Year 10 CCEA Mathematics: Summer Preview and Bridging Course | CCEA 数学：暑期预习与衔接课程

📚 Year 10 CCEA Mathematics: Summer Preview and Bridging Course | CCEA 数学：暑期预习与衔接课程

Summer is the ideal time to bridge the gap between Year 9 and the demands of Year 10 CCEA Mathematics. This course is designed to strengthen your foundational knowledge and introduce you to the key topics you will encounter in the first term, setting a confident tone for your GCSE journey. By working through number sense, algebra, geometry, data handling, and problem-solving skills, you will build a secure platform from which to tackle more advanced concepts.

暑期是衔接 Year 9 与 Year 10 CCEA 数学学习的理想时期。本课程旨在巩固你的基础，并提前接触第一学期将面临的关键主题，为你迈入 GCSE 学习奠定自信的基调。通过梳理数感、代数、几何、数据处理及问题解决能力，你将构筑一个稳固的平台，从容应对更深入的概念。

1. Number Sense and Operations | 数感与运算基础

In Year 10, you will build on your understanding of place value, working confidently with integers, decimals, and fractions. Make sure you can order and compare numbers of any size, including negative values, and use them fluently in the four operations.

在 Year 10，你需要进一步巩固位值概念，能够熟练处理整数、小数和分数。确保你可以对任意大小的数进行排序和比较（包括负数），并能在四则运算中流畅使用。

You will extend number theory to include prime factor decomposition using factor trees, and then apply these to find the highest common factor (HCF) and lowest common multiple (LCM) of two or more numbers. This skill proves essential when manipulating fractions and solving problems involving divisibility.

你将学习数论内容，包括用因数树进行质因数分解，并利用分解结果求两个或多个数的最大公因数（HCF）和最小公倍数（LCM）。这一技能在分数化简和涉及整除的问题中至关重要。

A key new skill is writing large and small numbers in standard form (a x 10ⁿ where 1 ≤ a < 10) and performing calculations with them. You may also meet simple surds, learning to simplify expressions like √12 = 2√3 and to rationalise denominators in simple cases.

一项重要的新技能是使用标准形式（a x 10ⁿ，其中 1 ≤ a < 10）表示极大或极小的数，并进行运算。你还可能接触简单的根式，学习如何化简如 √12 = 2√3 的表达式，以及在简单情形下将分母有理化。

---

2. Algebraic Manipulation | 代数式变形

Revisit the rules of algebra: collecting like terms, using index laws for multiplication and division, and expanding single brackets. For instance, 3x + 5y – x + 2y simplifies to 2x + 7y, while 4a x 3a² gives 12a³.

重温代数规则：合并同类项，运用指数律进行乘除，以及展开单项式乘括号。例如，3x + 5y – x + 2y 化简为 2x + 7y，而 4a x 3a² 得到 12a³。

In Year 10, you will learn to expand pairs of brackets using the FOIL method, such as (x+3)(x-2) = x² + x – 6. You will also reverse this process to factorise simple quadratic expressions of the form x² + bx + c, an essential skill for solving quadratic equations later.

Year 10 将学习使用首外内尾法展开两个括号，如 (x+3)(x-2) = x² + x – 6。你还会反过来将 x² + bx + c 形式的简单二次式进行因式分解，这是后续解二次方程的核心技能。

Substitution and formula rearrangement are equally important. Practice evaluating expressions for given values and making a variable the subject, such as changing v = u + at into a = (v – u)/t. These techniques are vital for applying maths in physics and other subjects.

代入求值和公式变换同等重要。练习代入求值，并尝试将变量变为公式的主题，例如把 v = u + at 变换为 a = (v – u)/t。这些技巧对于在物理等学科中应用数学至关重要。

---

3. Linear Equations and Inequalities | 一次方程与不等式

Confidently solving linear equations with unknowns on both sides is a must. Take 5x – 7 = 2x + 8: subtract 2x, add 7, and divide by 3 to get x = 5. Always check your answer by substituting it back into the original equation.

必须能够熟练求解两边均含未知数的一次方程。以 5x – 7 = 2x + 8 为例：两边减去 2x，加 7，再除以 3 得到 x = 5。始终将答案代回原方程进行检验。

Inequalities introduce the symbols >, <, ≥, ≤. You solve them similarly to equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number. Represent the solution set on a number line, using open circles for strict inequalities and closed circles for inclusive boundaries.

不等式引入了 >, <, ≥, ≤ 符号。其解法与方程类似，但务必记住当乘以或除以负数时需反转不等号。在数轴上表示解集时，空心圆表示严格不等，实心圆表示包含边界。

Word problems require you to translate real situations into algebraic statements. ‘Three more than twice a number is eleven’ becomes 2x + 3 = 11. Learning to formulate equations from written contexts is the first step toward mathematical modelling.

文字题要求你将实际情景转化为代数式。例如“一个数的两倍加三等于十一”表示为 2x + 3 = 11。学会从文字背景中建立方程是进行数学建模的第一步。

---

4. Graphs of Linear Functions | 一次函数图像

To draw the graph of y = 2x + 1, choose at least three x-values, calculate the corresponding y-values, plot the points, and join them with a straight line. Recognise that any equation of the form y = mx + c produces a straight line graph.

要画出 y = 2x + 1 的图像，至少选取三个 x 值，计算出对应的 y 值，描点并用直线连接。你需要识别出任何形如 y = mx + c 的方程都对应一条直线。

In the equation y = mx + c, m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis). A line with equation y = 3x – 2 has gradient 3 and crosses at -2. Parallel lines share the same gradient, and perpendicular lines have gradients that multiply to -1.

在 y = mx + c 中，m 表示斜率（倾斜程度），c 表示 y 轴截距（与 y 轴的交点）。y = 3x – 2 所表示的直线斜率为 3，交 y 轴于点 -2。平行直线斜率相同，而垂直直线的斜率乘积为 -1。

Graphs can be used to solve problems: the intersection of two lines gives the solution to a pair of simultaneous linear equations. You can also solve an equation like 3x – 4 = 2 by graphing y = 3x – 4 and y = 2 on the same axes and reading the x-coordinate of the intersection.

图像可用于解决问题：两条直线的交点即为联立一次方程组的解。你也可以通过在同一直角坐标系中画出 y = 3x – 4 和 y = 2，并读取交点横坐标，来求解 3x – 4 = 2 这样的方程。

---

5. Ratio, Proportion and Percentages | 比、比例与百分比

Simplify ratios such as 24:36 by dividing both numbers by their common factor 12, giving 2:3. When sharing £120 in the ratio 3:5, the total number of parts is 8, so each part is £15; the shares are £45 and £75.

化简比例如 24:36，两边同除以公因数 12 得到 2:3。按 3:5 的比例分配 £120 时，总份数为 8，每份 £15，因此两份为 £45 和 £75。

Understand direct proportion (y = kx) and inverse proportion (y = k/x). Identify proportionality from tables of values—in direct proportion the ratio y/x is constant, while in inverse proportion the product xy is constant. Use given data to find the constant k and solve unknown values.

理解正比例（y = kx）和反比例（y = k/x）。通过数值表识别比例关系——正比例中 y/x 比值恒定，反比例中乘积 xy 恒定。利用给定数据求出常数 k，进而求解未知数。

Percentage change is a core life skill. To increase by 15%, multiply by 1.15; to decrease by 20%, multiply by 0.8. For reverse percentage problems, if a price including 20% VAT is £240, the original price is £240 ÷ 1.2 = £200. These techniques appear in finance, shopping, and science.

百分比变化是一项核心生活技能。增加 15% 即乘以 1.15；减少 20% 则乘以 0.8。对于反推百分比问题

Published by TutorHao | Year 10 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）