Year 9 OCR Mathematics: Interdisciplinary Problem-Solving Practice | Year 9 OCR 数学：跨学科综合题型训练

📚 Year 9 OCR Mathematics: Interdisciplinary Problem-Solving Practice | Year 9 OCR 数学：跨学科综合题型训练

Year 9 OCR maths tests your ability to apply number, algebra, ratio, geometry and statistics in unfamiliar contexts drawn from science, geography, economics and everyday life. These cross-curricular problems reward careful reading and logical reasoning, not just quick arithmetic.

九年级 OCR 数学考查你将数、代数、比例、几何和统计应用于科学、地理、经济和日常生活等陌生情境的能力。这些跨学科题目考察的不仅是快速运算，更是仔细的审题和逻辑推理。

---

1. What Are Interdisciplinary Problems? | 什么是跨学科问题？

An interdisciplinary problem weaves together a maths skill and a real-world context. You might calculate the speed of a falling object (physics), mix a chemical solution (chemistry), or analyse population growth (geography). Your job is to identify the numbers, decide which maths tool to use, and then interpret the answer in context.

跨学科问题将数学技能与现实情境交织在一起。你可能要计算下落物体的速度（物理）、配制化学溶液（化学）或分析人口增长（地理）。你的任务是识别数据，选择合适的数学工具，并在情境中解释答案。

Typical formats include word problems, data tables, graphs and diagrams. OCR expects you to show clear working, use correct units and check whether your final answer makes sense in the given situation.

常见题型包括文字题、数据表格、图表和示意图。OCR 期望你展示清晰的解题步骤，使用正确的单位，并检查最终答案在所给情境中是否合理。

---

2. Speed, Distance and Time in Physics | 物理中的速度、距离与时间

The core relationship is distance = speed × time (d = s × t). When a train travels at 80 km/h for 2.5 hours, the distance covered is 80 × 2.5 = 200 km. Always confirm that the time unit matches the unit in the speed — hours paired with km/h, seconds with m/s.

核心关系是 距离 = 速度 × 时间（d = s × t）。当一列火车以 80 km/h 行驶 2.5 小时，行驶距离为 80 × 2.5 = 200 km。请始终确保时间单位与速度单位匹配——小时对应 km/h，秒对应 m/s。

Unit conversion frequently appears: 1 m/s = 3.6 km/h. To change km/h into m/s, divide by 3.6. For instance, 90 km/h ÷ 3.6 = 25 m/s. If an athletics track is 400 m and a runner completes it in 50 s, the average speed is 400 ÷ 50 = 8 m/s, or 8 × 3.6 = 28.8 km/h.

单位换算经常出现：1 m/s = 3.6 km/h。要将 km/h 转换为 m/s，除以 3.6。例如 90 km/h ÷ 3.6 = 25 m/s。若田径跑道一圈 400 m，一名跑者用 50 s 完成，平均速度为 400 ÷ 50 = 8 m/s，即 8 × 3.6 = 28.8 km/h。

Speed in km/h	Speed in m/s (÷3.6)
36	10
72	20
108	30

In an OCR problem, you may need to combine this with a graph showing distance over time. The gradient of a straight line on a distance–time graph equals the speed — a steep line means a faster journey.

在 OCR 题目中，你可能需要结合距离-时间图。距离-时间图上直线的斜率就是速度——直线越陡，速度越快。

---

3. Mixing Ratios in Chemistry and Cookery | 化学与烹饪中的混合比例

Ratios describe how parts of a mixture relate to one another. A disinfectant might be mixed from concentrate and water in the ratio 1 : 4, meaning one part concentrate to four parts water, giving five parts total.

比例描述混合物中各部分之间的关系。消毒剂可能由浓缩液与水按 1 : 4 的比例混合，即一份浓缩液兑四份水，共五份。

To scale up a recipe: if 400 ml of solution is needed, find the size of one part first. Total parts = 1 + 4 = 5, so 1 part = 400 ÷ 5 = 80 ml. Concentrate = 1 × 80 = 80 ml, water = 4 × 80 = 320 ml.

若要按比例放大配方：需要 400 ml 溶液，先求一份的大小。总份数 = 1 + 4 = 5，因此 1 份 = 400 ÷ 5 = 80 ml。浓缩液 = 1 × 80 = 80 ml，水 = 4 × 80 = 320 ml。

Cement, sand and gravel might be mixed in the ratio 1 : 2 : 3 for concrete. If you have 120 kg of gravel, the multiplier from 3 parts to 120 kg is ×40. Cement = 1 × 40 = 40 kg, sand = 2 × 40 = 80 kg. Always check that the sum of the individual masses equals the required total when appropriate.

制作混凝土的水泥、沙子和碎石可能按 1 : 2 : 3 的比例混合。如果有 120 kg 碎石，从 3 份到 120 kg 的倍数是 ×40。水泥 = 1 × 40 = 40 kg，沙子 = 2 × 40 = 80 kg。适当情况下，检查各部分质量总和是否等于所需总量。

---

4. Interpreting Graphs in Geography and Biology | 地理与生物中的图表解读

Composite graphs like climate charts combine a line for temperature (°C) and bars for rainfall (mm) on the same axes. A typical question asks you to find the month with the highest rainfall or to calculate the temperature range (max minus min).

复合图表如气候图将气温（°C）的折线与降水量（mm）的柱状图结合在同一坐标轴上。一道典型题目会让你找出降水量最高的月份，或计算温度范围（最高减最低）。

Scatter graphs are widely used in population studies and biology to show relationships between two variables, such as height and weight. You must judge whether the correlation is positive, negative or zero. A line of best fit can be drawn to estimate one variable for a given value of the other.

散点图广泛用于人口研究和生物学中，以显示两个变量之间的关系，如身高和体重。你需要判断相关性是正、负还是零。可以绘制一条最佳拟合线，根据一个变量的给定值估计另一个变量。

When reading any graph, check the scale on each axis carefully — the gap between gridlines might represent 2, 5, 10 or even 100 units. Also note whether the axis starts at zero; a truncated axis can exaggerate changes, so always read the labels.

当读取任何图表时，仔细检查每个坐标轴的刻度——网格线之间的间隔可能代表 2、5、10 甚至 100 个单位。还要注意坐标轴是否从零开始；被截断的坐标轴可能夸大变化，因此务必阅读标签。

---

5. Financial Mathematics: Budgeting and Interest | 金融数学：预算与利息

Percentage calculations dominate financial maths. A shop offers 15% off a £45 jacket: the discount is 0.15 × 45 = £6.75, so the sale price is £38.25. Reverse percentages might ask for the original price before tax or discount.

财务数学主要围绕百分比计算。一件 £45 的夹克打八五折：折扣为 0.15 × 45 = £6.75，因此售价为 £38.25。逆向百分比题可能会问税前或折扣前的原价。

Simple interest formula: I = P × r × t, where P is the principal, r is the annual rate as a decimal, and t is the time in years. Compound interest for annual compounding uses A = P × (1 + r)ⁿ. For example, £800 invested at 3% compound interest for 4 years yields A = 800 × (1.03)⁴ ≈ £900.20.

单利公式：I = P × r × t，其中 P 为本金，r 为十进制年利率，t 为时间（年）。按年复利的复利使用 A = P × (1 + r)ⁿ。例如，£800 以 3% 的年复利投资 4 年，得到 A

Published by TutorHao | Year 9 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）