cheschirecat
Premium Member
- Joined
- Jun 6, 2010
- Messages
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- Gender
- Male
- HSC
- 2011
Alrighty I'll just be rewriting the answers I got, if I got something wrong feel free to correct me since I'm just doing this off the top of my head with minimal working:
Question 1
a)![](https://latex.codecogs.com/png.latex?\bg_white 3.728)
b)![](https://latex.codecogs.com/png.latex?\bg_white n+5)
c)![](https://latex.codecogs.com/png.latex?\bg_white x=2)
d)
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7B5%7D%7B5x+2%7D)
e)![](https://latex.codecogs.com/png.latex?\bg_white -2%5Cleq%20x)
f)![](https://latex.codecogs.com/png.latex?\bg_white 2%5Csqrt%7B5%7D+2%5Csqrt%7B3%7D)
g)![](https://latex.codecogs.com/png.latex?\bg_white 16)
Question 2:
a)
i)![](https://latex.codecogs.com/png.latex?\bg_white 6)
ii)![](https://latex.codecogs.com/png.latex?\bg_white 2)
iii)![](https://latex.codecogs.com/png.latex?\bg_white 3)
b)
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7B4%5Cpi%20%7D%7B3%7D,%5Cfrac%7B5%5Cpi%20%7D%7B3%7D)
c)![](https://latex.codecogs.com/png.latex?\bg_white y+8x+7=0)
d)
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D=xe%5E%7Bx%7D%282+x%29)
e)
![](https://latex.codecogs.com/png.latex?\bg_white -%5Cfrac%7B1%7D%7B3x%7D+C)
Question 3:
a)
i)![](https://latex.codecogs.com/png.latex?\bg_white 15,000,000)
ii)![](https://latex.codecogs.com/png.latex?\bg_white 3,%20327,%20500,%20000)
b)![](https://latex.codecogs.com/png.latex?\bg_white %283,-1%29)
c)
i) Distance formula
ii)![](https://latex.codecogs.com/png.latex?\bg_white m_%7B1%7D%5Ctimes%20m_%7B2%7D=-1)
iii) perpendicular distance formula
iv)
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7B9%7D%7B5%7D)
v)
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7B54%7D%7B25%7D)
Question 4:
a)
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7Bsinx-xcosx%7D%7Bsin%5E%7B2%7Dx%7D)
b)![](https://latex.codecogs.com/png.latex?\bg_white 10)
c)![](https://latex.codecogs.com/png.latex?\bg_white y=3x%5E%7B2%7D-2x-1)
d)
i)
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D=%5Cfrac%7B-x%7D%7B%5Csqrt%7B9-x%5E%7B2%7D%7D%7D)
ii)![](https://latex.codecogs.com/png.latex?\bg_white -6%5Csqrt%7B9-x%5E%7B2%7D%7D+C)
e)
and ![](https://latex.codecogs.com/png.latex?\bg_white -2%5Cleq%20x%5Cleq%202)
or:
![](https://latex.codecogs.com/png.latex?\bg_white y\leq%204-x^{2})
![](https://latex.codecogs.com/png.latex?\bg_white y\geq%20\left%20|%20x%20\right%20|-2)
Question 5:
a)
i)![](https://latex.codecogs.com/png.latex?\bg_white 55296)
ii)![](https://latex.codecogs.com/png.latex?\bg_white n=20)
iii)![](https://latex.codecogs.com/png.latex?\bg_white 553)
b)
i)![](https://latex.codecogs.com/png.latex?\bg_white 0.6)
ii)![](https://latex.codecogs.com/png.latex?\bg_white 0.1)
iii)![](https://latex.codecogs.com/png.latex?\bg_white 0.3)
c)![](https://latex.codecogs.com/png.latex?\bg_white 2831%5Cfrac%7B2%7D%7B3%7Dm)
Question 6:
a)
i)![](https://latex.codecogs.com/png.latex?\bg_white 108%5E%7B%5Ccirc%7D)
ii) proof (might add it later)
b)![](https://latex.codecogs.com/png.latex?\bg_white %5Ctext%7BCircle%20with%20center%20%281,0%29%20and%20radius%204%7D)
c)
i)![](https://latex.codecogs.com/png.latex?\bg_white P%280,2%29)
ii)![](https://latex.codecogs.com/png.latex?\bg_white 2)
iii)![](https://latex.codecogs.com/png.latex?\bg_white C)
iv) 8
v)![](https://latex.codecogs.com/png.latex?\bg_white -2)
Question 7:
a)
i)
minimum turning point:![](https://latex.codecogs.com/png.latex?\bg_white %281,0%29)
Maximum turning point:![](https://latex.codecogs.com/png.latex?\bg_white %28-1,4%29)
Point of inflextion:![](https://latex.codecogs.com/png.latex?\bg_white %280,2%29)
ii) graph
b)
i)![](https://latex.codecogs.com/png.latex?\bg_white %5Ctext%7BWhen%20%7Dt=0,%20%5Cdot%7Bx%7D=0)
ii)![](https://latex.codecogs.com/png.latex?\bg_white e%5E%7B-2t%7D%3E%200%20%5Ctherefore%20%5Cddot%7Bx%7D%3E0)
iii)![](https://latex.codecogs.com/png.latex?\bg_white %5Ctext%7BWhen%20%7Dt%3E%200%20%5Ctext%7B,%20%7De%5E%7B-2t%7D%3C%201%5Ctherefore%20%5Cdot%7Bx%7D%3E%200)
iv)![](https://latex.codecogs.com/png.latex?\bg_white 8)
v) graph
Question 8:
a)
i) proof
ii)![](https://latex.codecogs.com/png.latex?\bg_white 24km)
b)
i)![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7B%5Cpi%20h%5E%7B2%7D%7D%7B2%7D)
ii)![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7B1%7D%7B2%7D)
c)
i) proof
ii) 1) proof 2)![](https://latex.codecogs.com/png.latex?\bg_white 1514.48)
Question 9:
a)
i) proof (might post later if someone wants it)
ii) proof (ditto, involves proving triangles BFC and DFE are similar)
b) i) proof
ii)![](https://latex.codecogs.com/png.latex?\bg_white 8)
c) graph
d) i)
ii)![](https://latex.codecogs.com/png.latex?\bg_white 9)
Question 10:
a)
i)![](https://latex.codecogs.com/png.latex?\bg_white 5.987%5Ctimes%2010%5E%7B-8%7D)
ii)
(or maybe 89)
iii)![](https://latex.codecogs.com/png.latex?\bg_white 10%5Cln%202)
b)
i) proof
ii) proof
iii)![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac1%7B%7D4%7B%7DP)
iv)![](https://latex.codecogs.com/png.latex?\bg_white 2)
v) Only possible to construct a Paddock in the shape of a sector if:
![](https://latex.codecogs.com/png.latex?\bg_white 0%3C%5Cvartheta%3C%202%5Cpi)
Rearranging i):
![](https://latex.codecogs.com/png.latex?\bg_white %5Cvartheta=%5Cfrac%7Bp%7D%7Br%7D-2)
Therefore:
![](https://latex.codecogs.com/png.latex?\bg_white 0%3C%5Cfrac%7Bp%7D%7Br%7D-2%3C2%5Cpi)
Rearranging:
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7Bp%7D%7B2%5Cpi%20+1%7D%3Cr%3C%5Cfrac%7Bp%7D%7B2%7D)
Apologies in advance for poor formatting.
Question 1
a)
b)
c)
d)
e)
f)
g)
Question 2:
a)
i)
ii)
iii)
b)
c)
d)
e)
Question 3:
a)
i)
ii)
b)
c)
i) Distance formula
ii)
iii) perpendicular distance formula
iv)
v)
Question 4:
a)
b)
c)
d)
i)
ii)
e)
or:
Question 5:
a)
i)
ii)
iii)
b)
i)
ii)
iii)
c)
Question 6:
a)
i)
ii) proof (might add it later)
b)
c)
i)
ii)
iii)
iv) 8
v)
Question 7:
a)
i)
minimum turning point:
Maximum turning point:
Point of inflextion:
ii) graph
b)
i)
ii)
iii)
iv)
v) graph
Question 8:
a)
i) proof
ii)
b)
i)
ii)
c)
i) proof
ii) 1) proof 2)
Question 9:
a)
i) proof (might post later if someone wants it)
ii) proof (ditto, involves proving triangles BFC and DFE are similar)
b) i) proof
ii)
c) graph
d) i)
ii)
Question 10:
a)
i)
ii)
iii)
b)
i) proof
ii) proof
iii)
iv)
v) Only possible to construct a Paddock in the shape of a sector if:
Rearranging i):
Therefore:
Rearranging:
Apologies in advance for poor formatting.
Last edited: