整数）：在CAIE课程中，whole number指非负整数，从0开始依次加1。它不包括负数。

Natural number: Natural numbers are the counting numbers. Usually they begin at 1 (1, 2, 3, …). Some definitions include 0, but in most Year 7 work count from 1.

正整数/自然数：自然数是用于计数的数，通常从1开始（1, 2, 3, …）。在解题时注意题目是否包含0。

Positive and negative numbers: Positive numbers are greater than zero. Negative numbers are less than zero and are written with a minus sign. Imagine positive as having money and negative as owing money.

正数与负数：正数大于零。负数小于零，前面有负号。可以把正数想象成自己的钱，负数想象成欠别人的钱。

Even and odd: Even numbers can be divided by 2 exactly and end in 0, 2, 4, 6, or 8. Odd numbers leave a remainder of 1 when divided by 2 and end in 1, 3, 5, 7, or 9.

偶数与奇数：偶数能被2整除，末位是0, 2, 4, 6, 8。奇数除以2余1，末位是1, 3, 5, 7, 9。

Prime number: A prime number has exactly two distinct factors: 1 and itself. For example, 7 is prime because only 1 × 7 works. The number 1 is not prime.

质数（素数）：质数有且只有两个不同的因数：1和它本身。例如7是质数，因为只有1 × 7。1不是质数。

Composite number: A composite number has more than two factors. 12 is composite because its factors are 1, 2, 3, 4, 6, 12.

合数：合数有超过两个因数。12是合数，因为它的因数有1, 2, 3, 4, 6, 12。

Factor: A factor is a number that divides exactly into another number. For example, 5 is a factor of 20. Factors come in pairs.

因数：一个数能被另一个数整除，后者就是前者的因数。例如5是20的因数。因数总是成对出现。

Multiple: A multiple is the result of multiplying a number by an integer. The multiples of 6 are 6, 12, 18, 24, …

倍数：一个数乘以任意整数得到的结果就是该数的倍数。6的倍数有6, 12, 18, 24, …

Square number: A square number is obtained by multiplying a number by itself. 3 × 3 = 9, so 9 is a square number, often written 3².

平方数：一个数与自己相乘得到平方数。3 × 3 = 9，所以9是平方数，记作3²。

Cube number: A cube number is the result of multiplying a number by itself twice. 2 × 2 × 2 = 8, written 2³.

立方数：一个数与自己相乘两次得到立方数。2 × 2 × 2 = 8，记作2³。

Rational number: Any number that can be written as a fraction where both numerator and denominator are integers (denominator not zero). All integers are rational.

有理数：任何可以写成分数形式的数，分子和分母都是整数且分母不为零。所有整数都是有理数。

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2. Operations Vocabulary | 运算词汇

Sum: The result of adding two or more numbers. ‘What is the sum of 8 and 5?’ means 8 + 5 = 13. Remember: SUM = Some U Must add.

和：两个或多个数相加的结果。‘8与5的和’意思是8 + 5 = 13。可以把‘和’想象成‘合在一起’。

Difference: The result of subtracting one number from another. The difference between 15 and 9 is 6, because 15 − 9 = 6. It is how far apart the numbers are.

差：一个数减去另一个数的结果。15和9的差是6，因为15 − 9 = 6。差表示两个数之间的距离。

Product: The result of multiplying. The product of 4 and 7 is 28. Think of ‘product’ like a factory producing many items – multiplication makes numbers grow fast.

积：相乘的结果。4与7的积是28。英文’product’一词也可指产品，想象工厂大量生产，乘积也会迅速变大。

Quotient: The result of division. 36 ÷ 9 = 4, so the quotient is 4. Tip: ‘quotient’ sounds a bit like ‘quiet division’.

商：相除的结果。36 ÷ 9 = 4，商就是4。中文‘商’可以联系商量的过程，除法就像平均分配时的商量。

Remainder: The amount left over when division is not exact. 14 ÷ 3 gives quotient 4 remainder 2. Remainder is always smaller than the divisor.

余数：除法不能整除时剩下的部分。14 ÷ 3 商为4余数为2。余数总是小于除数。

Divisible: One number is divisible by another if division leaves no remainder. 24 is divisible by 6 because 24 ÷ 6 = 4 exactly.

整除：如果一个数除以另一个数没有余数，就称前者能被后者整除。24能被6整除，因为24 ÷ 6 = 4。

Index (power or exponent): A small number written above and to the right showing how many times to multiply the base. 5³ means 5 × 5 × 5. 5² is read ‘5 squared’.

指数（幂）：写在右上角的小数字，表示底数要自乘多少次。5³表示5 × 5 × 5。5²读作‘5的平方’。

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3. Fractions and Decimals | 分数与小数

Numerator and denominator: The numerator is the top number, representing how many parts we have. The denominator is the bottom number, showing the total number of equal parts. Remember: Denominator Down.

分子与分母：分子是分数线上面的数，表示有几份。分母是下面的数，表示一共分成了几等份。记住‘分母’的‘母’是根源，在下。

Proper fraction: The numerator is smaller than the denominator, e.g., 2/5. Value is less than 1.

真分数：分子小于分母，如2/5。值小于1。

Improper fraction: The numerator is greater than or equal to the denominator, e.g., 7/4. Value is 1 or more.

假分数：分子大于或等于分母，如7/4。值大于等于1。

Mixed number: A whole number and a proper fraction together, like 1 ½.

带分数：由一个整数和一个真分数组成，如1 ½。

Equivalent fractions: Fractions that look different but represent the same amount, e.g., 1/2 = 2/4 = 4/8. Multiply or divide numerator and denominator by the same number.

等价分数：看起来不同但表示相同大小的分数，如1/2 = 2/4 = 4/8。将分子分母同时乘以或除以相同的数即可得到。

Simplifying (cancelling): Dividing numerator and denominator by a common factor to make the fraction simpler. 8/12 simplifies to 2/3.

约分：将分子分母同时除以公因数，使分数更简单。8/12约分成2/3。

Reciprocal: The reciprocal of a fraction is obtained by swapping numerator and denominator. The reciprocal of 3/4 is 4/3. Multiplying a number by its reciprocal gives 1.

倒数：把分数的分子分母交换位置就得到倒数。3/4的倒数是4/3。一个数乘它的倒数等于1。

Decimal places: Digits after the decimal point: tenths, hundredths, thousandths. 0.3 has 3 in the tenths place, meaning 3/10.

小数位：小数点后的数字分别代表十分位、百分位、千分位。0.3的十分位是3，表示3/10。

Terminating decimal: A decimal that stops, like 0.75. These come from fractions whose denominator has only prime factors 2 and 5.

有限小数：位数有限的小数，如0.75。它们来自分母只含质因数2和5的分数。

Recurring decimal: A decimal where digits repeat forever, such as 0.333… written with a dot above the repeating digit.

循环小数：小数点后有一段数字不断重复的小数，如0.333…，记作在重复数字上加圆点。

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4. Algebraic Expressions | 代数表达式

Variable: A letter or symbol used to stand for an unknown number. Often we use x, y, or n.

变量：用来表示未知数的字母或符号，通常用x, y, n等。

Constant: A fixed number that does not change. In the expression 3x + 7, 7 is a constant.

常数：固定不变的数。在表达式3x + 7中，7是常数。

Coefficient: The number multiplied by a variable. In 5y, 5 is the coefficient of y.

系数：与变量相乘的数字。在5y中，5是y的系数。

Term: A single number, variable, or product of numbers and variables separated by + or −. 3a, 4b², and −2 are terms.

项：由加号或减号分隔的一个数、一个变量或数与变量的乘积。3a, 4b², −2都是项。

Like terms: Terms that have exactly the same variable part (same letter and same exponent). 3x and 5x are like terms; 3x² and 5x are not.

同类项：所含变量及其指数完全相同的项。3x和5x是同类项；而3x²和5x不是。

Expression: A combination of terms without an equals sign. For example, 2a + 5b − 3.

表达式：由项组成但没有等号的式子，如2a + 5b − 3。

Equation: A mathematical statement showing two expressions are equal, using an equals sign. 2x + 1 = 7 is an equation.

方程：用等号连接两个表达式的语句，表示两边相等。2x + 1 = 7是一个方程。

Formula: A fact or rule written using symbols, usually showing a relationship. A = l × w is the formula for the area of a rectangle.

公式：用符号写出的规则或关系式，通常表示某种联系。A = l × w是长方形面积的公式。

Substitution: Replacing a variable with a given number. If x = 3, substituting into 2x + 5 gives 2(3) + 5 = 11.

代入：把变量替换成给定的数。若x = 3，代入2x + 5得到2×3 + 5 = 11。

Solve: Find the value of the variable that makes the equation true. To solve x + 4 = 10, we find x = 6.

解（方程）：求出使方程成立的变量的值。解x + 4 = 10，得到x = 6。

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5. Geometry Basics | 几何基础

Point: An exact location in space. It has no size, only position. We name a point with a capital letter, like A.

点：空间中的一个精确位置，没有大小，只有位置。通常用大写字母命名，如A。

Line: A straight path that goes on forever in both directions. It has no thickness. Arrows at both ends show it extends infinitely.

直线：向两端无限延伸的笔直路径，没有粗细。两端箭头表示无限延伸。

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