- A few months ago.
I made a video about a difficult Turkish exam question,
and that video seemed to resonate with a lot of people.
There were comments in Turkish
that were glad that people could see the pain
that they had to go through,
and there were plenty of comments lamenting the state
of the education system.
Let me show you some of the comments
that gained a lot of support.
This one translates to you only have a black pen
but create a rainbow.
This is a summary of the Turkish education system.
And this one says that the questions are of high quality,
but unfortunately, there is no system
that will take us to the answers of those questions.
Now, I have never studied in Turkey
and I don't know enough to agree or disagree
with these statements
but they do relate to a larger sentiment
that we see in many other countries.
And that is that the exam is not the challenge,
the real challenge is competing against the other students.
The exam in question is the AYT paper
used to gain entrance into Turkish universities.
The population of Turkey is 85 million
and over two million students are taking this test,
hoping to be in the top 50,000
to get into the good universities.
When entry is so competitive,
you see exams getting harder
to try and separate people.
But many are left feeling frustrated
by the fact that making exams harder
doesn't raise the quality of education
and instead can leave students feeling dejected
and hating school.
This comment said geography is destiny.
And this one said may God help Turkish,
Indian and South Korean students,
assumably talking about the tough exams they all have.
Another common thread
was people saying that even if you're lucky enough
to ace this exam, get into a good university
and graduate, that there are still not many jobs waiting
for you at the end.
This OECD unemployment rate data does show
that Turkey has a pretty high unemployment rate.
The latest figures are around 11.2%
whilst the USA and the UK are at 4%
and Australia, 4.2%.
It also seems like a lot of the top students aspire
to go overseas,
contributing to what they call brain drain
where a country's brightest people
aren't sticking around to help it grow.
I planned to work through another one
of the tough questions from the AYT exam paper
and I will get to doing that in this video
but first, I got distracted by another comment
that told me to check out the LGS exam
given to middle schoolers in Turkey
as a high school entrance exam.
It is very hard.
A math question this year
was taken from the university exam.
They are literally forcing students
to solve university level questions at age 13 to 14.
So naturally, I wanted to take a look.
Here's the paper and yes, it's really hard.
Apparently, students studying for this
are putting in eight plus hour study days,
making it the youngest example
of that kind of hard work I've seen for an exam yet.
Let's take a look at the last question
on the math section.
We've got these pie charts,
which show the distribution of televisions sold
in an electronics store in 2019 and 2020.
K, L and M are three different types of televisions.
It says that while the number of L brand televisions sold
in this store in 2020 decreased by 25
compared to 2019, the M brand televisions increased
in number by 40.
According to this,
what is the number of K brand televisions sold in 2019?
So we wanna know how many televisions
does this slice of pie represent?
That would be easy to do
if, for example, we knew how many televisions
were sold in total,
either in 2019 or 2020.
But that's not information that we have.
So this becomes quite tricky.
Please do have a go at solving it
and while you're at it,
I would like to quickly thank the sponsor
of this video, Babbel.
I've done a lot of translating
to try and read these exam questions
and the comments,
and I've actually been using Babbel
to learn just the basics
from the Turkish language
to make it easier for me
to pick out keywords.
Babbel is a top language learning app
that teaches real-world practical conversations
through 10-minute interactive lessons,
as well as podcasts, games, videos
and live classes.
Babbel teaches more than just vocab words
and also teaches you about the language's culture,
people, history and traditions.
(instructor speaking in foreign language)
(phone beeping)
(narrator speaking in foreign language)
(instructor speaking in foreign language)
(phone beeping)
(narrator speaking in foreign language)
Learning a new language is the perfect way
to work on yourself in 2022,
and Babbel is offering a 20-day money-back guarantee.
You can get 65% off
by going to my link, which is down in the description.
(instructor speaking in foreign language)
And now let's take a look at the solution.
So there might be a number of ways
to solve it but the simplest way I found
was to try and find out how many TVs each degree
of the pie represents.
I'm going to define this variable X,
which is how many TVs there are
in each degree of the pie in 2019.
And also, I'm going to define why,
which is the same thing
but for the 2020 pie chart.
Now let's look at the chart.
We will want to know how many degrees
are in this section K.
At first glance, it might look like it's 1/3, 120,
like this one down here but actually, it's not.
If this one here, L, is 90 degrees, M is 120,
and in total, this has to add to 360,
then K will actually be 150 degrees.
Over here it's a bit more simple.
We've got 90, 90 and so this one would have to be 180.
If we can find x,
then the problem will be solved
by finding 150 times x.
That will be how many TVs this chunk represents.
If that's 150x,
then this one here is 90x, 120x.
Since the number of M brand televisions increases
in number by 40,
then this section here will be 120x plus 40.
And since L decreases in number by 25,
this one here will be 90x minus 25.
And these segments can also be represented using y.
This one is also 90 degrees times y
and this one down here is 180y.
And since these represent the same number
of TVs in this chunk,
we can write 90x minus 25
is equal to 90y.
And for this one,
120x plus 40 is equal to 180y.
This is our key to solving the problem.
We've got two unknowns
but also two equations,
so we can solve this for both x and y.
Rearranging the top one for y
and subbing that into the second one,
I get x to be 3/2.
Remember what we wanted to solve the problem was 150x.
So 150 times 3/2.
Well, that is 450/2,
which is equal to 225,
meaning that C is the correct answer.
Now, it took me a few goes to get there
but if you found this easily, then congratulations,
you're as smart as a Turkish 13-year-old.
I can't help but think
that if you already are studying so hard
for exams this early
that by the time you get
to those tougher university entrance exams,
you may have already burned out.
But it seems like even getting into some
of the best high schools is a competitive process.
This is a question
from that notorious university entrance exam.
This is from the 2021 AYT mathematics paper.
Translated, it says that P of x
is a fourth degree polynomial
with real coefficients.
And it gives the inequality that P of x
is bigger than or equal to x.
It gives us three values of P of x
at x is one, two and three.
And it asks us to find the value of P of x
at x is equal to four.
Now, on an axes of x and P of x,
this line here represents
where P of x is equal to x.
Our function is called P of x
but it could just as easily have been called y
and you may recognize this
as more commonly called the line y equals x.
This inequality tells us
that the value of our function
will always exist above or at this line.
So in this region here.
In fact, we can plot some of the points.
At x is equal to one,
P of x is also equal to one,
so that point is on the line.
The same thing happens at x is equal to three.
In between that x is equal to two,
the value of P of x is four.
So it will be somewhere up here.
And since we know it's a fourth degree polynomial
or a quartic, we know it'll be a wibbly wobbly shape.
But because it can't pass down into this region down here,
it must look something like this.
And our question wants us to find the value
when x is equal to four.
So when it's somewhere up here,
finding the value of this polynomial
at any x value would be easy
if only we had the equation of this line.
But the equation of this line
is slightly hard to find
when we look at it on this perspective.
Instead, let's take a look at our inequality.
If we subtract x from both sides,
we have that P of x minus x
is bigger than or equal to zero.
Subtracting x off this function
makes it something that's easier to find an equation for
because it will intersect the x-axis.
Plotting P of x minus x,
we get something that looks more like this.
And you can see where I've got these points from.
I just subtracted x from these values here.
One minus one would give us a value of zero there.
Four minus two gives the coordinate two, two
and three minus three gives the coordinate three, zero.
I know the x-intercepts of this quartic,
so I can actually write its equation.
I'd get K, which is some scale factor
that we're yet to find.
X minus one squared
times x minus three squared.
If you're slightly unfamiliar with quartics,
you may wonder how I know that these are both squared.
Well, I can tell what they call the multiplicity
of the zeros by actually looking at the graph.
Also called the order, the multiplicity
is how many zeros are at the x-intercept.
For example, if the multiplicity was one,
that would be if this bracket wasn't squared.
It was just a single value of x.
In that case, the x-intercept
would be cut in a linear fashion.
The intercept would look something like this
or like this.
With a multiplicity of two,
that's when we would see an x squared
and the intercept would look like a quadratic,
something like this or this.
This is for a multiplicity of two
but also four, six, eight
and in fact any even number.
And a multiplicity of three
or of five, seven, nine
and any other odd number,
we would see something that looks like this
where the intercept is in there.
Fun fact is the higher this number of multiplicity,
the flatter this section will look.
Our x-intercepts come down and turn around
in that sort of quadratic function,
so that's why we can say that that would be squared.
If we're dealing with a quartic,
that is a power of x to the four,
then the total multiplicities added together
will equal four.
We do still want to find the value of K
and we can do that using these points here.
If we used x equals one,
we'd end up with one minus one is zero.
That would all be zero
and it wouldn't be useful for finding K.
Same thing would happen if we used three.
That's probably why they've given us this one in between.
If P of two minus two is equal to two,
we'd have K, two minus one is one squared,
two minus three is -1 squared.
That would all be one
and K would just be equal to two.
So this would be our final equation
for P of x minus x
and that's all we need
to be able to find P of four.
Plugging in x is equal to four,
it works out to give us the answer of 22.
Luckily, that's one of our options
and so we can say that B is the right answer.
I know that in the real exam,
you get a lot less time than I've taken here
but I'm trying to explain things as I go,
especially if this problem is an unfamiliar type for you.
What makes the exam even harder
is that this might be an unfamiliar question
to almost everyone.
It doesn't look like it appears in last year's exam
and so there's not really any warning
to prepare for something like this.
Interestingly, this exam made the news in Turkey this week
after a decision from the Council of Higher Education
to change the minimum passing score.
Whilst entry to the top universities
will remain very competitive,
students could still be placed in a less competitive program
after getting as little as one question correct.
In Turkey, there are many higher education institutes
but they're not all of the same quality.
Perhaps this decision could lead
to more low-quality institutes
offering degrees that don't help
to reduce the country's unemployment
or we'll see private universities now accepting anyone
who's willing to pay the tuition fee.
Thanks for watching this video
and again, let me know your thoughts down in the comments.
This video is in honor
of today's Patron Cat of the Day, Latte
sent in by Connor.
(tranquil music)