冲刺南外英语思维专题训练1解析卷

“冲刺南外”英语思维专题训练一解析卷
姓名成绩
1.Define a new operation（定义新运算）
1.Suppose 2△3=2＋3＋4=9，5△4=5＋6＋7＋8=26，x△3=15,then what is x?
【解析】x+x+1+x+2=15；3x+3=15；x=4
2.For any two integers a and b, define two calculations “☆”“⊙”：a☆b=a＋b＋1，a⊙b=a×b－1,work out the value of 4⊙［（6☆8）☆（3☆5）］.
【解析】6☆8=6+8+1=15；3☆5=3+5+1=9；15☆9=15+9+1=25；4⊙25=4×25-1=99
3.There is a mathematical calculation “☆”，for example:4☆8=16，10☆6=26，6☆10=22，18☆14=50，work out 8☆10.
【解析】根据给的例子可以知道新定义为：a☆b=2a+b。

则8☆10=2×8+10=26.
4.For any integers a and b, suppose a*b=2×a＋b，if x*2x*3x*4x*5x*6x*7x*8x*9x=3039,then what is x? 【解析】x*2x*3x*4x*5x*6x*7x*8x*9x=3039
4x*3x*4x*5x*6x*7x*8x*9x=3039
11x*4x*5x*6x*7x*8x*9x=3039
26x*5x*6x*7x*8x*9x=3039
57x*6x*7x*8x*9x=3039
120x*7x*8x*9x=3039
247x*8x*9x=3039
502x*9x=3039
1013x=3039
X=3
2.Write equations to solve problems（列方程解决问题）
5.There is a road on building, the length unfinished is 3 times as the length finished. Build 3000 more meters and the length unfinished will become 2 times as the length finished. How long is this road?
【解析】设已修的为x米，则未修的为3x米。

列方程为2（x+3000）=3x-3000；x=9000,；全长为9000×4=36000（米）
6.Measuring the height of a bridge on the bridge, if we fold the rope and drop the rope onto the surface of water vertically,8 meters would be left. If the rope is folded three times and dropped onto the surface of water ,2 meters of rope would be left. Please work out the height of bridge and the length of the rope? 【解析】设桥高为x米。

列方程为2（x+8）=3（x+2）；x=10；绳长2×（10+8）=36（米）
7.At the beginning, the money of Jia and Yi is respectively 6 times and 5 times of the money of Bing, then Jia get 180 yuan and Yi get 30 yuan,and the money of Jia is 1.5 times of Yi’s. What’s the total money Jia,Yi and Bing own originally?
【解析】设丙有钱数为x元。

列方程为6x+180=1.5（5x+30）；x=90；总钱数为90×（6+5+1）=1080.
8.A plane flies from A to B, it had planned to fly at the speed of 9km per minute. While it flied at the speed of 12km per minute and arrived at the destination 30 minutes earlier than planned. What’s the distance between A and B?
【解析】设原计划用x分钟。

列方程为9x=12（x-30）；x=120；路程为9×120=1080（千米）
3.Cuboids and cubes（长方体和正方体）
9.Make a cuboid with 4 cubes of the same size(as shown in the figure),the surface area decreased 32 square centimeters. What’s the volume of each cube?
【解析】减少8个小正方形，32÷8=4=22；23=8（立方厘米）
10.A cuboid will become a cube when its width increases 5 centimeters, and the surface area will increase 160 square centimeters. What’s the volume of the cuboid?
【解析】160÷4÷5=8，这就是正方体的棱长；原来的长方体的体积就是8×8×（8-5）=192cm3.
11.There is a rectangular box ,its length, width and height are respectively 40cm,12cm and 7cm when measured from the inside. put rectangular blocks with the dimension of 5cm×4cm×3cm into the box, how many can you put into the box at most?
【解析】画图分析，这些小长方体正好能装满大长方体。

则（40×12×7）÷（5×4×3）=56（个）。

12.There are a rectangular iron with the dimension of 9cm×7cm×3cm and a cubic iron whose side length is 5cm.Melt these two irons and make a new rectangular iron with the bottom area of 20 square centimeters. What’s the height of this new rectangular iron?
【解析】用总体积除以底面积就等于高：（9×7×3+53）÷20=15.7（厘米）
13.There is a cubic block whose length is 1m.Cut it into 3 slices along the horizontal direction, and cut each slice into 4 strips, then cut each strip into 5 pieces, we will get 60 rectangular blocks. What’s the sum of the surface areas of these 60 rectangular blocks?
【解析】三次切法分别增加了4、6、8个面，所以这些小长方体的表面积总和就是6+4+6+8=24m2 14.If the length of a cuboid increases 5cm, the volume will increase 150 cubic cm; and if the width increases 4cm,the volume will increase 160 cubic cm; and if the height increases 3cm,the volume would increase 144 cubic cm. What’s the surface area of the original cuboid?
【解析】150÷5=30（平方厘米），这就是宽乘高；160÷4=40（平方厘米），这就是长乘高；144÷3=48（平方厘米），这就是长乘宽。

则这个长方体的表面积就是（48+30+40）×2=236（平方厘米）
15、There is a cuboid whose length, width and height are respectively 21,15,12 centimeters. Now cut it and get a biggest cube, then cut the left part and get a second biggest cube as you can, and then cut the left part and get third biggest cube as you can. What’s the volume of the final left part?
【解析】从最大的原则来想，第一次截掉的是棱长为12厘米的正方体；第二次截掉的是棱长9厘米的正方体；第三次截掉的是棱长6厘米的正方体。

则剩下的体积是21×15×12-123-93-63=1107（立方厘米）
16.As shown in the picture, an ant set off from point A and crawls along the side, the route is not repeated. What’s the longest distance and the shortest respectively when it went back to poi nt A?
【解析】最短距离就是走两个宽和两个高，即（10+5）×2=30（厘米）；最长距离就走四个长、两个宽和两个高，即16×4+10×2+5×2=94（厘米）。