## Programs for Yr 12 Applicable Maths:

 Title Function Instructions Remarks (ax+b)^n To expand using Binomial Theorem the binomial (ax+b)^n, with a, b, n, being constants. You will be prompted for values of a, b, and n. The program will then display the expanded polynomial. The polynomial is stored in M1 in vector form. Binomial  Approximation This calculates a normal approximation to a large binomial distribution problem. You will be prompted for the number of Bernoulli trials, the probability of a positive outcome, whether the number of positive outcomes is <, >, <= or >= the given target, and the target (the given number of positive outcomes). Newton-Raphson  Aplet Uses the Newton-Raphson Method to find a root of an equation given a starting point. Run the aplet.  After the instruction message box, enter the equation in F1(X). If you wish, you may plot the equation at this stage.  Use VIEWS to select Solve Equation...  You will be prompted for an initial guess, and the aplet will iterate the equation until it either encounters a mathematical error, or the iteration converges on a root (to 8 decimal places), or 30 iterations are carried out without convergence.  If no errors are encountered, the aplet's NUM view will be displayed with all intermediate values of X. If the aplet encounters an error, the HOME screen will be displayed. Press NUM to view the iteration's progress up to the point of the error.  The four columns in NUM are as follows:   X:  The current guess   F1(X):  The function at the                  current guess   F2(x):  The derivitave of the                 equation at the                 current guess   F3(X):  The next guess  Press VIEWS and select New Function to enter another equation, or press SYMB to view the current equation, derivative, and next guess equation. Notes:  1. Unlike the rest of this collection, this IS an aplet and should be loaded from the LIB view. 2. I've also written a Newton-Raphson aplet. Mine is intended as a teaching tool and is very visual. Quin's is intended as a working tool. MakeTransMatrix Generates a transformation matrix given geometric transformations You will be prompted initially for the number of translations required. You can then select the translations, in the order  that they are applied, to be reflections, shears, rotations, or dilations (scaling operations). For each translation you  may be required to supply additional information. The resulting matrix is stored in M9. The 'Rotation' transformation  uses the current HOME angle setting FindTransMatrix Finds a transformation matrix given two points and their images. You will be prompted for a point, it's image, another point, and it's image. This is useful for questions like:    A(x1, y1)->A'(x2, y2)    B(x3, y3)->B'(x4, y4)  What matrix will transform A to A' and B to B'? Some point combinations cannot be described with a linear transformation matrix, and so this program cannot solve them.  The points are entered as complex numbers (x, y). The resulting matrix is stored in M3. ShowTransMatrix Demonstrates the effect of a translation matrix on a user-defined shape. The main menu consists of four options, Define Shape, Transform, Set Axes, and Exit.  Define Shape: This allows the user to define a shape to be drawn. By default this is a 2x2 square with vertices at (-1, -1), (1, -1), (1, 1), and (-1, 1).  Transform: This draw the axis and the initial shape. Press any key to continue. The shape is then drawn after the transformation has been applied, so the two shapes can be compared. Press any key to continue.  Set Axes: This allows the axis ranges to be changed from inside the program. This program calls another program 'DrawAxes', which MUST be on your calculator before running 'ShowTransMatrix'. Prob. from Z-Score Replace the "Cumulative Probabilities For The Normal Distribution" table in the SEA Tables Book. You will be prompted for a z-score, and the direction of the  area [P(Z<=z) or P(Z>=z)]. The program will display the  probability. This is covered in the Prob Distributions aplet in my collection. (CC) Z-score from Prob. Provide an inverse function for the 'Prob. from Z-score' program. You will be prompted for a probability (between 0 and 1). The area under the curve y=erf(X), representing this probability, can be to the left of the Z-score in question, to the right, or centered. The Z-score will then be displayed. Press any key. This is covered in the Prob Distributions aplet in my collection. (CC) Linear System Solver To solve an NxN system of linear equations You will be prompted for the number of variables. Then each equation is input in vector form.  For Example:  ax + by + ... = c  dx + ey + ... = f  etc...  is entered as  [a, b, ..., c] ENTER [d, e, ..., f] ENTER etc... ENTER The value of each variable is displayed, in the order used in the equations. In the example, the results would be x=, y=, etc.