I have in the following posts been trying to find some of the things, that you can use CAS in GeoGebra to. There are of course several other uses, such as Binominal examination, Statistics , Chi ² test, Solution af differential equations m.fl.

CAS is an acronym for Computer Algebra System. In a broad terms this is about, that you can use the computer to calculate things, that you before would need for additional mathematical steps on. The computer uses a system to understand it, as you enter and then find a solution on the basis of the given rules.

In GeoGebra you can find CAS in the menu Show (from version 4.2).

Examples

Calculator

CAS-portion is in principle an advanced calculator. You can devote +,-,* and /, but also a lot of other funktioner. You can get the answer as integer / decimaltal using. or as exact calculation by using the. -button. Af second funktioner can devote their(), cos(), tan().

 

Commands on Danish:

Here is a link to an overview of the Danish commands, you can use the CAS portion.
http://wiki.geogebra.org/da/Kategori:CAS_kommandoer

Commands in English:

Here is a link to an overview of the Danish commands, you can use the CAS portion.
http://wiki.geogebra.org/en/CAS_Specific_Commands

 

Equation Solving – Traditional, simple

You can get GeoGebra to find the solution of your equation by doing the following;

1. Try to enter the equation 5x 3 = 2x 12 i CAS. (Do not press Enter!!)
2. Either press the button (Calculate) or the button (Solve numeric).
3. Now you have the solution to the equation.

 

Equation Solving – As you think it!

The good thing in CAS is, that you can write the expression, as you think it and without having to rewrite.

For example,:
Peter has 25 kr. and would like to buy a toy for 39 kr. How much money does he needing, before he can buy the toy?

1. Write 25 + ? = 39 and press the button (Calculate) or the button (Solve numeric).
2. Now you've got the answer.
   The good thing about this method is, to many kids still not thinking, that the task is a subtraction task (39-25 = 14), but often think, what should I put to 25 to 39. This way of thinking they can now use using. CAS.

 

Equation Solving – Solving equations with 2 or more unknowns

CAS portion also has an option to calculate the solution to the equations with 2 or more unknowns. If for example, we have the following 2 equations with 2 unknowns x and y.

1. x y = 3
2. 4x 3 y = 1

So there is a solution by done so:

1. Type the following Calculate[{x y = 3, 4x 3 y = 1},{x,y}]
2. Press Enter på tastaturet.

 

If there are, for example is 3 unknowns x,y and z, so they must be printed between {}. Ie. {x,y,z}.

 

Using Variables

You can decide, that a variable must be equal to a given expression:

Write for example, the formula for calculating the area of ​​a triangle

1. Write area:= 0.5 * h * G and press Enter
2. Write h:= 2 and pres Enter
3. Write G:= 4 and pres Enter
4. Write area and then press -button.
5. Now you can now simply change eg h:= 3, write area and press -button. It will change the area.

 

To isolate a variable or rewrite the formulas

You can isolate a variable or rewrite a formula by using the function. Sometimes, you typically have the area of ​​a triangle and be the baseline, but lack height. Let's say, the area is 14 and the baseline is 4. It writes therefore into the formula A = 0.5 * h * G.

1. Write 14= 0.5 * h * 4 and then press -button.
2. Now you've got the height.

 

Fraction calculations

You can using. CAS also make computing fractions.

\[\frac{2}{3} + \frac{4}{5}\]

1. Write the equation above by typing 2/3+4/5 and use the button (Calculate).
2. (Button Printer facit as a fraction, while the button write upshot as a decimal or integer.)

Find the lowest common denominator in command Common Denominator[ <expression>, <expression> ]. For example if you need to find the common denominator of the 2 fractions \[\frac{2}{3} and frac{4}{5}\].

1. Write Common Denominator[ 2/3 , 4/5 ] and the pres -button.

 

Factorization

You can use Geogebra to rationalize the equations. Find example, square phrases m.m.

1. For instance try to enter the equation x ^ 2 + x – 6 i CAS. (Do not press Enter!!)
2. Either press the button -button (Factor).
3. Now you factorization (x + 3) (x – 2).

 

Led

You can use GeoGebra to calculate eg square sentences, as \[(2x ^ 2 3)^2]

1. Write (2x ^ 2 3)^ 2) and the pres -button.

 

Prime and Prime Factors

GeoGebra has a few options, when it comes to prime. You can for example find

Next Prime[<numbers>]
Previous Prime[<numbers>]
Prime Factors[ <numbers> ]
ErPrimtal[ <numbers> ]

 

Funktioner

You can also leave CAS drawing functions. All you have to do to get it to work is, you must a colon (:) before the equal sign operational regulation.

1. Write f(x):= 2x 4 and pres Enter.
2. Write g(x):= 3x 1 and pres Enter.
3. Write f = g and the pres -button.Now you have found the intersection of the 2 graphs and the solution to the equation 2x 4 = 3x 1

 

Try the following commands:
TilfældigPolynomium[ <Grade>, <Minimum Coefficients>, <Maximum of Coefficients> ]

 

Funktioner – Enhanced

You can also work with functions in a little more expanded scope. First you have to assign for example the function f(x) a general regulatory. It could be a quadratic function. So it will have regulation \[f(x)=ax^2 bx c].

You must assign f(x) this regulatory. Therefore, you must use a colon in front of the = sign. Also remember once drawn between ax and bx. Therefore,:

1. Write f(x):= A * x ^ 2 b * x c
   
2. Press Enter.
3. Write Calculate[{f(1)= 0, f(3)= 0, f(0)= 3},{a,b,c}]
4. Press Enter.

This way you have been, what a,b,c values ​​that fit with the function must go through (1,0), (3,0) and (0,3).

 

Reduction

It is also possible to work with reduction. You write simply the arithmetic, to be reduced. See the examples in the image below.