📚 Year 7 OCR Mathematics: Core Knowledge Points Overview | Year 7 OCR 数学：核心知识点梳理
In Year 7, students following the OCR mathematics curriculum build a solid foundation across key areas: number, algebra, geometry, statistics, and probability. Mastering these core topics ensures confidence for future study. This article outlines the essential knowledge points, paired with bilingual explanations to support learners.
Year 7 OCR 数学课程涵盖数、代数、几何、统计和概率等核心领域，掌握这些基础知识将为后续学习奠定扎实基础。本文梳理了核心知识点，并提供中英双语解释，帮助学习者更好地理解。
1. Place Value and Rounding | 数值和四舍五入
Place value means the value of each digit in a number depending on its position. For example, in 8,365 the digit 8 is in the thousands place, so it represents 8,000. Understanding place value helps with ordering numbers and performing operations correctly.
数值（Place Value）指的是一个数字中每个数字根据其位置所具有的值。例如在数字 8,365 中，8 在千位上，因此表示 8,000。理解数值有助于正确排序数字和进行运算。
Rounding is a way to simplify a number while keeping its value close to what it was. To round to the nearest ten, look at the units digit: if it is 5 or more, round up; if it is 4 or less, round down. The same rule applies when rounding to hundreds or thousands.
四舍五入是一种简化数字的方法，同时保持它的大小大致不变。四舍五入到十位时，看个位数字：如果是 5 或更大，则向上入；如果是 4 或更小，则向下舍。同样的规则也适用于四舍五入到百位或千位。
2. Negative Numbers | 负数
Negative numbers are numbers less than zero, written with a minus sign in front. They are used to represent temperatures below zero, debts, or depths below sea level. On a number line, negative numbers are to the left of zero.
负数是小于零的数，前面带有一个负号。它们常用于表示低于零的温度、债务或海平面以下的深度。在数轴上，负数位于零的左侧。
- (-2) = 4 + 2 = 6. Year 7 students practise working with negative numbers in all four operations.
加上一个负数等同于减去它的正数值：5 + (-3) = 5 - 3 = 2。减去一个负数则等同于加上正数：4 - (-2) = 4 + 2 = 6。Year 7 的学生需要练习在四则运算中使用负数。
3. Factors, Multiples and Primes | 因数、倍数与质数
A factor is a whole number that divides exactly into another number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. A multiple is the product of a number and any integer; the first five multiples of 7 are 7, 14, 21, 28, 35.
因数是可以整除另一个整数且没有余数的整数。例如 12 的因数有 1、2、3、4、6 和 12。倍数是指一个数与任意整数的乘积；7 的前五个倍数依次是 7、14、21、28、35。
A prime number has exactly two distinct factors: 1 and itself. Prime numbers include 2, 3, 5, 7, 11, and so on. Note that 1 is not a prime because it only has one factor. Prime factorisation involves breaking a number into a product of prime factors, useful for finding highest common factors (HCF) and lowest common multiples (LCM).
质数（素数）只有两个不同的因数：1 和它本身。质数包括 2、3、5、7、11 等。注意 1 不是质数，因为它只有一个因数。质因数分解是将一个数分解为质因数的乘积，这对求最大公因数（HCF）和最小公倍数（LCM）很有帮助。
4. Fractions | 分数
uch as ½ = ²⁄₄ = ³⁄₆. To simplify a fraction, divide both numerator and denominator by their highest common factor.
分数表示整体的一部分，由分子（上）和分母（下）组成。等值分数具有相同的值，例如 ½ = ²⁄₄ = ³⁄₆。化简分数时，用分子和分母同时除以它们的最大公因数。
When adding or subtracting fractions, they must have the same denominator. If not, find a common denominator first. To multiply fractions, multiply the numerators together and the denominators together. Dividing by a fraction is the same as multiplying by its reciprocal.
进行分数的加、减运算时，分数必须具有相同的分母。如果分母不同，需要先找到公分母。分数相乘时，分子乘分子，分母乘分母。除以一个分数等同于乘以它的倒数。
5. Decimals and Percentages | 小数和百分数
Decimals are based on place value: the first digit after the decimal point is tenths, the next is hundredths, and so on. Rounding decimals follows the same rules as rounding whole numbers. Adding and subtracting decimals requires decimal points to be aligned.
小数基于数值位置：小数点后第一位是十分位，第二位是百分位，以此类推。小数四舍五入的规则与整数相同。小数的加、减运算需要对小数点对齐。
A percentage means 'out of 100'. To convert a percentage to a fraction, write it over 100 and simplify. To convert between decimals and percentages, multiply or divide by 100. Understanding the link between fractions, decimals, and percentages helps solve problems involving discounts, comparisons, and proportions.
百分数（百分比）表示“百分之几”。将百分数转换为分数时，将其写成分母为 100 的分数再化简。小数和百分数之间的转换可以通过乘以或除以 100 完成。理解分数、小数和百分数之间的联系有助于解决涉及折扣、比较和比例的问题。
6. Introduction to Algebra | 代数基础
uch as 2a + 5b. Simplifying expressions involves collecting like terms, e.g. 4y + 2y = 6y.
代数使用字母（变量）表示未知数。像 3x 这样的项表示 3 乘以 x。代数式是项的集合，比如 2a + 5b。化简代数式需要合并同类项，例如 4y + 2y = 6y。
. One-step equations can be solved by using inverse operations: if x + 5 = 12, then x = 7.
代入法是指用给定的数字替换变量并计算出数值。例如，若 x = 3，那么 2x + 4 = 2(3) + 4 = 10。一步方程可以通过逆运算来求解：若 x + 5 = 12，则 x = 7。
7. Coordinates and Plotting Points | 坐标与描点
Coordinates are written as ordered pairs (x, y), where x is the horizontal position and y is the vertical position. The origin is the point (0,0). Moving right increases the x-coordinate; moving up increases the y-coordinate.
坐标以有序数对 (x, y) 的形式表示，其中 x 是水平位置，y 是垂直位置。原点为 (0,0)。向右移动增加 x 坐标，向上移动增加 y 坐标。
Points can be plotted on a coordinate grid and joined to form shapes. Midpoints of a line segment can be found by averaging the x-values and y-values of the endpoints. These skills prepare students for graphing linear equations later.
点可以绘制在坐标网格上，并连接起来形成图形。线段中点的坐标可以通过两端点 x 值和 y 值的平均数求得。这些技能为学生以后绘制线性方程图像做准备。
8. Angles and Lines | 角与线
An angle is measured in degrees (°). Angles are classified as acute (less than 90°), right angles (exactly 90°), obtuse (between 90° and 180°), and reflex (greater than 180°). Angles on a straight line add up to 180°.
角的大小以度（°）为单位。角分为锐角（小于 90°）、直角（等于 90°）、钝角（介于 90° 到 180° 之间）和优角（大于 180°）。直线上的角之和为 180°。
Vertically opposite angles formed when two lines cross are equal. Angles at a point sum to 360°. Knowledge of these rules, along with alternate and corresponding angles on parallel lines, helps solve missing-angle problems.
两条直线相交时形成的对顶角相等。绕一点一圈的角度之和为 360°。掌握这些规则，以及平行线上的内错角和同位角知识，有助于解决求角度的问题。
9. Triangles and Quadrilaterals | 三角形和四边形
Triangles can be classified by their sides: equilateral (3 equal sides), isosceles (2 equal sides), and scalene (no equal sides). By angles, they can be acute, right, or obtuse. The angles inside any triangle always sum to 180°.
三角形可以按边分类：等边三角形（三条边相等）、等腰三角形（两条边相等）和不等边三角形（没有边相等）。按角分类，三角形可以是锐角三角形、直角三角形或钝角三角形。任何三角形的内角之和总是 180°。
Quadrilaterals are four-sided shapes. Important types include squares, rectangles, parallelograms, rhombuses, trapeziums, and kites. Each has specific properties about side lengths, parallel sides, and angle sizes. The sum of interior angles in a quadrilateral is 360°.
四边形是有四条边的图形。重要的类型有正方形、矩形、平行四边形、菱形、梯形和筝形。每种图形都有关于边长、平行边以及角度的特性。四边形的内角和为 360°。
10. Perimeter, Area and Volume | 周长、面积和体积
shape; the area of a rectangle is length × width, measured in square units like cm² or m².
周长是指二维图形外部边界的总长度。对于矩形，周长 = 2 × (长 + 宽)。面积衡量图形内部的空间；矩形面积 = 长 × 宽，单位是平方单位，如 cm² 或 m²。
Area of triangle = ½ × base × height
三角形面积 = ½ × 底 × 高
nits, e.g. cm³. Students also learn to find areas of compound shapes by splitting them into simpler shapes.
体积是指三维立体内部的空间大小。对于长方体，体积 = 长 × 宽 × 高，单位是立方单位，如 cm³。学生还将学习通过分割成简单图形来计算组合图形的面积。
11. Statistics: Mean, Mode, Median and Range | 统计：平均数、众数、中位数和极差
The mean is the average of a set of numbers, found by adding them all together and dividing by the number of data points. The mode is the value that appears most often. The median is the middle value when the data are ordered from smallest to largest.
平均数（均值）是一组数据的平均值，通过所有数值相加再除以数据个数求得。众数是一组数据中出现次数最多的值。中位数是将数据按从小到大的顺序排列后处于中间位置的数值。
The range is the difference between the largest and smallest values, showing how spread out the data are. These four measures help describe data sets and are often used when interpreting charts and graphs such as bar charts, pictograms, and line graphs.
极差是最大值与最小值的差，反映了数据的分散程度。这四种统计量有助于描述数据集，并在解释柱状图、象形图和折线图等图表时经常使用。
12. Probability Basics | 概率基础
Probability describes how likely an event is to happen, using a scale from 0 (impossible) to 1 (certain). It can be written as a fraction, decimal, or percentage. For example, the probability of flipping a fair coin and getting heads is ½.
概率用从 0（不可能）到 1（必然）的尺度来描述事件发生的可能性。它可以写成分数、小数或百分数。例如，抛一枚均匀硬币，正面朝上的概率是 ½。
tcomes ÷ total number of outcomes. The sum of probabilities of all possible outcomes is always 1. Students learn to list outcomes systematically and to use probability words such as 'likely', 'unlikely', 'even chance'.
如果所有结果发生的可能性相等，概率 = 有利结果数 ÷ 所有可能结果数。所有可能结果的概率之和总是 1。学生将学习系统地列出结果，并使用诸如“很可能”、“不太可能”、“机会均等”这样的概率描述词。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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