Congratulations to our Year 12 Virtual Summer School competition winners!
- Freddie, Ealing
- Matyl, Harrow
- Sadia, Harrow
- Anjaniba, Ealing
- Jiya, Ealing
- Vaishali, Harrow
- Taejah, Harrow
- Musawer, Ealing
- Henry, Ealing
- Hana, Ealing
- Kate, Ealing
- Valerie, Harrow
Each of you have won an Amazon voucher. This will be sent to the email address you provided in your competition cover sheet; please get in touch with us at firstname.lastname@example.org if you haven’t received yours by the end of the week.
Below you can read the winning entries to each of the Year 12 competitions. The full details for each competition as well as the rest of the Virtual Summer School material continue to be available on the timetables for the Year 12 Virtual Summer School, STEM here and Humanities here.
Click here to read more about last week’s Virtual Summer School programme!
Academic Poster Project
During this week, you will learn about fake news, and the impact it has on our world. Start by reading the Oxplore page on fake news. Based on what you have read, create an academic poster to submit at the end of this week, examining how fake news has impacted on a topic of your choosing. Click here to review the full details and guidelines for this assignment.
Humanities 1st place: Kate, Ealing
Humanities runner-up: Freddie, Ealing
Humanities runner-up: Jiya, Ealing
Humanities Finalist: Taejah, Harrow
STEM 1st place: Matyl, Harrow
STEM runner-up: Sadia, Harrow
STEM runner-up: Anjaniba, Ealing
STEM Finalists: Valerie, Harrow and Hana, Ealing
In addition to the Academic Poster Projects, Year 12s also competed in a series of daily challenges. Humanities students considered a series of ‘Big Questions’ from Oxplore, while STEM students completed a series of maths problems set by Dr Tom Crawford. Following the conclusion of each daily competition, Humanities students were able to see how others voted, while STEM students could check their work against the solution to each day’s problem. Below you can see each day’s winning entry for both the Humanities and STEM strands…
Daily Competition: Monday
Humanities: Should we believe history books?
Review Monday’s competition here!
Whilst it is true that historians may disagree with one another on matters of history, ultimately, they do reach a consensus on the fundamental aspects of history. For example, henry the VIII had six wives. History books give us an insight into the past and if it seems that they are altered, then it is up to the individual to find out more through the use of other historians and pieces of evidence. History books should be believed however only as a foundation for our opinions of historical events, people should use history books to formulate their own conclusions.
STEM: Crossing the desert
You are responsible for driving an important person across the desert, but the cars that you have been given can only hold enough petrol to cover half of the distance. Being a desert, there are of course no petrol stations along the way. However, you have access to as many cars as you need and can transfer petrol between them.
What is the minimum number of cars that you will need and how can you complete the journey?
Click here to see Monday’s competition in fully, and here to see the video solution.
Daily Competition: Tuesday
Humanities: Does truth exist?
Tuesday’s full competition details can be found here.
Truth is momentary. In GCSE history (medicine), we were taught that flagellation was a medical treatment ‘known’ to work. Then, birds flying around Churches would ‘certainly’ clear the air. After, masks with imported herbs were known as the ‘absolute’ cure. Now, we look at how much we have progressed since the 15th century, we see absolute truths were definitely absolute, just not true. What is absolutely true is mathematics, also believed by Plato as the closest thing to true knowledge, but again, the calculations are only ‘true’ insofar, and there may be new mathematical understandings when this century has surpassed.
STEM: Cannibals and hats
You are walking through the jungle with two friends when all of a sudden you are attacked by a group of cannibals. Fortunately, they do not eat you straightaway, but instead devise a puzzle that you must solve to avoid being eaten. The setup is as follows:
You are each tied to a pole such that you can only see forwards. The poles are placed in a line such that the person at the back can see the two people in front of them, the person in the middle can see one person in front of them, and the person at the front cannot see anyone else. See diagram below.
The cannibals produce five hats: 3 are black and 2 are white. You are all then blindfolded and a hat is placed on each person’s head at random. The other two hats are hidden.
The blindfolds are removed and you are told that you will be set free provided that one of the group can correctly guess the colour of the hat that they are wearing. An incorrect guess will cause you all to be eaten.
The person at the back says that they do not know the colour of their hat. The person in the middle says that they also do not know the colour of their hat. Finally, the person at the front says that they DO know the colour of their hat.
The questions is: what colour hat is the person at the front wearing and how did they know the answer?
Review Tuesday’s full competition post here, and its video solution here.
Daily Competition: Wednesday
Humanities: Should under-18s be allowed to vote?
Wednesday’s full competition details can be found here.
Under 18s should not be able to vote due to the (average) lack of psychological maturity. Although most people’s ability to rationalise is fully developed by the age of 16, the emotional maturity of an individual of the same age is not developed until they’re in their 20s, this is essential as emotional maturity can cloud one’s ability to make rational decisions. The age of 18 is a balance between psychological maturity and ensuring that younger voices are represented. In addition, 18-21s should be registered automatically to encourage a greater turnout among the younger population.
STEM: Exponential versus polynomial growth
In the lecture on disease modelling we talked about the exponential function 3x and derived a formula for calculating when it would ‘beat’ a polynomial function xk for some whole number k.
Q1. Calculate the smallest whole number value of x for the exponential function to ‘win’ when:
Q2. If we now instead consider the exponential function 2x, what is the general formula for calculating when it will ‘beat’ the polynomial function xk for some whole number k?
What is the smallest whole number value of x for the exponential 2x to ‘win’ when k=4?
See Wednesday’s full question here, and view the video solution here.
Daily Competition: Thursday
Humanities: Is fantasy better than real life?
Click here to see the full competition post!
Many people are happy living their technology-filled lives, and how do we define ‘better’? For those in love with fantasy and its magic, adventure, and comradeship, the genre offers an escape from our mundane, structured, and isolated lives. Putting aside the danger – no fantasy story is complete without a huge battle where someone is likely to die – these stories are just so exciting. They teach us about honour and friendship, and we are captivated by the whisper of opportunity. Even the prudent Bilbo Baggins became bold and adventurous, making him a lot happier. It has been scientifically proven that risk-taking is good for us. Are we just too careful nowadays? Do our imaginations show us our desires?
STEM: SIR model and the reproductive number R0
In the disease modelling lecture we discussed the basic reproductive number R0 in the context of an epidemic and derived its formula as:
- How can we reduce the value of R0?
- If we take R0 = 3 as was originally estimated for the initial spread of COVID-19, and assume that the entire population is initially susceptible, what values could r and a take?
- Using the values you calculated in Q2, plot the appropriate graphs at mathigon.org/pandemic and use them to answer the following questions:
- What is the maximum % of the population that is infected at any one time?
- What happens to the graphs if you increase the value of the transmission rate r? What happens if you decrease the value of r?
- What happens to the graphs if you increase the value of the recovery rate a? What happens if you decrease the value of a?
- What happens to the graphs when you increase the ‘incubation time’ (bottom slider) to a value above zero? What do you think this represents?
Click here to see Thursday’s full competition post, and here to see Thursday’s video solution.