🎯 能力诊断测试

一场足球赛在下午 4:30 结束。如果比赛进行了 1 小时 45 分钟，比赛是什么时候开始的？A soccer match ended at 4:30 PM. If the match lasted for 1 hour and 45 minutes, what time did it start?

拿一张正方形的纸对折 1 次，让折好的两部分完全重合。想一想：这样的折法一共有多少种？Fold a square piece of paper once so that the two folded parts match exactly. How many different ways can this be done?

两个两位数 $AB$ 和 $CD$ 的和是 100（即 $AB + CD = 100$）。那么 $A + B + C + D$ 的和是多少？The sum of two two-digit numbers $AB$ and $CD$ is 100 (i.e., $AB + CD = 100$). What is the sum of $A + B + C + D$?

在分母是 10、分子小于 10 的分数中，比 1/2 大的最小分数是多少？先想一想：1/2 相当于十分之几。Among all the fractions whose denominator is 10 and whose numerator is smaller than 10, what is the smallest fraction that is greater than 1/2? (Think: 1/2 is equal to how many tenths?)

妈妈给小敏买了 4 件不同的上衣和 3 条不同的裤子。每次穿 1 件上衣和 1 条裤子，小敏一共有多少种不同的穿法？Mom bought Xiaomin 4 different tops and 3 different pairs of pants. If she wears exactly 1 top and 1 pair of pants each time, how many different outfits can Xiaomin make?

笼子里有鸡和兔，从上面数共有10个头，从下面数共有28条腿。用假设法：先假设10只全是鸡，腿共有10×2=20条，比实际少28-20=8条——这8条腿正是被当成鸡的兔子少算的。笼中的兔有多少只？In a cage there are chickens and rabbits. Counting from above, there are 10 heads; counting from below, there are 28 legs. Using the assumption method: first assume all 10 animals are chickens, giving 10 × 2 = 20 legs — 28 - 20 = 8 fewer than the actual number. These 8 missing legs belong to the rabbits that were counted as chickens. How many rabbits are in the cage?

A、B 两站相距 375 千米。两列火车同时从两站出发，相向而行，一列火车每小时行 60 千米，另一列每小时行 45 千米。在相遇之前，当两列火车还相距 60 千米时，它们已经行驶了几小时？Station A and Station B are 375 km apart. Two trains start from the two stations at the same time and travel toward each other. One train travels 60 km per hour, and the other travels 45 km per hour. Before they meet, when the two trains are still 60 km apart, how many hours have they been traveling?

A、B 两城相距 400 千米。甲、乙两车同时从两城出发，相向而行，甲车每小时行 60 千米，乙车每小时行 40 千米。经过几小时两车相遇？Town A and Town B are 400 km apart. Two cars start from the two towns at the same time and drive toward each other. One car travels 60 km per hour, and the other travels 40 km per hour. After how many hours do the two cars meet?

文具店原来有一批笔记本：上午卖出了这批笔记本的一半，接着又购进 30 本；下午又卖出了此时剩下的一半，最后还剩 40 本。文具店原来有这批笔记本多少本？A stationery store has a batch of notebooks. In the morning it sells half of them, then receives 30 more; in the afternoon it sells half of what it has at that point, leaving 40 notebooks. How many notebooks were in the batch at first?

一盒巧克力，小美第一天吃掉总数的 1/4，第二天吃掉剩下的 2/5，这时还剩 18 块。这盒巧克力原来有多少块？（注意易错点：第二天吃的是「剩下的 2/5」，不是总数的 2/5。）Mimi has a box of chocolates. On the first day she eats 1/4 of all the chocolates in the box. On the second day she eats 2/5 of the remainder, and 18 chocolates are left. How many chocolates were in the box at first? (Watch out: it is 2/5 of the remainder, not 2/5 of the whole box.)

一件商品的成本是 60 元，售价是 75 元。下面哪个算式正确地求出了这件商品的利润率？An item costs 60 yuan and is sold for 75 yuan. Which of the following calculations correctly finds the profit margin of this item?

把一块棱长 6 厘米的正方体木料削成一个尽可能大的圆柱（圆柱的底面是正方体一个面上所能画出的最大的圆，高与正方体的棱长相等）。削去部分的体积是多少立方厘米？（结果用含 π 的式子表示）A wooden cube has edges of 6 cm. It is carved into the largest possible cylinder: the cylinder's base is the largest circle that fits on a face of the cube, and its height equals the cube's edge. What is the volume of the wood carved away? (Express your answer in terms of π.)

数轴上，点 A 表示的数是 a，点 B 表示的数是 b。已知 |a| = 6，|b − 1| = 2，那么 A、B 两点间的距离最大是____。On a number line, point A represents the number a and point B represents the number b. Given |a| = 6 and |b − 1| = 2, what is the greatest possible distance between points A and B?

已知关于 x 的方程 (x + m)/6 + x/3 = x/2 + 1/3。如果任何数都是这个方程的解（无论 x 取何值等式都成立），那么 m = ___Consider the equation in x: (x + m)/6 + x/3 = x/2 + 1/3. If every number is a solution of this equation (it holds no matter what value x takes), then m = ___

瓶里装有一些浓度为 20% 的糖水。蒸发掉 50 克水后，浓度升到 30%。要想让浓度达到 50%，还需再加入____克糖。A bottle contains some 20% sugar solution. After 50 g of water evaporates, the concentration rises to 30%. To raise the concentration to 50%, how many grams of sugar must be added?