VCE Specialist 3/4 Question Thread!

[pi]

Just wondering are we required to know about similarity and congruency for triangles in specialist maths???

That is something you should have learnt in high school maths, so I'd say it's assumed knowledge for Methods and Spesh.

[Splash-Tackle-Flail]

With trigonometric functions, do we need to know how to prove all the trig symmetrical properties, or just be able to apply them?

[keltingmeith]

With trigonometric functions, do we need to know how to prove all the trig symmetrical properties, or just be able to apply them?

If by symmetry properties, you mean and the similar, one great way of doing these is to think of translations made on the actual graph.

[grannysmith]

How do I factorise the following by inspection?

if is a factor.

[keltingmeith]

How do I factorise the following by inspection?

if is a factor.

First thing I'd do is expand it out:



Next, I'd play with it until I had a bunch of terms with a z-2i in it:



Now we can factorise that z-2i out:



To further factorise, I would use the quadratic equation on the second factor to find its factors, and then state in fully factorised form.

EDIT: So apparently I missed that that quadratic factorises nicely LOL. See kinslayer's post below for its nice factorisation~

[kinslayer]

Alternatively, using the knowledge that (z-2i) is a factor, we can write the following:



(I did this because the coefficient on is 1 and the constant term is 6i.)

Now expand:



Now compare to the original form of P(z) and equate coefficients. Looking at the coefficient on z, we must have that . That means a = -2 and



edit: A third way would be to simply note that , which is usually what is meant by factoring "by inspection"...

[SE_JM]

Hello,
Could someone please help me with this question?
Find the area of the region between an equilateral triangle of side length 10 cm and the circumcircle (the circle that passes through  the three vertices of the triangle).

Thank you!!

[kinslayer]

Hello,
Could someone please help me with this question?
Find the area of the region between an equilateral triangle of side length 10 cm and the circumcircle (the circle that passes through  the three vertices of the triangle).

Thank you!!

http://en.wikipedia.org/wiki/Equilateral_triangle

If is the sidelength of the triangle, the radius of the circumscribed circle is . To derive this, look at the diagram under "Principal Properties" and consider the right-angled triangle formed with the line as hypotenuse.

We have (where r = h_a)

But , so .

The area of the region is the area of this circle less the area of the triangle. Hopefully you can do the rest!

[SE_JM]

Sorry,
I still don't get it
I'm doing 1&2 right now. Could you explain in more detail?
Thank you

[Eiffel]

Show that the minimum value of the gradient to the curve

why do you need to find f''(x) and let it equal 0, get this value of x and sub into f'(x) ?

if i let f''(x) = 0 , isn't this telling me the point of inflection for f(x). ?

what about:  Find the maximum value of the gradient to the curve y = 10 + 3x^2 − 2x^3.

[pi]

Maximum value of f(x) -> f'(x)=0 etc.
Maximum value of gradient of f(x) -> maximum value of f'(x) -> f''(x)=0 etc.

[Eiffel]

Maximum value of f(x) -> f'(x)=0 etc.
Maximum value of gradient of f(x) -> maximum value of f'(x) -> f''(x)=0 etc.

wait can you explain, because if i let f'(x) = 0 this tells us the x values of f(x) where m = 0, how is this a maximum gradient

[pi]

wait can you explain, because if i let f'(x) = 0 this tells us the x values of f(x) where m = 0, how is this a maximum gradient

That's my first line, not my second line, see common parts in bold!

Maximum value of f(x) -> f'(x)=0 etc.
Maximum value of gradient of f(x) -> maximum value of f'(x) -> f''(x)=0 etc.

Maximum gradient is what is written in the second line, if your "gradient function" is f'(x) (ie. derivative of f(x)), then you need to derive one more to find the maximum of that GRADIENT function.

[kinslayer]

Sorry,
I still don't get it
I'm doing 1&2 right now. Could you explain in more detail?
Thank you

No worries. First go to the link I posted. Circumcircle is another word for "circumscribed circle" and the radius of the circle is given in the article (sqrt(3)/2 * a, where a = 10).

Now you have the radius of the circle, and you can work out the area of the circle. The area of the bit between the circle and the triangle is the area of the circle take away the area of the triangle, which is half the base times the height. The base you know is equal to 10cm. Now make a right-angled triangle with adjacent side 5cm and angle 60 degrees, and use trigonometry (remember SOHCAHTOAH) to calculate the height.

Now you have both areas and you can subtract one from the other to get the answer.

[knightrider]

When they are using triangles and shapes to describe angles.

What does it mean when they say and and

what angles are they referring to in a triangle.

Say they let one point be a, and the other two b and c.

Can someone show me an example with a triangle and what exactly these angles are referring to?

Thanks