SC mathematics Marathon (2 Viewers)

dionb2014

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Yeah just like the science Marathon Guys and girls. Just show your working and whatever.
What is the line perpendicular to -
Y=2x+7
 

reality3435

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not trying to burst your bubble but isn't maths a little hard to ask over the net?

anyhow

m1 = 2 (given)
m1 * m2 = -1 (product of gradients of perpendicular lines is -1)
2m2=-1
m2=-1/2

:. the gradient of the line perpendicular to y = 2x+ 7 is -1/2

For what values of a is Y=ax a tangent to y= (x^2) - x -2 (sorry i'm not sure if this is school cert standard)?
 

dionb2014

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You would think so but I have seen extension 2 math marathons with hundreds of Posts. Probs thousands.
 

dionb2014

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It will obviously be better to go into the exam with experience in harder questions than just hard enough. What band are you aiming for.
Q)
 

bleakarcher

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not trying to burst your bubble but isn't maths a little hard to ask over the net?

anyhow

m1 = 2 (given)
m1 * m2 = -1 (product of gradients of perpendicular lines is -1)
2m2=-1
m2=-1/2

:. the gradient of the line perpendicular to y = 2x+ 7 is -1/2

For what values of a is Y=ax a tangent to y= (x^2) - x -2 (sorry i'm not sure if this is school cert standard)?
Let:
y1=ax
y2=x^2-x-2
When y1=y2,
x^2-(a+1)x-2=0
Discriminant=(a+1)^2-4(-2)=a^2+2a+9
In order for the line y=ax to be tangent to the parabola, the discriminant must be 0,
a^2+2a+9=0
Discriminant=2^2-4(9)=-32 which is less than 0
Hence, there are no values for a over R for which the line is tangent to the parabola
 

nightweaver066

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Why are people posting questions irrelevant to the SC or even year 10?

 

bleakarcher

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Why are people posting questions irrelevant to the SC or even year 10?

a) Kite.
b) 62 cm
c) A=(1/2)bh=(1/2)*24*7=84 cm^2
d) i) By the Pythagorean theorem:
AC=sqrt[7^2+24^2]=25 cm
ii) Let the length of BD be x.
(1/2)x*25=2*84
x=[2*2*84]/25=13.44 cm
 
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It will obviously be better to go into the exam with experience in harder questions than just hard enough. What band are you aiming for.
Q)
Band 6 of course :) I agree it's better to experience harder questions before an exam, but SC maths questions are on a whole new level. That's not to say there aren't any odd questions here and there, plus it's easy to get too cocky and make silly mistakes.
 

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