IGCSE OCR Maths: Practical Guide to Mathematical Experiments | IGCSE OCR 数学：实验操作指南

📚 IGCSE OCR Maths: Practical Guide to Mathematical Experiments | IGCSE OCR 数学：实验操作指南

Mathematics is often perceived as a purely theoretical subject, but many concepts can be explored through hands-on experiments and practical investigations. In the IGCSE OCR Mathematics course, developing a deeper understanding of topics such as functions, geometry, probability, and statistics often requires active engagement with tools like graphing calculators, compasses, and spreadsheets. This guide provides a series of practical experiments designed to reinforce key mathematical ideas and boost problem-solving skills in line with the OCR specification.

数学通常被视为纯理论学科，但许多概念可以通过动手实验和实际探究来探索。在 IGCSE OCR 数学课程中，要深入理解函数、几何、概率和统计等主题，往往需要积极使用图形计算器、圆规和电子表格等工具。本指南提供了一系列实验操作，旨在强化关键数学思想，并提升符合 OCR 规范的问题解决能力。

1. Graphing Functions with a Graphing Calculator | 使用图形计算器绘制函数图像

Graphing calculators are powerful tools for visualising functions and their transformations. By plotting linear, quadratic, and trigonometric functions, you can observe the effects of changing coefficients on the shape and position of graphs.

图形计算器是可视化函数及其变换的强大工具。通过绘制线性、二次和三角函数，你可以观察系数变化对图像形状和位置的影响。

Step 1: Switch on your calculator and press Y= to open the function editor.

步骤1：打开计算器，按下Y=键打开函数编辑器。

Step 2: Enter the function y = x² by typing X,T,θ,n followed by x².

步骤2：输入函数 y = x²，依次按下X,T,θ,n键和x²键。

Step 3: Press GRAPH to display the parabola. Adjust the window using WINDOW to set Xmin=-5, Xmax=5, Ymin=-2, Ymax=10.

步骤3：按下GRAPH显示抛物线。使用WINDOW调整窗口，设置 Xmin=-5, Xmax=5, Ymin=-2, Ymax=10。

Step 4: Add a second function y = (x-2)² and observe the horizontal shift. Compare the graphs side by side.

步骤4：添加第二个函数 y = (x-2)²，观察水平移动。将两个图像并排比较。

Step 5: Experiment with y = -x², y = x²+3, and other variations. Note how the coefficient ‘a’ in y = ax² affects the steepness and direction.

步骤5：尝试 y = -x²、y = x²+3 等变体。注意 y = ax² 中系数 a 如何影响陡峭度和方向。

This practical exploration deepens understanding of transformation rules: f(x)+k shifts vertically, f(x+h) shifts horizontally, and -f(x) reflects in the x-axis.

这一实践探索加深了对变换规则的理解：f(x)+k 垂直移动，f(x+h) 水平移动，-f(x) 关于 x 轴反射。

Transformation: y = af(b(x – h)) + k

2. Constructing Geometric Figures with Compass and Ruler | 尺规作图构建几何图形

Classical construction using a compass and straightedge is an excellent way to internalise properties of shapes and angles. You can construct perpendicular bisectors, angle bisectors, equilateral triangles, and more, directly linking geometry to logical reasoning.

使用圆规和直尺进行古典作图是内化图形和角度性质的绝佳方式。你可以构造垂直平分线、角平分线、等边三角形等，将几何与逻辑推理直接联系起来。

Experiment: Construct an equilateral triangle given a side length AB.

实验：给定边长 AB，构造等边三角形。

Step 1: Draw a line segment AB of length 6 cm with the ruler.

步骤1：用直尺画一条长 6 cm 的线段 AB。

Step 2: Set the compass width to AB. Place the compass point at A and draw an arc above the segment.

步骤2：将圆规宽度设为 AB。将圆规脚尖放在 A 点，在线段上方画一条弧。

Step 3: Without changing the compass width, place the point at B and draw another arc intersecting the first arc at point C.

步骤3：保持圆规宽度不变，将脚尖放在 B 点，画另一条弧与第一条弧相交于点 C。

Step 4: Connect A to C and B to C to complete the equilateral triangle. Verify that all sides are equal using the ruler.

步骤4：连接 A 到 C 和 B 到 C，完成等边三角形。用直尺验证所有边相等。

This construction demonstrates that the triangle is equilateral because AC = AB and BC = AB by the definition of a circle. Further tasks: construct bisectors and the circumcircle.

该作图表明三角形是等边的，因为根据圆的定义 AC = AB 且 BC = AB。进一步任务：构造

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