A Collection of Applets
by Sione Palu

Teacher Exchange || Math Tools

Important note to the user:

The following applets require a Java plug-in to be able to run. Follow the links provided for each applet and then click on one. If your computer is detected to have no Java plug in, you will be prompted to download it from Sun Microsystems. Once you have the Java plug-in installed, you will be able to view the applets. Also note that some applets may take a while to load, so please be patient.

Teachers:

If you have any topic(s) in maths that you would like to see an applet available here, you are welcome to suggest the topic by sending me, Sione Palu, an email message. If I can develop it, I will send an email notification when it is available here or if I cannot develop it, I will let you know that it isn't possible.

Background information:

Sione Palu is originally from Tonga but now lives in Ponsonby, Auckland, New Zealand....read more >>

Polynomial Roots Applet

This applet solves only the real roots of polynomial equations up to a maximum of order five. Complex number solutions are not available, however it can be included in the future if users request such features.

y = ax⁵ + bx⁴ + c x³ + d x² + e x + f

The user can supply the coefficients (a, b, c, d, e, and f) of the polynomial through text boxes.

Frequency Distribution Applet

The applet calculates the event space of throwing six-sided dice and tossing coins. The user can select any number of dice up to a maximum of 4 and similarly any number of coins up to a maximum of 10. All the possible outcome of coins landing with the number of "Tails" facing up and all the possible outcome of the sums of the dice face-value are calculated and their frequency distributions are plotted.

Completing The Square Applet

The applet completes the square for quadratic equations. Currently, only quadratic equations where the coefficients of the square term is positive one (+1) or minus one (-1).

y = x² + bx + c      OR      y = -x² + bx + c

The user types in the values for parameter b and c into text boxes. Fractional values are not available, but will be implemented in the future.

Poly Fit Applet

This applet fits the best polynomial of a specified order to the data supplied by the user (least squares method). The maximum allowable polynomial order to be specified is 10 if the number of points (data pair) supplied is 12 or more. If the number of data pair supplied is less than 12, then the maximum order would be (p - 2) where p is the number of points (data pair). If 4 points are supplied then the maximum order would be (4 - 2) which is 2. An example of fitting the user data to a polynomial of order 3.

y = ax³ + bx² + cx + d

The applet calculates the coefficients a, b, c,and d of a third order polynomial that closely matches (approximates) or fit the user supplied data pairs. The error estimates at each point are also calculated. The user can interpolate or extrapolate any points according to the best fit polynomial by specifying any values for "x" in a text box. The simplest polynomial fitting is the order one which is the linear regression:

y = ax + b

Statistical Analysis Applet

The user supplies data (positive only) and the applet calculates most of the common "descriptive" statistics parameters such as mean, variance, standard deviation, median, mode, upper and lower quartiles, range, kurtosis and skew. Robust statistical analysis such as percentile, moment, trim mean and outliers are also calculated. The applet has also made available to automatically plot user data in frequency, cumulative frequency, percentage cumulative frequency, probability and cumulative probability.

Number Works Applet

This applet calculates numbers, such as prime numbers, prime factors, least common multiple (LCM), greatest common divisor (GCD) or also called highest common factor (HCF), ratio simplifications. The applet is suitable for junior high school mathematics.

Polynomial Differentiation Applet

The applet calculates the first derivative and second derivative of a polynomial supplied by the user. The maximum order available is 5 and the minimum allowable polynomial order is 2.

y = ax⁵ + bx⁴ + c x³ + d x² + e x + f

The user enter the coefficients (a, b, c, d, e, and f) of the polynomial through text boxes. Fractional number coefficients such as 2/3 or -7/5 are allowed but not numbers which involves decimals such as -2.4 or 7.8 etc. The applet also calculates the stationary points, region of function increase or decrease, concavity change over points (also called points of inflection) and regions of function concavity. Function evaluations of the polynomial together with its first derivative and second derivative can be done by specifying a value for "x" . The equations of the tangent and normal at this user specified value for "x" are also calculated.

Complex Numbers Applet

This applet does symbolic calculation of complex numbers. This means that you can enter integers and fractions for the component values of a complex number (real and imaginary). Values with numbers that involve decimals such as 2.7 or -1.8 are not allowed to be entered. This applet uses pretty math printing (TEX notation) which is unusual to print numbers with decimals as pretty math. Options for complex number calculations are:

• Drawing the coordinates of a complex number and its conjugates in the complex plane.
• Additions and subtractions of complex numbers.
• Calculation of the modulus and argument of a complex number.
• Multiplications and divisions of complex numbers.
• Complex numbers raised to the power of integers.
• Finding all the principal roots (nth roots) of a complex numbers.

The applet is suitable for senior high school mathematics. It can also be used for fraction calculations such as additions, subtractions, multiplications and divisions in junior high school mathematics lessons although not highly recommended. If the applet is used for fraction operations, then all imaginary parts of any complex number have to be set to zero, eg: Z1 = 2/3 + 0*J , Z2 = -1/2 + 0*J , where Z = Z1 + Z2 = 7/6 + 0*J

Send comments to: Sione Palu - sionep@xtra.co.nz