Demento's Year 10 maths practice paper thread (1 Viewer)

Demento1 · Sep 30, 2012

Fawun said:
yes

everythings positive

Here is your chance to impress me and beat me at my 'own game'. Maths was never my best subject, although I wish it seemed so to me.

Fawun · Sep 30, 2012

lolnope cant even do the first question let alone any of the questions

how is this a fawun friendly test lmao

kazemagic · Sep 30, 2012

HSC2014 said:
LOL. DON'T MAKE IT SOUND SO SIMPLE. I struggled on that for weeks. The concept of it and harder questions hurt your head.

cant even rmbr on how to do them lol

RealiseNothing · Sep 30, 2012

Fawun said:
lolnope cant even do the first question let alone any of the questions

how is this a fawun friendly test lmao

Do you know sum and products of roots for a quadratic?

kazemagic · Sep 30, 2012

RealiseNothing said:
a) Given:

$f(x) = ax^2 + bx + c$

Show that:

$-\frac{b}{c} = \frac{1}{\alpha} + \frac{1}{\beta}$

Where $\alpha ~$and$~ \beta$ are distinct roots of the quadratic.

b) Hence state why:

$\frac{b}{c} > \frac{1}{\alpha} + \frac{1}{\beta}$

If $b > 0$ and $c > 0$

c) Graph $f(x)$ if $a = 0$ and call this $g(x)$

d) Find the area of the triangle enclosed by the 'x' and 'y' axis, and $g(x)$ and call this $A_{g(x)}$ which stands for "area of $g(x)$ "

e) Graph $f(x)$ on the same set of axis, given only one of the roots of $f(x)$ is positive and it is known that $|\alpha| > \frac{c}{b} ~$and$~ |\beta| > \frac{c}{b}$

f) Consider now that the line $y=c$ is a tangent to the unit circle. What is the only possible value of $c$ ?

g) Now consider the value of $c$ from the last part. Denote the area of the unit circle as $A_{UC}$

What is the value of $b$ if $4A_{g(x)} = A_{UC}$

h) Keep these two values for $c$ and $b$

It is given that the area bounded by the 'x' axis, $g(x)$ and the line $x=n$ is equal to $A_{UC}$

Find 'n'.

i) Jim can only make unit circles. He can make any integer amount of them as he pleases. He starts off with one unit circle, then adds another next to it, then another, and so on. Show that no matter how many unit circles he has, the combined areas of these unit circles is never equal to the area formed by an isosceles right angled triangle with hypotenuse length $\frac{4}{b}$

j) Hence find the ratio of the areas of:

1) Unit circle.
2) The right angled isosceles triangle.
3) A square with side length $n$ from part (h).

End Of Question

lol that took longer than expected. Not sure if this question is any good or anything, nor if it's too difficulty, but give it a try I guess.

bitch pls im not even gonna look at it. its gonna make me feel bad

Sy123 · Sep 30, 2012

Have y10 learnt

$\alpha + \beta = \frac{-b}{a} \\ \\ for \ \ ax^2+bx+c=0$

Where alpha and beta are roots.?

I had the impression that they were introduced in y11.

HSC2014 · Sep 30, 2012

kazemagic said:
cant even rmbr on how to do them lol

It get's annoying when there is multiple absolute values. And also graphs are just -_____________- y= |x+3|-|1-x| Too many times I got this wrong I don't even want to look at it.

kazemagic · Sep 30, 2012

Sy123 said:
Have y10 learnt

$\alpha + \beta = \frac{-b}{a} \\ \\ for \ \ ax^2+bx+c=0$

Where alpha and beta are roots.?

I had the impression that they were introduced in y11.

well its directed at fawun, so she prob learnt it

Demento1 · Sep 30, 2012

RealiseNothing said:
Do you know sum and products of roots for a quadratic?

I think this is slightly out of the question...

Fawun · Sep 30, 2012

RealiseNothing said:
Do you know sum and products of roots for a quadratic?

???

no

Sy123 said:
Have y10 learnt

$\alpha + \beta = \frac{-b}{a} \\ \\ for \ \ ax^2+bx+c=0$

Where alpha and beta are roots.?

I had the impression that they were introduced in y11.

No

that's why i'm like wth when I read it

RealiseNothing · Sep 30, 2012

Sy123 said:
Have y10 learnt

$\alpha + \beta = \frac{-b}{a} \\ \\ for \ \ ax^2+bx+c=0$

Where alpha and beta are roots.?

I had the impression that they were introduced in y11.

I thought it was done in year 10. Might be wrong. Anyway if anyone doesn't know:

$-\frac{b}{a} = \alpha + \beta$

and

$\frac{c}{a} = \alpha \beta$

Fawun · Sep 30, 2012

HSC2014 said:
It get's annoying when there is multiple absolute values. And also graphs are just -_____________- y= |x+3|-|1-x| Too many times I got this wrong I don't even want to look at it.

Haha that was in my test yesterday. I skipped it and left it blank. Lost 3 marks

SpiralFlex · Sep 30, 2012

RealiseNothing said:
I thought it was done in year 10. Might be wrong. Anyway if anyone doesn't know:

$-\frac{b}{a} = \alpha + \beta$

and

$\frac{c}{a} = \alpha \beta$

Best derive it.

twinklegal19 · Sep 30, 2012

RealiseNothing said:
I thought it was done in year 10. Might be wrong. Anyway if anyone doesn't know:

$-\frac{b}{a} = \alpha + \beta$

and

$\frac{c}{a} = \alpha \beta$

Do they have to prove them?

(it's not that hard, definitely year 10 level)

enoilgam · Sep 30, 2012

Fawun said:
Haha that was in my test yesterday. I skipped it and left it blank. Lost 3 marks

How did you go if you dont mind me asking?

HSC2014 · Sep 30, 2012

Fawun said:
Haha that was in my test yesterday. I skipped it and left it blank. Lost 3 marks

Did you check your solutions to see if they met the conditions !?!?

Fawun · Oct 1, 2012

twinklegal19 said:
Do they have to prove them?

(it's not that hard, definitely year 10 level)

just because you're smart miss twink le gal

Fawun · Oct 1, 2012

enoilgam said:
How did you go if you dont mind me asking?

I haven't gotten my marks back but it was alright. I missed 6 questions that were both worth 3 marks and it was out of 20 altogether so the max I would get is 14/20

THere is still hope of me passing!

HSC2014 said:
Did you check your solutions to see if they met the conditions !?!?

It was a test. How can I check the solutions?! lol

RealiseNothing · Oct 1, 2012

SpiralFlex said:
Best derive it.

twinklegal19 said:
Do they have to prove them?

(it's not that hard, definitely year 10 level)

I really cbf'd getting them to prove it right now. I started making that question at 9:50, finished it at 11:35 or something. Just relaxing now lol.

SpiralFlex · Oct 1, 2012

Can't believe it's been almost 2 years since I first posted in the Year 10 section (though it wasn't called stage 9-10 before)

Time goes by so fast.

What are we discussing about again?

Demento's Year 10 maths practice paper thread (1 Viewer)

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