Mathematics Question Thread

[amelia20181]

how do you do this

use simpson's rule to find an approximation for

[amelia20181]

need help with an integration question

use the trapezoidal rule to find an approximation for

[emily_p]

how do you do this

use simpson's rule to find an approximation for

need help with an integration question

use the trapezoidal rule to find an approximation for

Attached two photos of calculations.

First image (Simpson’s Rule Q)
6 subintervals/strips means 7 function values
- work out width of each strip using h = (b-a)/n
- work out each x value for the function values
- work out each y value for the corresponding x value
- substitute into the Simpson’s Rule formula

For Trapezoidal rule question you’re given the function values, so:
- find out width of strips
- sub into Trapezoidal Rule formula

Hope this helps! If you aren’t sure about anything let me know and I’ll try to clarify.

[amelia20181]

how do you do

[S200]

how do you do

For question 14

This graph is the inverse to an exponential graph.
Take the graph of y=e^x, and reflect it across the line y=x

The domain of the first becomes the range of the second and vice versa...

[envisagator]

how do you do

By this stagye in hsc maths you should be quite familiar with the basic graph of y=lnx
For a recap, Domain refers to what values of x the curve exists
Range: refers to what y values exists for the curve.

So, the domain for y=lnx = x>0, and range is all real y
If you are unsure how this came about, use Geogebra - its a graphing calculator, helps with determining domain and range if you cant picture what the curve looks like.
https://www.geogebra.org/graphing

[envisagator]

For question 14

This graph is the inverse to an exponential graph.
Take the graph of y=e^x, and reflect it across the line y=x

The domain of the first becomes the range of the second and vice versa...

It is a good way to figure out the domain and range, but, inverse function is a mathematics extension 1 course.

[S200]

It is a good way to figure out the domain and range, but, inverse function is a mathematics extension 1 course.

Yeah Ok. I don't know my way around HSC maths that well sorry...

[amelia20181]

how do you sketch curves with exponentials

which textbook do you think its best to use for 2unit maths? Is grove the easiest textbook

Mod Edit: Post merge, use Modify to avoid posting twice in a row!

[vic321]

how do you sketch curves with exponentials

which textbook do you think its best to use for 2unit maths? Is grove the easiest textbook

Mod Edit: Post merge, use Modify to avoid posting twice in a row!

Hey!

If you're stuck, you could just sub in x values into your calculator and plot them on the number plane. However, it is good to know the basic form of an exponential. You can use desmos, a graphing website to help you if you aren't sure.

Hope that helps

[jamonwindeyer]

how do you sketch curves with exponentials

which textbook do you think its best to use for 2unit maths? Is grove the easiest textbook

Mod Edit: Post merge, use Modify to avoid posting twice in a row!

I'd also suggest checking out this cheat sheet for sketching functions, including exponentials, it might help a bit!

As for textbook - I would say Grove is the easiest one out there. Cambridge tends to be the most difficult. Fitzpatrick is in the middle - At least that is my view. The "best" is a matter of preference I'd say!!

[amelia20181]

how do you do this

[jamonwindeyer]

how do you do this

Hey! So for the first bit, the total cost is given by the the cost per hour, multiplied by the number of hours spent travelling:



Now \(h\) can be found, because we know it is travelling 1500km at a speed of \(s\) kilometres per hour (we assume the units match, at least). So:



So we sub that in above:


The rest of the question is your usual process:

- Differentiate the function
- Find where that derivative is equal to zero to find a maxima/minima for speed
- Prove it is a minimum using second derivative check (or otherwise)
- Sub this speed back into the cost function to get a value

This is something you should have been doing a lot of in this topic, but if you've had trouble with it feel free to post some working and we can try and guide you!

[amelia20181]

also


Mod Edit: Post merge, use 'Modify' to add to your previous posts.

[S200]

also

Shouldn't be that hard to solve from there...

Mod Edit: Fixed LaTex, think the site glitched for a second! - Jamon