7.袋中有12個白球、8 個紅球，每次隨機抽取1球，取後不放回，直到所有球取完為止。求取球過 程中至少有一次遇到取得之白球、紅球個數相等之機率為__________

8.如圖，於△ABC 中，P、Q 為 的三等分點(即 == )，且 D 為的中點，若 與 、 分別相交於 E、F，則=__________

9.設甲袋中有2白球，乙袋中有3紅球，今每次自各袋中隨機取一球作交換，趨於穩定時，甲袋中 有1白球1紅球之機率為________

二、計算題（每題 8 分，共 24 分） 1.設方程式之三根為α 、β 、 γ，試求以 、 、 為三根之三次方程 式。

2.將偶數數列 排列為以下陣列，第i列第 j 行為a ij  ,例如，  a32=  18，試求一般項 αij

3.如圖，有一個底半徑為 5 公分的圓柱體，被一個通過直徑 AB 且與底面夾45° 角的平面所截，試 求所截出的立體體積。

Part 4 Short essay writing 20% Some people argue that studying in a foreign country has many advantages; others think that the disadvantages outweigh the advantages and argue students should stay in their own country to study. Briefly consider both sides of the issue and state which position you support. Give examples to support your arguments.

III: Short essay writing: 1. The following passage is taken from a famous commencement speech. Based on the passage, please discuss: what advice does the speaker try to share with us and what does this passage mean to you? “Climb the mountain not to plant your flag, but to embrace the challenge, enjoy the air and behold the view. Climb it so you can see the world, not so the world can see you. Go to Paris to be in Paris, not to cross it off your list and congratulate yourself for being worldly.”

2. Internationally, people are voicing concern over environmental issues, like air and water pollution, the depletion of natural resources, and the extinction or endangerment of many plant and animal species. Please explain how an individual can alter his or her living habits to protect the environment. Give specific details and examples to support your explanation.

1. What is molar concentration of K+ in a solution that contains 63.3 ppm of K3Fe(CN)6(329.3 g/mol)?(4%)

2. What concentration of sodium chloride in water is needed to produce an aqueous solution isotonic with blood (II=7.70 atm at 25℃)(4%)

115年 - 115 國立高科實驗高級中等學校_專任教師甄選_國中部︰數學領域數學專長#138920

114年 - 114-1 臺北市立松山高級商業家事職業學校_教師甄選題目：數學#138394

114年 - 114 新北市立國民中學_教師聯合甄選試題： 數學科#127346

114年 - 114 國立臺灣藝術大學_綜合學科測驗﹕數學#126930

114年 - 114 國立彰化高級中學_教師甄選初試試題：數學科#126821

114年 - 114 臺北市立陽明高級中學_正式教師甄選試題：高中數學科#126749

114年 - 114 國立師大附中_教師甄選︰數學#126229

113年 - 113 金門縣國民中學正式教師聯合甄選初試試題：數學#120861

113年 - 113 新北市公立高級中等學校教師聯合甄選試題：數學#120730

113年 - 113 桃園市國民中學新進教師甄選試題：數學科#120523