UKMT Senior Individual Maths Challenge 2016 - Preparation and Tips

Reply 140

sqrt(e/m)=c

OP

12

Original post by Mathspro2580

For 9 i don't see how y= -X^2 +1 passes through two. I thought it would only pass through (0,1) :frown:

.
less chance for a gold cuz I'm wrong :frown:

If x=1, you have -(1^2)+1=-1+1=0 (1,0)
If x=0, you have -(0^2)+1=-0+1=1 (0,1)

Reply 141

TheConfusedMedic

21

Original post by LaurenLovesMaths

For some reason I really struggled to do Q8 - I think it was difficult to draw an accurate diagram and I struggled with counting haha

Other than that I think the rest of my answers were correct, and that I got 100 marks :smile:

pretty happy with that!

Yeah for some reason I did (2+4+6+8+10+12)*2 but not really sure why :lol:

100 is insane though!! Well done :smile:

Reply 142

Superdjman1

7

How do you do question 24?

Reply 143

sqrt(e/m)=c

OP

12

Original post by maths00

The numbers in the boxes go:

10, 13, 16, 19, 22, 25

How did you get that? It works, but I just want to know how, for the future.

Reply 144

ShatnersBassoon

4

Original post by 123Master321

I accidentally did 2017 digits rip, think I got 115 in the end, didnt read scalene on Q4 wbu

I did exactly the same. Damn.

Original post by sqrt(e/m)=c

Can people explain how they got their answers for:
11, 20, 23, 13, 15, 21 and 24.
Thanks

11. I have a series of long, awkward and confusing simultaneous equations I used to solve this, but I don't think they'd help you. The numbers in the boxes were 10, 13, 16, 19, 22 and 25, increasing by 3 each time, if that helps.

13. If you've come across this spiral before you should know the side lengths of each square, but if not hopefully you can see that (going from the start of the spiral) they are 1, 1, 2, 3 and 5. Each spiral is the circumference of a quarter circle - a circle has circumference 2πr, so the part of the spiral will have length πr/2. Sub in 1, 1, 2, 3, 5 and add them up; you get π(1+1+2+3+5)/2 = 12π/2 = 6π.

And the others you mentioned were almost an exhaustive list of the ones I couldn't answer, so I'm afraid I can't help you there.

EDIT:

Original post by surina16

Yeah for some reason I did (2+4+6+8+10+12)*2 but not really sure why :lol:

This is how I did it! Everyone else seemed to be drawing it out, which I thought was too tedious to be the intended method. So I drew n = 2 and n = 3, and used the given diagram of n = 4 to work out a pattern. For instance, for n = 4, there were 2, 4, 6, 6, 4 and 2 squares (2+4+6+6+4+2 = (2+4+6)*2) on each 'row' going diagonally upwards. Comparing with n = 3 and n = 2, I found you just kept adding on the next even number so with n = 7, there are (2+4+6+8+10+12)*2 = 84 squares.

(edited 7 years ago)

Reply 145

LaurenLovesMaths

14

Original post by surina16

Yeah for some reason I did (2+4+6+8+10+12)*2 but not really sure why :lol:

100 is insane though!! Well done :smile:

Thank you!! :smile:

Reply 146

TheConfusedMedic

21

Original post by sqrt(e/m)=c

Thanks, but damn you :wink:

I misread the question too and did the same thing as you :redface:

Reply 147

physicsgirl98

1

Original post by maths00

The numbers in the boxes go:

10, 13, 16, 19, 22, 25

How did you work that out? I did some long complicated simultaneous equations ahah

Reply 148

maths00

7

Original post by sqrt(e/m)=c

Can people explain how they got their answers for:
11, 20, 23, 13, 15, 21 and 24.
Thanks

11: I got the numbers 10, 13, 16, 19, 22, 25
23: I used Pythagoras to find the distance between opposite corners of the cuboid (this is the diameter of the sphere) then I used Pythagoras to find the length of a cube whose distance between opposite corners is equal to this length.
13: The smallest squares contain a half circle, with arc length (2*pi*r)/2 = (2*pi*1)/2 = 2*pi/2 = pi
The next smallest square contains a quarter circle with radius 2 so its arc length is 2*pi*r/4 = pi
The next has radius 2 + 1 = 3, with a quarter circle arc length again, and so on.
Then you add them all up: pi + pi + 3/2*pi + 5/2*pi = 6*pi
15: I continued the side of each rectangle so that it met the adjacent line, creating three tiny triangles. Then I played with the angles a bit and it's not too hard from there

q 11. enjoy :smile:

OP

Thanks.
I did really similar thing, but figure that I forgot to subtract a C, thereby giving me X=17.

(edited 7 years ago)

Reply 151

maths00

7

Original post by physicsgirl98

How did you work that out? I did some long complicated simultaneous equations ahah

There was probably a better way of doing it, but I just tested each answer in the 'X' box, then found the average of X and 25 to find the box second from the end. Then I called the box to the left of X 'Y', then tested whether each one worked or not.

Reply 152

sqrt(e/m)=c

OP

12

Original post by maths00

11: I got the numbers 10, 13, 16, 19, 22, 25
23: I used Pythagoras to find the distance between opposite corners of the cuboid (this is the diameter of the sphere) then I used Pythagoras to find the length of a cube whose distance between opposite corners is equal to this length.
13: The smallest squares contain a half circle, with arc length (2*pi*r)/2 = (2*pi*1)/2 = 2*pi/2 = pi
The next smallest square contains a quarter circle with radius 2 so its arc length is 2*pi*r/4 = pi
The next has radius 2 + 1 = 3, with a quarter circle arc length again, and so on.
Then you add them all up: pi + pi + 3/2*pi + 5/2*pi = 6*pi
15: I continued the side of each rectangle so that it met the adjacent line, creating three tiny triangles. Then I played with the angles a bit and it's not too hard from there

Thanks a lot.

Reply 153

qeyoo

7

Original post by surina16

That's what I thought but apparently it's 7! = 5040

No it's not....

Posted from TSR Mobile

Reply 154

d010534

11

Guys,
I answered 14 questions and now I'm worried. Can I at least get a Bronze??

Reply 155

Mathspro2580

5

Original post by d010534

Guys,
I answered 14 questions and now I'm worried. Can I at least get a Bronze??

don't worry bronze is like 8 or 9 right. u will probably get silver. Maybe gold ( but unlikely) :smile:

Reply 156

TheConfusedMedic

21

Original post by qeyoo

No it's not....

Posted from TSR Mobile

Ah great haha I was really happy with my answer of 84 but everyone was telling me it was 7 factorial :rolleyes:

Reply 157

d010534

11

Original post by Mathspro2580

don't worry bronze is like 8 or 9 right. u will probably get silver. Maybe gold ( but unlikely) :smile:

really?! thank you!! I'm so worried (I'm in year 13 so I can't ever do this again) so I really want to get a certificate at least!!

Reply 158

qeyoo

7

Original post by d010534

Guys,
I answered 14 questions and now I'm worried. Can I at least get a Bronze??

Yes, you can get max 25+14x4= 81, last year it was 50 for a bronze

Posted from TSR Mobile

Reply 159

d010534

11

Original post by surina16

Ah great haha I was really happy with my answer of 84 but everyone was telling me it was 7 factorial :rolleyes:

I legit drew out the thing and counted the squares like but oh well, I still got the answer right!! :colondollar:

UKMT Senior Individual Maths Challenge 2016 - Preparation and Tips

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