MAT (Oxford Maths Admissions Test) 2021 in 10 minutes or less

Yesterday over 5000 applicants took the Mathematics Admissions Test, the entrance test used for Undergraduate Mathematics at Oxford, and other courses at Oxford and other universities. It's a 2 1/2 hour exam. Here Dr James Munro gives you all the answers in 10 minutes or less.

The MAT is used by Maths at Oxford to help us decide which candidates to invite for interview.

[LucyWangYuxin]

Gives me flashbacks to last year when I ran back to my room to watch James’ video to check my answers and the internet at school crashed!! Best of luck everyone xx ❤️

[ShaunakDesaiPiano]

The flashbacks are crazy! Good luck everyone for the interview shortlisting 😄

[Isabella-fbck]

I'm gonna cry, why did I think I could do this

[forthrightgambitia]

For C... I got the answer like this: the tangent of e^x is just... e^x by basic calculus. So using the definition of a straight line the equations

e^p = e^p(x - p)
e^q= e^q(x - q)

In the examples y = 0 and x = a or b respectively.

e^p = e^p(a - p)
e^q = e^q(b - q)

e^p = e^p(a - p)
e^q = e^q(b - q)

1 = a - p
1 = b - q

a - p = b - q
p - a = q - b (times by -1)

[brmbrmcar]

Looks a lot more fun when you're not actually sitting it lol. A year ago I came out of the MAT feeling terrible and wanting to cry, now I'm in Oxford crying over a lack of social life. I would just give some advice; firstly your MAT isn't all that important compared to interview for most colleges if you can get one, so don't worry about your score not being 90, you'll be fine. Also they can and do look through your MAT script if your score is marginal, so if you did anything silly so you can't pick up a lot of marks they can still see any maths you did do that looks good, but don't worry about things looking like a mess or your handwriting being 'terrible', it's all understandable and they don't care about your handwriting, trust me!

[PadawanNeel]

The worst mat paper I've done and it was the actual one that mattered. Made too many silly errors in the multiple choice

[mistymodhu]

Can the physics department make PAT solution videos please?

[akiraalexander]

I just sat that yesterday and I’m so flipping happy to see I got all of Q1 right PHEW!

[dongshenwu]

The most annoying thing that can happen in MAT is to know exactly how to do a multiple-choice (1F) but made an algebraic slip in the calculation... It feels so much worse than not knowing how to do it in the first place :(( Why can't Oxford gives some mark for the working of MC😭

[alexfisher]

i sat this test 2 days ago and now i wanna cry

[titouanvasnier]

I loved the MAT of this year, the problem 1 and 2 were great !

[oliverqueen]

I don’t have clue how to answer like 90% of the questions and this only like a year away for me 😭

[CannedMaths]

😇😇😇
Q5 completely caught me off... My predicted wasn't that great so I hope I could get to the interview stage...!!
Regardless, it was a fun go!!

[Joe-pjds]

@Oxford Mathematics when roughly will μ1 (Average score) be released? Thank you.

[ababoumohamed]

This is what those interested in Mathematics from all over the world should be demanding:
The International Mathematical Union must establish a Committee for Comparing Mathematics in order to study the ancient Mathematics that prevailed at the Babylonians, the Pharaohs, ancient India, the Maya, the Greeks and the Romans(Mathematics devoid of illusion and the myth of infinity), and compare it with the Mathematics currently adopted within an educational curriculum, which is those Mathematics mixed with illusion and the myth of infinity ... and thus, towards knowing which Mathematics are suitable for education and study, and which meet scientific conditions that qualify them for academic reception.

[pengwang]

I will write my answers to all Q1 problems here. Just to encourage discussions. I think this year's Q1 is much easier than 2020. Q1E is a bit new and but eventually, it's just a basic problem of permutation and combinaiton. For the final question Q1H, we need to be careful with Choice A and D. All other problems are pretty easy to solve. :)

Q1A.
Recall the area is the sum of 12 isosceles triangles. Recall the A = 1/2absin(C). The total area is 3.



Q1B.
Just need to be careful that a is greater than zero, easy to find $a = 3^{2/3}$



Q1C.

Let us choose an arbitrary point on curve $y=e^x$, and draw the tangent which crosses the x-axis at u. Easy to find that $y’=e^t=(e^t-0)/(t-u)$, which is $1=t-u$ after simplifications. Thus, we can deduce $1=p-a=q-b$. The answer is c.



Q1D.
First, let $e^x=1-e^x$, then $x=ln(1/2)$. Then integrate:




Q1E.
We know 10 needs to be written as the sum of 6 positive integers, and those integers are either 1 or 3. The only possible way is $10 = 1+1+1+1+3+3$。Thus, two out of the six vectors are (3, 2). There are $C_6^2=15$ ways to pick any two vectors out of six. There are in total $2^6=64$ possible ways to allocate (1, 1) or (3, 2) to the six vectors. Thus, the probability of the sum of the six vectors being (10, 8) is $C_6^2/2^6=\frac{15}{64}$



Q1F.
We know the line formed by two points (a, a^3-3a) and (2, 0) is tangent to the curve $y=x^3-3x). Thus, slope of the straight line is the same as 1st derivative of the curve at $x=a$. So we get $3a^2-3 =\frac{a^3-3a}{a-2}$, which is reduced to $a^3-3a^2+3=0$. We can easily plot $f(a)=a^3-3a^2+3$ by letting $a=-2, -1, 0, 1, 2$ and we can tell the curve of $f(a)$ crosses x-axis 3 times.



Q1G.
Recall sinx = cos(pi-x), (sin(x))2+(cos(x)^2)=1, and sin(45 deg) = sqrt(2)/2, and sin(90 deg)=1. Easy to get the answer is 45.5.



Q1H.
Let sin(x)=t, we can find when t = 1 or 1/3 y=0, and x = pi or x=arcsin(1/3) or x = pi-arcsin(1/3). Also easy to find when t= -1 so x=1.5pi y has the maximum value. Three zeros eliminate b, c, e, and the maximum value happening after the zeros eliminate a, so the answer is a.



Q1J.
Apparently, ABCD is a diamond. AC is perpendicular to BD. Vector AC dot product Vector BD = 0, obviously true. Then, AD = DC, leading to (a-b)^2=(c-d)^2, which is the same as (a-b+c-d)(a-b-c+d)=0. Also AB is parallel to DC, (b-c)/(a-b)=(d-a)/(c-d). Easy to find only $a-b+c-d=0$ holds. Answer is d.

[Dz-iunk]

Hi, James. I am sorry to break it to you but this is not helping 😭I honestly didn't understand a single bit you said. Please make a full video. I am sure most people would find it helpful too.

[CC-mksv]

Pain. Got the first two wrong due to arithmetic mistakes! Lost out 8 easy marks, sad that

[erickjian]

@Oxford Mathematics I wonder how many marks does the last two parts of Q5 worth ?

[chetantyagi]

Do the CS major students need the same score as maths major students at Oxford?