Back in the 10th grade I undertook a a highly prestigous mathematics challenge in which I got full marks by answering 16 questions over a few months. I will post the questions one at a time, with each question being posted when the previous question has been answered. There's many ways in answering these questions, but it is unlikely that google will be of much use (sorry 😛). Let's see how good ATOT is at higher maths. The questions vary in difficulty.
If everyone is stuck, I will try to find where I wrote down my answers, although I'm not too sure I still have them (its been quite a few years)
By the way, the questions are worded perfectly, they were written up by genius mathematicians and is sponsored by the education department.
Without further adeu, here is the first question.
Problem 1
The distance between villages A and B is 65km. Three backpackers, Lisa, Mary and Nora, who are at A, want to get to B. They have a motorbike able to carry up to two people at a constant speed of 50 km/h and each of the backpackers can walk at a constant speed of 5 km/h. They all started their journey at 8am: Lisa and Mary went on the bike while Nora walked. After a certain time, Mary got off the bike and continued her trip on foot. Lisa immediately turned back and after picking up Nora turned towards B again and started riding without losing any time. All three of them arrived at B at the same time. When did they arrive at B?
EDIT:
Problem 1 has been solved!
The next one should be easy, a few of the last ones will be VERY challenging.
Problem 2
Find all positive integers N such that 32N + 97 is divisibe by 4N - 1.
EDITX2:
Problem 2 has been solved!
Problem 3
Simplify
{[x^2 + 6xy + 9y^2]/[x^2 - 9y^2]}/{[x^2 + 3xy - 2x - 6y]/[x^3 - 3yx^2 - 4x + 12y]}
If everyone is stuck, I will try to find where I wrote down my answers, although I'm not too sure I still have them (its been quite a few years)
By the way, the questions are worded perfectly, they were written up by genius mathematicians and is sponsored by the education department.
Without further adeu, here is the first question.
Problem 1
The distance between villages A and B is 65km. Three backpackers, Lisa, Mary and Nora, who are at A, want to get to B. They have a motorbike able to carry up to two people at a constant speed of 50 km/h and each of the backpackers can walk at a constant speed of 5 km/h. They all started their journey at 8am: Lisa and Mary went on the bike while Nora walked. After a certain time, Mary got off the bike and continued her trip on foot. Lisa immediately turned back and after picking up Nora turned towards B again and started riding without losing any time. All three of them arrived at B at the same time. When did they arrive at B?
EDIT:
Problem 1 has been solved!
The next one should be easy, a few of the last ones will be VERY challenging.
Problem 2
Find all positive integers N such that 32N + 97 is divisibe by 4N - 1.
EDITX2:
Problem 2 has been solved!
Problem 3
Simplify
{[x^2 + 6xy + 9y^2]/[x^2 - 9y^2]}/{[x^2 + 3xy - 2x - 6y]/[x^3 - 3yx^2 - 4x + 12y]}
