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SMC Answers
just got back. ill start them off
20. Which is the lowest positive integer by which 396 must be multiplied by to make a perfect cube?
well 396 = 3*132 = 2*3*66 = 6*11*2*3 = (2^2)(3^2)(11)
when this is multipled by (11^2)(2)(3), or 726, the result is (11^3)(2^3)(3^3) = (11*2*3)^3
So the answer is 726
20. Which is the lowest positive integer by which 396 must be multiplied by to make a perfect cube?
well 396 = 3*132 = 2*3*66 = 6*11*2*3 = (2^2)(3^2)(11)
when this is multipled by (11^2)(2)(3), or 726, the result is (11^3)(2^3)(3^3) = (11*2*3)^3
So the answer is 726
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25. Positive integers x and y satisfy the equation:
sqrt[x + sqrt(y)/2] - sqrt[x - sqrt(y)/2] = 1
Which of the following is a possible value of y?
Well,
sqrt[x + sqrt(y)/2] - sqrt[x - sqrt(y)/2] = 1
sqrt[x + sqrt(y)/2] = 1 + sqrt[x - sqrt(y)/2]
x + sqrt(y)/2 = 1 + 2.sqrt[x - sqrt(y)/2] + x - sqrt(y)/2
sqrt(y) - 1 = 2.sqrt[x - sqrt(y)/2]
y - 2.sqrt(y) + 1 = 4x - 2.sqrt(y)
y + 1 = 4x
Becuase x and y are integers, y + 1 must be divisible by 4, so y = -1 (mod 4)
The only number congurent to -1 (mod 4) in the answers is 7, and 7+1=4*2, so y=7 and x=2
sqrt[x + sqrt(y)/2] - sqrt[x - sqrt(y)/2] = 1
Which of the following is a possible value of y?
Well,
sqrt[x + sqrt(y)/2] - sqrt[x - sqrt(y)/2] = 1
sqrt[x + sqrt(y)/2] = 1 + sqrt[x - sqrt(y)/2]
x + sqrt(y)/2 = 1 + 2.sqrt[x - sqrt(y)/2] + x - sqrt(y)/2
sqrt(y) - 1 = 2.sqrt[x - sqrt(y)/2]
y - 2.sqrt(y) + 1 = 4x - 2.sqrt(y)
y + 1 = 4x
Becuase x and y are integers, y + 1 must be divisible by 4, so y = -1 (mod 4)
The only number congurent to -1 (mod 4) in the answers is 7, and 7+1=4*2, so y=7 and x=2
Alex H
I've been told i got 74. Is that a bronze?
Probable a silver. I think it's about 60 for a Bronze, 70 for a silver, 80 for a gold and 90+ to be invited along too BMO1.
Wat did you all put for the continuous curve question?
mik1a
I'm not sure but I said 2, f(x) = x^3 or -x^3
Cool, I said 2.
Loads of my mates put 16 though!
If it was 2, I think it wud be more like f(x) = (x-1)(x+1)x or -x(x+1)(x-1)
I did the SMC today - thought it was harder than the one last year.
I asked my maths teacher about the continuous graph question and she said "16" because you can divide the graph into four sections each of which can be above or below the x-axis. So thats 2*2*2*2 possibilities. I put 12, I tried to draw them all out at the end but gave up and just guessed
I asked my maths teacher about the continuous graph question and she said "16" because you can divide the graph into four sections each of which can be above or below the x-axis. So thats 2*2*2*2 possibilities. I put 12, I tried to draw them all out at the end but gave up and just guessed
Gemini
I did the SMC today - thought it was harder than the one last year.
I asked my maths teacher about the continuous graph question and she said "16" because you can divide the graph into four sections each of which can be above or below the x-axis. So thats 2*2*2*2 possibilities. I put 12, I tried to draw them all out at the end but gave up and just guessed
I asked my maths teacher about the continuous graph question and she said "16" because you can divide the graph into four sections each of which can be above or below the x-axis. So thats 2*2*2*2 possibilities. I put 12, I tried to draw them all out at the end but gave up and just guessed
Lol, damn.
I thought though that as it sed, " Given y=f(x) is a continuous curve", this caused 14 of the combinations to be omitted.
Edit: I've finally understood the question...
deianra
I PUT SIXTEEN!!!!!
I might actually have done okay this year!!!
I might actually have done okay this year!!!Cool.
Lol, this one is looking like my worst year.
When I first tried this Q I completely missed the point. I tried to figure out equations that would fit the graph...and got completely stuck 
Everyone else that I know who took it said that, even my maths teacher at first. But even if you did flip it around the x-axis the graph would still be continuous, just strange
Everyone else that I know who took it said that, even my maths teacher at first
. But even if you did flip it around the x-axis the graph would still be continuous, just strange 
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can someone please explain what principle domain is and why the answer is a not c?Maths
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