数学绘本
第一册
Table of Contents
- 小六
- Fraction Addition
- 初一
- 11 Nets of the Cube
- 初二
- 八年级 十字架
- 勾股圆方图
- 几何第9题
- 点阵
- 多项式乘多项式
- 一线三等角
- 圆转动模型
- 模板
- 王福生模板
- 剪纸
- 模板
- 模框
- 正方体展开图
- 两圆之间的位置关系(王福生)
- 多项式乘多项式（王福生）
- 平方差
- 初三
- Circle Terminology
- 高一
- Sections of Cylinders
- 高二
- Exponential Functions: Graphs
- 高三
- Derivative of Sine & Cosine Functions (Quick Investigation)
Fraction Addition
Acknowledgement: Inspired by John Ulbright's applet "Adding Fractions - Visual" ([url=https://ggbm.at/szwBQ7wa]https://ggbm.at/szwBQ7wa[/url])
11 Nets of the Cube
八年级 十字架
Circle Terminology
[color=#000000]There are many vocabulary terms we use when talking about a circle. [br]The following app was designed to help you clearly see and interact with each term. [br][br]Explore this app for a few minutes. Then answer the questions that follow. [/color]
Note: LARGE POINTS are moveable.
How would you describe or define a [b]CIRCLE[/b] as a locus (set of points that meets specified criteria)?
How would you describe the term [b][color=#38761d]RADIUS[/color] [/b][i]without using the words "half" or "diameter" [/i]in your description?
What does the term [b][color=#9900ff]CHORD[/color] [/b]mean here in the context of a circle?
How would you describe the term [b][color=#ff7700]DIAMETER[/color] [/b][i]without using the words "two", "double", or "diameter" [/i]in your description?
How would you describe/define the term [b][color=#cc0000]SECANT[/color][/b]?
What does it mean for a line to be [b][color=#1e84cc]TANGENT [/color][/b]to a circle?
Sections of Cylinders
Drag the blue points to see the different sections of the cylinder.
Anthony Or. GeoGebra Institute of Hong Kong
Exponential Functions: Graphs
The following applet displays the graph of the exponential function [math]f\left(x\right)=c\cdot a^{kx}+d[/math]. [br]Interact with the applet below for a few minutes, then answer the questions that follow.
[b][color=#000000]Questions:[/color][/b][br][br][color=#000000]1) How does the parameter [/color][color=#cc0000][b]a[/b][/color] [color=#000000]affect the graph of the exponential function? Explain. [br] What happens if [/color][color=#cc0000][b]a > 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? What happens if [/color][color=#cc0000][b]a < 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? [br][br][/color][color=#000000]2) How does the parameter [/color][b][color=#1e84cc]k[/color][/b][color=#000000] affect the graph? Explain. [br] If you need a hint, refer back to [url=https://www.geogebra.org/m/HJvZSUna]this worksheet[/url]. [br][br][/color][color=#000000]3) What does the parameter [/color][color=#980000][b]d[/b][/color][color=#000000] do the graph? Explain. [br][br][/color][color=#000000]4) Suppose [/color][color=#cc0000][b]a < 1[/b][/color][color=#000000]. [br] Given this constraint, is it possible to get the graph of this exponential function to look the way it does[br] when [/color][color=#cc0000][b]a > 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? Explain. [/color]
Derivative of Sine & Cosine Functions (Quick Investigation)
In the applets below, graphs of the functions [math]f\left(x\right)=sin\left(x\right)[/math] and [math]f\left(x\right)=cos\left(x\right)[/math] are shown. [br]In each applet, drag the BIG WHITE POINT along the graph of the displayed function. [br][br]The y-coordinate of the point being traced out = the slope of the tangent line to the graph of f. [br]Interact with each applet for a few minutes, then answer the questions that follow.
1)
Based on your observations, if [math]f\left(x\right)=sin\left(x\right)[/math], can you write an expression for [math]f'\left(x\right)[/math]?
2)
Based on your observations, if [math]f\left(x\right)=cos\left(x\right)[/math], can you write an expression for [math]f'\left(x\right)[/math]?
3)
Use the limit-definition of a derivative to prove that if [math]f\left(x\right)=sin\left(x\right)[/math], then [math]f'\left(x\right)=cos\left(x\right)[/math].
4)
Use the limit-definition of a derivative to prove that if [math]f\left(x\right)=cos\left(x\right)[/math], then [math]f'\left(x\right)=-sin\left(x\right)[/math].