1选择题
The population of our city is about 2,600,000. Which of the following shows this number in scientific notation?
- A. 2.6×10⁶
- B. 26×10⁵
- C. 0.26×10⁷
- D. 2.6×10⁷
答案：A
解析：科学记数法的表示形式为a×10ⁿ，其中1≤|a|<10，n为整数。2,600,000用科学记数法表示为2.6×10⁶。易错点：选项B和C的a值不在1到10之间，选项D的指数错误。
2选择题
—What's the opposite of the number -5? —It's ______.
答案：A
解析：相反数的定义：只有符号不同的两个数互为相反数。-5的相反数是5。易错点：混淆相反数与倒数的概念，误选C或D。
3填空题
The absolute value of (1 - √3) is ______.
答案：√3 - 1
解析：计算绝对值时，需要先判断绝对值符号内数的正负。因为√3≈1.732，所以1-√3<0。根据绝对值性质，负数的绝对值等于它的相反数，因此|1-√3| = √3 - 1。易错点：忘记判断正负，直接写成1-√3。
4填空题
If the square root of a number is 4, then the number is ______.
答案：16
解析：根据平方根的定义，如果√x = 4，那么x = 4² = 16。易错点：可能误答为±4，但题目问的是“the number”，即被开方数本身。
5解答题
Solve the equation: 1/(x-1) = 2/(x+1).
答案：解：方程两边同时乘以最简公分母 (x-1)(x+1)，得：
1·(x+1) = 2·(x-1)
x + 1 = 2x - 2
移项，得：x - 2x = -2 - 1
合并同类项，得：-x = -3
系数化为1，得：x = 3
检验：当x=3时，(x-1)(x+1) = (3-1)(3+1) = 2×4 = 8 ≠ 0
所以，原方程的解是 x = 3。
解析：解分式方程的关键步骤是去分母和验根。易错点：1）去分母时，漏乘不含分母的项；2）解完后忘记检验，可能导致将增根（使分母为零的解）当作原方程的解。
6解答题
Simplify the expression: 3a²b - 2ab² + 5a²b - ab².
答案：解：原式 = (3a²b + 5a²b) + (-2ab² - ab²)
= (3+5)a²b + (-2-1)ab²
= 8a²b - 3ab²。
解析：本题考查整式的加减运算，即合并同类项。关键在于正确识别同类项（所含字母相同，并且相同字母的指数也分别相同的项）。易错点：1）将不同类项错误合并；2）合并时符号出错。
7阅读理解题
Read the following passage and answer the question.
Many students find math difficult because they don't practice enough. However, some students believe that understanding the basic concepts is more important than doing many exercises. They think if you truly understand a formula, you can solve various problems with it. Others disagree, saying that practice helps you remember the steps and avoid mistakes. What do you think is more important for learning math well: understanding concepts or practicing exercises?
答案：Open-ended. A possible answer could be: I think both are important. Understanding concepts helps you know why you are doing something, while practicing helps you do it correctly and quickly. You need to understand the 'why' and practice the 'how'.
解析：本题为开放性阅读理解题，考查学生对文本信息的理解和观点表达能力。回答时应结合文中提到的两种观点，并清晰地陈述自己的看法。易错点：完全脱离文本内容进行回答，或者观点表达不清。
8作文题
Write a short passage (about 80 words) about your study plan for the coming math exam. You should include: 1) What topics you need to review. 2) How you plan to study them. 3) What your goal is.
答案：Sample:
For the coming math exam, I need to review several important topics. First, I will go over the rules for operations with real numbers, especially scientific notation and absolute value. Second, I will practice simplifying expressions by combining like terms. Third, I will solve more equations, especially fractional equations, and remember to check for extraneous solutions. I plan to study by doing exercises every day and asking my teacher for help when I have problems. My goal is to get a high score and build a solid foundation for high school.
解析：本题考查学生运用英语进行计划描述的能力。写作时需注意：1）内容完整，覆盖题目要求的三个方面；2）语言表达清晰、准确，使用恰当的连接词；3）注意书写规范。易错点：遗漏要点，语法错误，或者内容过于简单空洞。