[English version]
According to SinChew Daily and Goxuan, some students cried on the spot, vomitted, table flipped, or asked the teacher for a longer duration during the Primary School Leaving Examination (PSLE) held by the Ministry of Education of Singapore.
One question goes like this:
Helen and Ivan have the same number of coins.
Helen has some number of 50cents and 64 20cents, with a total mass of 1.134kg
Ivan has some number of 50cents and 104 20cents
(1) Who has more money than the others ? And by how much ?
(2) say each 50cent is 0.0027kg more than a 20cent, what is the mass of Ivan total coins
Solution:
(Desktop Site is recommended)
In the beginning, it seems terrifying, that is one of the main objectives of the exam.
But luckily, since the question
is a "relative type question" (a question that asks what is the relationship between parameters) rather than an "absolute type question" (a question that asks what is the absolute value of each parameter),
we can try to cancel out what both Helen and Ivan have in common, the rest is the difference and the answer.
let's turn the question into something we can see, and simplify it
(use smaller numbers and understand the concept first)
let's say "🔴" is a 50cent and "⚪" is a 20cent
so we should have something like:
H: 🔴🔴🔴🔴 .... 🔴🔴|🔴🔴🔴🔴🔴🔴|⚪⚪ .... ⚪⚪
I: 🔴🔴🔴🔴 .... 🔴🔴|⚪⚪⚪⚪⚪⚪|⚪⚪ .... ⚪⚪
<------L part------->|<----M part--->|<----R part---->as you can see, the question is actually just asking for differences, (obvious for question 1 by indirect for question 2, don't worry, I'll explain)
so what matters, is not the L part, is not the R part, instead, it should be the difference between Helen and Ivan, the M part.
(1)
When we want to find out who has more money,
both Helen's L part and Ivan's L part will cancel each other and
both Helen's R part and Ivan's R part will cancel each other
what is left is the M part.
so the total difference of cash should be = the width of M Part × the cash difference of each coin
So let's go back to the original question.
So the width of M Part should be 104 - 64 = 40, and the picture should originally look like this:
H: 🔴🔴🔴🔴 .... 🔴🔴|🔴🔴🔴....🔴🔴🔴|⚪⚪ .... ⚪⚪
I: 🔴🔴🔴🔴 .... 🔴🔴|⚪⚪⚪....⚪⚪⚪|⚪⚪ .... ⚪⚪
? | 40 | 64
<------L part------->|<------M part----->|<----R part---->so the difference is
40 x (50c - 20c) = 40 x 30c = 120c
since we know that Helen is has less 20cents then Ivan,
meaning Helen has more 50cents then Ivan,
meaning Helen has more money than Ivan,
and Helen has 120cents more than Ivan (question 1 solved)
(2)
we can also apply the same Idea here, instead of cash value, we are dealing with mass.
so the total difference of total mass should be = the width of M Part × the mass difference of each coin
so the difference of mass in the original question should be
40 x 0.0027kg = 0.108kg
since we know that the total mass of Helen's coins is 1.134kg, then
the total mass of Ivan's coins should be 1.134kg - 0.108kg = 1.026kg (question 2 solved)
Often, a question that is a "relative type question" will allow you to cancel common values, and what matters is the difference.
PS: I am not academically good at maths, I am like other students: failing my math exams all the time during high school.
Here is the original link with no answers:
https://goxuan.my/trending/entertainment-news/studentcryexam
[中文版]
据星洲日报，新加坡举行小学毕业会考（PSLE），让部分应试的12岁学童当场大哭、呕吐、掀桌、或向监考老师乞求更多答题时间。
其中一题如下：
海伦（Helen）和伊凡（Ivan）拥有数量相同的铜板。
海伦有一些50分铜板和64枚20分铜板，铜板重量为1.134公斤。
伊凡有一些50分铜板和104枚20分铜板。
请问：
1. 谁的钱比较多？多出多少钱？
2. 假设每枚50分铜板比20分铜板重0.0027公斤，伊凡的铜板最多有几公斤重？
解题：
（建议使用桌面型模式）
刚开始时，会觉得这一题很恐怖，但当然这是考试题目的其中一个目标。
不过幸运的是
这两个题目都是”相对性的题目“，这样的话，我们可以抵消海伦和伊凡共同有的东西，剩下有差别的就是答案。
我们可以把题目视觉化，同时做一些必要的简化
（使用比较小的数字，先掌握好概念）
假设"🔴" 是一枚50分铜板，则"⚪"是一枚20分铜板。
那么情况大致上会是这个样子：
H: 🔴🔴🔴🔴 .... 🔴🔴|🔴🔴🔴🔴🔴🔴|⚪⚪ .... ⚪⚪
I: 🔴🔴🔴🔴 .... 🔴🔴|⚪⚪⚪⚪⚪⚪|⚪⚪ .... ⚪⚪
<------L 部分------->|<----M 部分--->|<----R 部分---->题目问的是海伦和伊凡的不同之处，
由此可见，关键不是 L部分，也不是R部分，而是 两人不一样的M 部分
（1）
当我们在探讨”谁的钱比较多？“时，
海伦的 L部分 和 伊凡的 L部分 会互相抵消（因为它们都是一样的，不用比较）
海伦的 R部分 和 伊凡的 R部分 也会互相抵消
剩下的 就是 M部分
所以 两人相差的钱 = M部分的宽度 × 价钱差别
回到原先的题目的话，
M部分的宽度应该是 104-64=40，那么示意图大致上应该是：
H: 🔴🔴🔴🔴 .... 🔴🔴|🔴🔴🔴....🔴🔴🔴|⚪⚪ .... ⚪⚪
I: 🔴🔴🔴🔴 .... 🔴🔴|⚪⚪⚪....⚪⚪⚪|⚪⚪ .... ⚪⚪
? | 40 | 64
<------L 部分------->|<------M 部分----->|<----R 部分---->所以 两人相差的钱 = 40 x (50分 - 20分) = 40 x 30分 = 120分
既然海伦的 20分铜板比 伊凡的少；
也就是说海伦的 50分铜板比 伊凡的多，
也就是说海伦的钱比伊凡的多，多了 120分。(第一题解答完毕)
（2）
我们也可以使用相同的概念。
但是这一题我们对付的不是 价钱，而是质量。
所以 两人铜板相差质量 = M部分的宽度 × 铜板质量差别
回到题目
两人铜板相差质量是 = 40 × 0.0027kg = 0.108kg
既然 50分铜板比20分铜板质量多，且海伦有的50分铜板比伊凡多，
海伦的铜板质量比伊凡的大。
所以伊凡的铜板质量因该是 1.134kg - 0.108kg = 1.026kg（第二题解答完毕）
在大部分时候，相对性的题目将会允许我们抵消一些东西，而剩下来的就是答案。
PS:我数学没有你想象中的好，我也和其他学生一样，在中学时期常常”烤烂“数学考试
原帖子链接在这里：
https://goxuan.my/trending/entertainment-news/studentcryexam
Comentários