methods Questions - Merspi

What should my average test/SAC score be to get a 35 study score in methods?

2010-07-29T22:41:46Z

a raw 35, before it gets scaled.

Finding the rate of change of the angle of elevation

2010-05-01T13:07:26Z

An airplane is flying in a straight horizontal direction and at a constant height of 5000 metres. The angle of elevation of the airplane from a fixed point of observation is α. The speed of the airplane is 500km/hr.

What is the rate of change of angle α when it is 25 degrees? Express the answer in degrees/second and round to one decimal place.

How important is 'formatting' to examiners?

2010-07-28T10:40:21Z

The 2008 Math methods VCAA exam presented the following question:

Let y = (3x^2 – 5x)^5. Find dy/dx

The examiner's solution was:

Let f(x) = (3x2 – 5x)^5 = u^5 , u = 3x^2 – 5x then f 1(x) = 5(6x – 5)(3x^2 – 5x)^4

Are we expected to hold true to the conventions if we are to gain marks here?

If instead we had written this in our booklets, exactly as below without any (f(x)) or additional explanation like u=..., or any other additional things like that, would we get the marks?

(6x-5) (3x^2 -5x)^4 5(6x-5)(3x^2 -5x)^4

I'm not asking about the actual answer which is true, but the 'formatting' and presentation.

What are all the relationships between sin and cos?

2010-07-20T08:30:35Z

What are all the relationships between sin and cos?

I know that they are derivatives of one another (with modification) and also that when they are squared and added together they produce 0. What other rules relate them to one another or to something together?

Could you show me an integration problem with a +/- sign

2010-07-20T08:10:25Z

Could you show me an integration problem with a +/- sign in the function you are asked to integrate. Please provide the solution to it too. Thank you.

How do you find the exact solution of this trigonometric problem?

2010-07-21T07:53:17Z

How do you find the exact solutions of:

2 sin(2 pi x) cos(2 pi x)+sqrt(3) (2 pi x) = 0

How do I solve this quartic equation?

2010-06-02T11:11:44Z

I know 3 points: (0,0) (34,3) and (68,0)
I also know the gradient at the origin (0,0) is -0.123,
and the gradient at (68,) is 0.123

If the general equation is y = ax⁴ + bx³ + cx² + dx + e

How do I find a, b, and c? I know that d = -0.123 and e = 0.

Please help! :(

Is the period of |sin 4x| equal to pi/4 or pi/2?

2010-06-09T00:16:21Z

Is the period of |sin 4x| equal to π/4 or π/2?

Wouldn't it be π/4, since we go '2π over n'? The solution says it is π/2 instead.

How do I do 'CDF' stuff on the CAS calculator?

2010-07-06T15:29:34Z

How do I do 'CDF' and 'PDF' stuff on the CAS calculator?

What does discrete have to do with rounding off?

2010-07-06T14:52:26Z

Since X represents discrete values, Pr(1.488 <= x <= 5.272) become Pr(2<=X<=5).

I don't understand the logic here. What does discrete have to do with rounding off?

How do I solve this linear approximation question?

2010-05-02T00:42:03Z

Show that f(x)=1/(2-x) can be approximated by f(x)=(1/2)+(x/4) for x close to 0.

I am sure this is a linear approximation question, but I don't get it at all. Could I please have some help? Thanks so much.

Finding equations for graphs of exponential functions

2010-03-22T11:06:03Z

Find the values of b and B if the general equation of the graph shown is y = ex + b + B. Give your answers correct to 2 decimal places.

I was not able to use simultaneous equations to solve this:

I ended up with: e^1+b +e^b = -4

From there, factorizing was no good....

Can you show me the steps through this?

Indicies in matrices

2010-05-23T06:53:34Z

How do we raise things to 'powers' and 'inverse powers' in matrix form or using matrix method?

Chemistry and math

2010-07-03T08:51:59Z

Why does the term equilibrium constant get used when equilibium isn't constant, it's dynami

Also, when you are doing mathematical proofs, can you prove things by simplifying everything down to (change both sides) so that it is:

1=1

or do you HAVE to make one side's form change so it matches the other, which is harder.

Is the 'mean' or 'average' the same in meaning to the 'expected value'

2010-07-04T09:55:35Z

Is the 'mean' or 'average' the same in meaning to the 'expected value'

Solving two equations simultaneously

2010-01-21T19:57:27Z

Hi all!

Using simultaneous equations - how can we solve y = x + 2 and y = (2/(x+1)) - 1?

Thanks!

How does the change-of-base log formula work?

2010-04-26T10:20:21Z

Can somebody please explain how this formula works?

log_bx = log_ax / log_ab

How would you perform matrix transformations to non-linear graphs?

2010-02-21T06:25:07Z

How would you you apply matrix transformations that adjust the 'axis' using trigonometric values - to quadratics and all sorts of graphs other than the 'linear' graphs that are dealt with in my year 11 math methods book?

Integrate 1/(x^2 +x+2)

2010-06-18T05:46:03Z

Can't remember how to do these :(

Integrate 1/(x^2 +x+2)

How do I change this into a single fraction?

2010-06-09T00:06:05Z

How do I put:

2 sqrt(x² + 3) + x(2x+1)/sqrt(x² + 3) into a single fraction?

If cos x = 0.75, determine the value of sin(3pi/2 - x) + cos(pi + x)

2010-05-20T07:54:47Z

Really stuck with this one, don't recall doing these in the text book

How do we determine the exact value of 4cos(7pi/6), 8sin(5pi/4) and tan(7pi/3)?

2010-05-19T12:15:35Z

I know it's suppose to be basic, but I somehow forgot them =P

4cos(7pi/6) 8sin(5pi/4) tan(7pi/3)

Can you direct me to a good video to learn probability?

2010-05-01T09:51:11Z

Could you direct me to a relevant video that covers only (or mostly, or only slightly more) than what is relevant to VCE Math Methods Unit 4 Probability chapter? One example I've found is on youtube by a publisher called 'KhanAcademy', but it is not quite as relevant as it could be - since video's like this are usually made for a wider audience. Can you direct me to a good video to learn this chapter?

How do I solve this exponentials/algebra question?

2010-05-11T23:39:06Z

The number of a type of bacteria is modelled by the formula n = A(1-e^-Bt) where n is the size of the population at time t hours. A and B are positive constants. When t=2, n=10000 and when t=4, n=15000. Show that 2e^-4B-3e^-2B+1=0

I've tried using simultaneous equations in various ways but had no luck so far.

Thanks

Solve this linear approximation question

2010-05-02T09:17:28Z

Given that y = x⁴ - 5x³, find in terms of a the approximate increase in y as x increases from 2 to 2+a where a is small.

Thank you!

Should I include units in differentiation problems?

2010-04-07T04:28:11Z

Should we include (and will we be marked down if we don't) units like: m²/sec when answering questions on the rate of change in differentiation questions?

And, I understand that when finding the anti-derivative of a gradient function, where the x axis is located is irrelevant (since there is unknown +C value). However, how do I determine how long each of the arms of the actual function should be? Are they proportional to the gradient function's "arms"?

For example: if there was a 2 cm gradient function straight line, and after the 2 cm it reaches the x-axis and it has its own gradient is negative. Then, would the quadratic of order 2 that forms have an "arm" that goes up to its maximum or minimum after 2 cm?

How do I find the base value of a logarithm and exponential so that there is only one intersection?

2010-04-04T12:50:41Z

Hey, I'm having difficulty with this question, any help appreciated!

If a^x = log_a(x) has exactly one solution, find the value of a correct to three decimal places.

Solutions Error in Differentiation Chapter of Maths Quest 12?

2010-04-07T05:42:56Z

I believe there is an error in the Maths Quest 12 Differentiation Chapter 7 (Q7j)

Shouldn't the answer be [4,∞) because of the 4 in bold?

Back of book solutions: (4,∞)

When can I use the "union" in set notation for writing domains?

2010-04-06T02:09:40Z

I've seen domains in the following form:

(-∞,-2) U (3,∞).

So is it equally valid to use the following form as well?

x < -2 U x > 3

How is this dilated?

2010-04-05T08:18:38Z

I had a question to ask how 2log_e(3x+6)-1 was transformed from log_e(x)

I said:

Dilated from the x axis by a factor of 2
Dilated from the y axis by a factor of 1/3
Translated 1 unit down
Translated 2 units left

However, the answers omit the "Dilated from the y axis by a factor of 1/3"

Is this a misprint or am I wrong in this instance?