Demento's Year 10 maths practice paper thread (2 Viewers)

RealiseNothing

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Yes please



Yes for the love of god you should.



Thank god for people who make youtube videos on maths. Honestly, I don't know what i'd do without those people (srs)
I'll make you a good question.

What topic(s) do you want?
 

Demento1

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Yes please

Yes for the love of god you should.

Thank god for people who make youtube videos on maths. Honestly, I don't know what i'd do without those people (srs)
Don't worry. Spiral will make youtube videos for maths and get over a million subscribers.
 

RealiseNothing

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Any of these topics:

- quadratics
- surds
- coordinate
- trig
- polynomials

those are my okay ones lol i'm not the best at them though
a) Given:



Show that:



Where are distinct roots of the quadratic.


b) Hence state why:



If and


c) Graph if and call this


d) Find the area of the triangle enclosed by the 'x' and 'y' axis, and and call this which stands for "area of "


e) Graph on the same set of axis, given only one of the roots of is positive and it is known that


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


g) Now consider the value of from the last part. Denote the area of the unit circle as

What is the value of if


h) Keep these two values for and

It is given that the area bounded by the 'x' axis, and the line is equal to

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

j) Hence find the ratio of the areas of:

1) Unit circle.
2) The right angled isosceles triangle.
3) A square with side length 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.
 
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HSC2014

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Btw what does it mean by roots? I've seen that word thrown around a lot in polynomials and stuff (I havn't learnt it yet). Does it literally mean.. square root? or is it like basis or something.
 

RealiseNothing

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Btw what does it mean by roots? I've seen that word thrown around a lot in polynomials and stuff (I havn't learnt it yet). Does it literally mean.. square root? or is it like basis or something.
Say we had a function, the roots are the values of 'x' which make that function 0. If you graphed the function, the roots would be where the function crosses the 'x' axis.

For example, let's consider the quadratic:



This can be factored to:



So we want this to be 0 right? That means that or

These are the roots of the quadratic as they are what make it equal to 0.
 

HSC2014

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Say we had a function, the roots are the values of 'x' which make that function 0. If you graphed the function, the roots would be where the function crosses the 'x' axis.

For example, let's consider the quadratic:



This can be factored to:



So we want this to be 0 right? That means that or

These are the roots of the quadratic as they are what make it equal to 0.
Are they the same thing to x-intercepts then?

Edit: Post #100 woot.
 

Fawun

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No one write solutions or hints or anything yet

I wanna try this ALL BY MY SELF
 

Fawun

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Or if you're going to post solutions to something, write it in big red letters or whatever so i know to skip your post
 

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