1. 已知a為二次方程式3x²-2x-663=0的一個解，試求的值。

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33. The article below describes the ionic compound and its properties. Read the article and underline some key words of the properties. In an ionic compound, the ions are packed together in a regular arrangement called a lattice. Within the lattice, oppositely charged ions attract one another strongly. The Figure below shows a tiny part of the crystal of sodium chloride. Many trillions of sodium ions and chloride ions would be arranged in this way in the crystal make up the giant ionic structure. Each sodium ion in the lattice is surrounded by six chloride ions, and each chloride ion is surrounded by six sodium ions. Due to the strong electrostatic forces holding the crystal lattice together, a lot of energy is needed to separate the ions. There ionic compounds have the following properties. ● They are usually solids at room temperature, with high melting points  ● They are usually hard substances but brittle due to lack of ductility, see figure below.   ● They cannot conduct electricity when solid, because the ions are not free to move it the solid state. However, in the molten state and in aqueous solution, they conduct electricity. ● They mainly dissolve in water. This is because water molecules are able to bond with both the cations and anions, which breaks up he lattice and keeps the ions apart. 33a. According to the article of the ionic compound and its properties, finish the cross-words puzzle. [8 marks]

2. 設 x ＞ 0，且，試求的值。

3. 已知實數 a,b,c 滿足 a ≥ 0，b ≥ 1，c ≥ -1 以及 a+4b + c + 3 =，試求 a+b+c的值。

4. 數學中有個基本概念稱作「集合」，是一個收集特定元素所形成的物件。例如，A = {1,2,3}這個集合收集了1,2,3這三個正整數，又可以說1,2,3這三個元素「屬於」集合A。此外，如果集合B的所有元素也都屬於集合A，則說集合B是集合A的「子集」。例如，B1={1,2}，B2={3,2}都是集合A = {1,2,3}的子集。 根據上述語言，如果集合U= {1,2,3,...... ,2023}，且集合M 是滿足「只要n屬於M，17n便不屬於M的所有U的子集中擁有最多元素的一個，試問集合M的元素個數有多少個？

5. 有一個填符號遊戲，只要在最下層的O中填入符號「+」或「-」，則上層中所有的O就會自動顯示符號「+」 或「-」其中之一。規則如下：(1) 若相鄰的兩個O中符號相同，則上面的O顯示「+」，如圖一所示(2) 若相鄰的兩個O中符號不同，則上面的O顯示「-」，如圖二所示在圖三中，若要使得最上層的O中顯示「+」，則最下層有多少種填法？

6. 將正整數1,2,3,4,5,6,7,8,9,10,…依下列規則排列，若將橫排稱為列，直排稱為行，我們可以用列與行來描述某個正整數的位置。例如：第2列第3行的數字為9。若2023在第m列第n行，試求數對（m,n）。

7. 如右圖，以為直徑作半圓，O為圓心，C為中點。為圓O的切線，，若D為此半圓上的一點且，試求的長。