The Online Course Management system was developed in 2012 by George Moon to address the issue of creating course books at Burnside High School in Christchurch, New Zealand. The course books are designed to inform students, staff and parents of the many courses that are available for students to choose for their next year of study. In the past, the system that the school used consisted of large amounts of paperwork and duplication. Not only did this system require a lot of effort from staff, but the course book cost the school thousands of dollars to produce, as it had to be sent off to be published into a large book that would be read by students for a week, then likely thrown out. This year the school decided to digitise the course book, so that students would look at their courses online. Earlier this year, the school believed that the new School Management System (SMS) ‘KAMAR’ would be able to handle all of the necessary information, however this was not the case. Because of this, they needed a simple solution that would collate all of the course data, and then output it as a course book. I developed my project to do this. It is a web based program that is accessible by staff on their computers which enables them to enter in all of the course and assessment data for their departments. As it is all securely stored on a central database, it reduces duplication and staff workload, as well as the added environmental bonus of less paper being used. The program also outputs data in a number of ways including as a coursebook PDF (digital document which can be uploaded or printed), an Excel spreadsheet and a webpage for easy viewing. It can be sorted or printed by different categories (such as level, faculty, department), which proved to be a very useful feature. Following some research on areas such as design principles, browser compatibility and screen resolution (computer screen size), the program was designed to make best use of this this information. For example, most of the computers that staff would access the website on were of a similar size screen, so I made sure that my website worked well for them. I also used my research on design principles to try and create a simple, clean interface that users with limited computer skills would easily be able to navigate around. The outcome was real, as it was used by the school to generate their coursebook this year. Following a 95% student completion rate of course selection many months earlier than previous years, the system (although it had some issues) was pronounced a success, and the school is looking to use it in the years to come. There are a number of steps I am looking to take in the future with this program including the potential sale to other schools, so they can take advantage of the features it has to offer.

如下圖所示，在一邊有6個圓圈的正三角形棋盤，將某個圓圈擺上皇后，此為皇后的根據地，箭號所指的三個與邊平行的方向，是皇后所能管轄的範圍，且兩個皇后不能互相管轄到對方的根據地，不是根據地的圓圈可以兩個皇后共管。我們的研究在討論一邊有n個圓圈的正三角形棋盤中使每個圓圈都被管轄到時，最少需要幾個皇后以及最多可放幾個皇后。為了解最少需要的皇后數，我們採用算術推理以及從三個方向(↘、↙、←)的考慮、由外而內的一整排來作邏輯上的推理得到了一邊有1~12個圓圈的正三角形棋盤的最少皇后數，並嘗試透過電腦程式的執行求出更大邊圓圈數棋盤的最少皇后數。最多皇后數部分，我們透過數學歸納法得到了所有邊數情況的最多皇后數。

在這充滿創新的時代，智慧型機械的發展顯的非常樂觀，也發展得非常快速。用電子結合機械可說是最佳搭檔，可以預料以後智慧型機械會越來越聰明，到那時家裡也不用請傭人，買個機器人就行了，工廠裡再也看不到搬運工及插零件的女工，都將被高效率的機器人帶替。 我們也熱愛於這方面的研究，經過多次製作，發展了第二部機械人，第一部無機械手臂，第二部增加了一支兩個自由度及自動尋找目標物的手臂，使得它更具有智慧。 在製作機械人上，最困難的就是感知器的製造，而我們依據最簡單的物理現象製造出交通號誌識別感知器，障礙物感知器等。當然這些感知器如何和它的頭腦——電腦連結也是一門學問，需要不斷地實驗改造，改造實驗，現在製造出來的智慧型機械人，雖然還沒有發揮到最理想，但是它是我們花費相當多的時間所造成出來的結晶。相信以後我們會再造出更理想的機械人。

一、參展作品的件數、深度、廣度，均有明顯的進展。 二、團隊的研究，包括教師適宜的指導，學生誠心的合作，更進步。 三、作品的展示及說明，比前精彩、生動、可愛。 四、各種新儀器乃至電腦的使用，已經相當普遍。 五、國際上重視的地科問題研究－如酸雨、溫室效應、地震等等，出現不少，頗順世界潮流。 六、有關鄉土作品，相當具有特色，符合教育課程目標。

液體中之球體運動與液體的黏滯性有關，本實驗找出球體半徑與終端速度之間的關係。利用攝錄機作為紀錄工具，拍攝三種材質（壓克力、玻璃、水晶）的球體在沙拉油中的自由落體過程。使用電腦影像處理軟體將影像分解成幅影像，時間的解析度為1/30秒。測量球體的高度與時間，分析高度與時間的變化情形，發現終端速度與球體半徑之間的關係。 流體中之運動方程Fdrag = -k1V，無法符合實驗結果。我們的實驗結果顯示油中的自由落體的運動方程應該是Fdrag = -（k1V+ k2V2）。由不同材質的壓克力球（~1.18g/cm3）、玻璃珠（~2.47g/cm3）與水晶球（~2.66g/cm3）所獲得的終端速度（Vt）與球體半徑（a）的關係為a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt） + 0.00575，其中ρ與ρ'分別為球體密度與沙拉油密度（0.90 g/cm3）。 再者，在相同半徑的條件下，密度越大的球體終端速度越大，在靜止下落後，越久達到終端速度。 The motion of a sphere which is falling through a fluid is subject to the fluid viscosity. In this study, we find out the relation between the radius of a sphere and the terminal velocity. We used a digital camera to record the sphere's descent in the oil. The three kinds of sphere we choose are acrylic（~1.18g/cm3）, glass （~2.47g/cm3）and crystal （~2.66g/cm3）. Frame-by-frame analysis of the video footage yielded rough estimates of the sphere's location within 1/30 seconds accuracy for statistically consistent results. By measuring the location and time and analyzing them, we find out the relation between the radius of a sphere and the terminal velocity. The expression of the drag force,Fdrag = -k1V, is not cosistent with our results. The study indicates the expression of the drag force should be Fdrag = -（k1V+ k2V2）. The expression for the terminal velocities of the three kinds of sphere is of the form：a3(ρ-ρ') = 0.00003（a Vt）2 + 0.00021（a Vt）+ 0.00575, where a is the radius, ρ is the sphere density and ρ' is the oil density（0.90 g/cm3）. In addition, if the radius is the same, the terminal velocity of a denser sphere is higher and the time to approches the terminal velocity is longer.

Gi(x)遊戲是指「將編號1,2,3,...,x號的同學圍成一圈，報數1,2,1,2,…，由1號開始報數，報數i的站著、報數3-i的蹲下」，其中i=1,2 。假設整個遊戲需要玩gi(x)輪，而最後站立者之編號為fi(x)，則經過我們仔細的觀察、歸納、研究與討論，得到以下的結果： 一. 設有 人參與1,2,1,2,…報數遊戲Gi(x)，其中i=1,2。 (1) 若3x2n-2≦x≦3x2n-1 (n=1,2,3,...)，則g1(x)=n。 (2) 若3x2n-2

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