<p>In this task students will use simple and compound interest calculations to investigate the investment and borrowing options for purchasing a covered veranda to provide shelter for students at school in hot or wet weather.</p> <p>The task aligns with the Year 9 Australian Curriculum for mathematics, providing students with the opportunity to Solve problems involving simple interest (ACMNA211).</p>

<p>Linear Relations assignment covering distance between points, gradient, equation of lines, graphing and solving of simultaneous equations.<br /> Students generate four random points and a horizontal line using a supplied Excel spreadsheet. These four points are then used to carry out a series of calculations. Firstly, students calculate the distance between points, giving their answers in exact surd form and a decimal approximation. Next students determine the equation of three lines passing through the points, by calculating the slope and the value of the y-intercept. These equations are then converted into general form. Students then determine the axis intercepts for the three lines. Using all of the information, the three lines are graphed. Finally, simultaneous equation techniques are used to find the points at which the lines intersect.</p> <p>The package includes a solution checker, written in Geogebra, that teachers can use to check the correctness of individual solutions.</p>

<p>Students use two-dimensional vectors to model the movements of ships, missiles and asteroids as seen in the classic Asteroids video game.</p> <p>Asteroids is a classic video game from the late 1970s that requires players to manoeuvre their way through an asteroid storm, whilst destroying the asteroids with missiles.</p> <p>To move their rocket ship, players can apply forward or reverse thrust, however the velocity from the thrust is added to any existing velocity to determine the new velocity. In effect the movement of the rocket can be determined using vector operations.</p>

<p>This task uses counting, probability and discrete random variables techniques to investigate the underlying mathematics of poker machines.</p> <p>Students will use simulation software written in Python to design, develop and analyse a poker machine game with a variety of winning outcomes. Counting and combinatorics are used to analyse their design to ensure that it satisfies the expected “Return to Player” requirements.</p> <p>Once they have designed their game, students will modify the simulation software so that it correctly models their game. The simulation code is then run, with students recording and analysing the outcomes over a number of trials, with each trial consisting of a fixed number of games.</p> <p>Through mathematical analysis, the investigation will highlight that players, will in the long run lose, and indeed the more they play, the more they will lose.</p> Teacher Instructions <p>This task consists of the following files:</p> <ul> <li>Counting-Investigation.docx containing the task description, as given to the students</li> <li>Simulators.zip contains the simulator code to be given to students, together with example solution code files for the teacher’s use, consisting of: <ul> <li>pokie_simulator_studentversion.py the file to be given to students</li> <li>pokie_simulator_soln_part1.py sample solution for steps 1 and 2 of the task</li> <li>pokie_simulator_part2_sample1.py sample solution for steps 3 and 4 of the task</li> <li>pokie_simulator_part2_sample2.py sample solution for steps 3 and 4 of the task</li> <li>pokie_simulator_stats samples solution for steps 1 and 2 that includes statistical analysis of the results using the Statistics package</li> <li>pokie_simulator_bust a modified version of the code that analyses how many games need to be played before the player goes bust</li> </ul> </li> <li>Setup-Instructions.pdf contains instructions for setting up Python and getting the simulator working</li> </ul>

<p>In this investigation, students will use Geogebra and Python to explore triangle similarity and trigonometric ratios.</p> <p>Students begin by using enlargement transformations in Geogebra to explore properties relating to angles, side lengths, ratios between sides, and area of an enlarged triangles in comparison to the original triangle.</p> <p>Next, students create a right angle triangle together with enlargements of this triangle, and investigate the ratio between sides in the triangles, leading to the introduction of the three trigonometric ratios of sine, cosine and tangent.</p> <p>As an extension, students can also write, use or adapt code that calculates trigonometric ratios for sine and cosine for a given angle. Students are introduced to sine and cosine series expansions and given guidance on how to implement these expansions by writing code in Python.</p> Teacher Instructions <p>This resource consists of the following files</p> <ul> <li>Trigonometry-investigation.docx task sheet for students. Can be modified to add or remove sections</li> <li>Trigonometry-investigation.pdf copy of task sheet as pdf file.</li> <li>sine_series.zip contains a Python code file for calculating trigonometric ratios using series expansions</li> <li>Setup-Instructions.docx instructions for setting up the Python code. Only required in students do step 3.</li> </ul>