《2025年假期面对面南方出版社七年级数学沪科版》

1. 下列变形错误的是 (B)
A. 若$m = n$,则$-3m = -3n$
B. 若$m = -n$,则$m + n = 1$
C. 若$m + 2 = n + 2$,则$m = n$
D. 若$-2x = 4$,则$x = -2$

答案： B

2. 下面四组数值中,是二元一次方程组$\left\{\begin{array}{l} x + y = 8,\\ 5x + 3y = 34\end{array}\right. $的解的是 (C)
A. $\left\{\begin{array}{l} x = -4,\\ y = 3\end{array}\right. $
B. $\left\{\begin{array}{l} x = -1,\\ y = 9\end{array}\right. $
C. $\left\{\begin{array}{l} x = 5,\\ y = 3\end{array}\right. $
D. $\left\{\begin{array}{l} x = 1,\\ y = 7\end{array}\right. $

答案： C

3. 解方程$\frac {x - 5}{2} + \frac {x - 1}{3} = 1$时,去分母后得到的方程是 (C)
A. $3(x - 5) + 2(x - 1) = 1$
B. $3(x - 5) + 2x - 1 = 1$
C. $3(x - 5) + 2(x - 1) = 6$
D. $3(x - 5) + 2x - 1 = 6$

答案： C

4. 若关于x的方程$2x - kx + 1 = 5x - 2$的解为$x = -1$,则k的值为 (C)
A. 10
B. -4
C. -6
D. -8

答案： C

5. 若$\left\{\begin{array}{l} x = 1,\\ y = 2\end{array}\right. $是关于x,y的二元一次方程$ax - 2y = 1$的解,则a的值为 (B)
A. 3
B. 5
C. -3
D. -5

答案： B

6. 已知方程组$\left\{\begin{array}{l} ax - by = 4,\\ ax + by = 2\end{array}\right. $的解为$\left\{\begin{array}{l} x = 2,\\ y = 1,\end{array}\right. $则$2a - 3b$的值为 (B)
A. 4
B. 6
C. -6
D. -4

答案： B

7. “今有鸡兔同笼,上有三十五头,下有九十四足,问鸡兔各几何”是《孙子算经》卷中著名数学问题. 意思是:鸡兔同笼,从上面数,有35个头;从下面数,有94条腿. 问鸡兔各有多少只? 若设鸡有x只,兔有y只,则所列方程组正确的是 (B)
A. $\left\{\begin{array}{l} x + y = 35,\\ 4x + 2y = 94\end{array}\right. $
B. $\left\{\begin{array}{l} x + y = 35,\\ 2x + 4y = 94\end{array}\right. $
C. $\left\{\begin{array}{l} x + y = 94,\\ 4x + 2y = 35\end{array}\right. $
D. $\left\{\begin{array}{l} x + y = 94,\\ 2x + 4y = 35\end{array}\right. $

答案： B

8. 元朝朱世杰所著的《算学启蒙》中,记载了这样一道题:“良马日行二百四十里,驽马日行一百五十里,驽马先行一十二日,问良马几何日追及之?”其大意是:快马每天行240里,慢马每天行150里,慢马先行12天,问快马几天可追上慢马? 则快马追上慢马的天数是 (D)
A. 5天
B. 10天
C. 15天
D. 20天

答案： D