Standard Math Q+A Thread

[stephanieazzopardi]

Hi all!

Is anyone able to explain how to work out simultaneous equations? Both the substitution and elimination method.
Thank you all

Hey Dani!

It was lovely meeting you yesterday, and i hope you got lots out of the lectures!

Ok. Simultaneous equations.
Let's look at the Substitution Method first:
Say we have to solve 2x + y = 7 and x = y - 4. Let's go through it step-by-step.
1) Number the equations (1) and (2)
2x + y = 7 (1)
x = y - 4 (2)
Note: If your equations are not in this form, try and make y or x the subject of at least one of the equations by rearranging them

Substitute (2) into (1)
2(y - 4) + y = 7

Expand, simplify and solve
2y - 8 + y = 7
2y + y = 15
3y = 15
y = 5

Substitute y = 5 into (2)
x = 5 - 4
x = 1

Write final points of intersection
x = 1, y = 5
So 1, 5.

Now, let's look at how we would solve the same two sets of equations simultaneously using the Elimination Method
Number the equations (1) and (2)
2x + y = 7 (1)
x = y - 4 (2)

Make y the subject of both equations because the two coefficients of y are equal
y = -2x + 7 (1)
y = x + 4 (2)

Subtract (2) from (1). Note: the order doesn't matter
0 = -3x + 3
Further explanation:
y - y = 0
-2x - x = -3x
7 - 4 = 3

Rearrange and solve
3x = 3
x = 1

Substitute x = 1 into (2)
y = 1 + 4
y = 5

Write final points of intersection
x = 1, y = 5
So 1, 5.

By the way, if you are asked to solve two sets of equations simultaneously, then pick the method that you find easiest and solve it like that. As you can see from the example above, you will always end up with the same answer, whether you are using the substitution or elimination method. I personally prefer the substitution method because I find it easier/faster. In the exam, they can specify for you to use either substitution or elimination method so make sure you know both really well! I really hope this helped and thank you for using the forums!

[Gregs]

Hi I was just wondering if anyone could help me with the CSSA trial exam question 28b)

The following formula can be used to calculate the number of standard drinks in a container of alcoholic beverage:

N=VA/1.27

Where:
N= number if standard drinks
V= volume of container in litres
A= the percentage of alcohol in the drink (%alc/vol)

White wine has 11.5% alc/vol.

How many millilitres of white wine is equivalent to one standard drink? Answer to the nearest millilitre

Cheers, Gregs

[RuiAce]

Hi I was just wondering if anyone could help me with the CSSA trial exam question 28b)

The following formula can be used to calculate the number of standard drinks in a container of alcoholic beverage:

N=VA/1.27

Where:
N= number if standard drinks
V= volume of container in litres
A= the percentage of alcohol in the drink (%alc/vol)

White wine has 11.5% alc/vol.

How many millilitres of white wine is equivalent to one standard drink? Answer to the nearest millilitre

Cheers, Gregs

[Gregs]

Thanks for that, it helped a lot
I was dividing it by 11.5% rather than just 11.5 so i was getting ~11 000ml
couldn't wrap my head around it

[RuiAce]

Thanks for that, it helped a lot
I was dividing it by 11.5% rather than just 11.5 so i was getting ~11 000ml
couldn't wrap my head around it

Yeah I suspect that's going to be a common mistake. My advice is just to double check the units whenever they give you them. For that question the units actually included the percentage sign as is.

[unnecessaryfeelings]

**This is my first post in this website so hopefully this is how you do it!! haha**

I really suck when it comes to conversions *such as MB to GB, cm^3 to L, Watts to Kilowatts* because I don't really know much from them as I only done General Math 2 in Year 12 and only know whats on the formula sheet haha

Is there a sheet or a summary of all the conversions that I need to know in terms of measurement?

-Nicole

[jamonwindeyer]

**This is my first post in this website so hopefully this is how you do it!! haha**

I really suck when it comes to conversions *such as MB to GB, cm^3 to L, Watts to Kilowatts* because I don't really know much from them as I only done General Math 2 in Year 12 and only know whats on the formula sheet haha

Is there a sheet or a summary of all the conversions that I need to know in terms of measurement?

-Nicole

Hey Nicole! Welcome to the forums!

Steph's Mathematics General 2 Notes have just what you need:





You can purchase the full set of notes here!

Let me know if you need a hand finding things around the site!

[stephanieazzopardi]

**This is my first post in this website so hopefully this is how you do it!! haha**

I really suck when it comes to conversions *such as MB to GB, cm^3 to L, Watts to Kilowatts* because I don't really know much from them as I only done General Math 2 in Year 12 and only know whats on the formula sheet haha

Is there a sheet or a summary of all the conversions that I need to know in terms of measurement?

-Nicole

Hey Nicole! In addition to Jamon's post (which I thank him for), these are some capacity formulas worth knowing

Hope that all helps 

[Daliaradosevic]

Hey so I was just wondering whats the best most effective way to study finance maths because no matter how hard I try and do multiple practice questions of all weighing (hard or easy) I never seem to understand it!! Please suggest some ideas thank you!!

[jamonwindeyer]

Hey so I was just wondering whats the best most effective way to study finance maths because no matter how hard I try and do multiple practice questions of all weighing (hard or easy) I never seem to understand it!! Please suggest some ideas thank you!!

Are you attempting the questions with your notes open and your formulas accessible? If not, that's the best way to start, make it as easy on yourself as possible

Otherwise, you might need to just re-teach yourself! This happens to me to, sometimes I just need to start from scratch and learn a whole topic again; usually I come away with an even stronger understanding than I had the first time I learned it. Try using your textbook, Youtube videos, anything you can find! Otherwise, feel free to post some specific questions here and we'll do our best to step you through them

[kmorritt]

Hi, Ive been struggling to understand how to find an obtuse angle for this question. As you can see i got the first two completely wrong.
Could you please help? Thanks

[RuiAce]

Hi, Ive been struggling to understand how to find an obtuse angle for this question. As you can see i got the first two completely wrong.
Could you please help? Thanks

It's actually a bit hard to see the question; the diagram is a bit too small and thus the writing has gone tiny. So I can't exactly do the question.

So here's some advice. With cos(theta) = something negative, you can just say theta = cos^-1(that negative thing)
With sin(theta) = something negative, however, you actually have to do theta = sin^-1(that negative thing) + 180^o

I'm not too sure how they teach it in general to tailor a response that's perfectly helpful though

[jamonwindeyer]

Hi, Ive been struggling to understand how to find an obtuse angle for this question. As you can see i got the first two completely wrong.
Could you please help? Thanks

Hey there!! So I'm going to confer with our General Lecturer on this, because I believe this is something that's a tad beyond the scope of the General course. It's in there, but right on the edge, because the syllabus asks you to:

- Establish the ratios for obtuse angles using a calculator
- Determine the sign of the ratios for obtuse angles

At no stage are you asked to specifically find obtuse angles, so this is borderline

In any case, let me lend a hand with the first of those questions!



So we've got a negative angle here, uh oh! This doesn't make sense in this scenario, and as Rui correctly says, we fix this by adding 180 degrees to the angle. So:



You don't need to understand why it works, you just need to understand THAT it works (unless Steph comes along tomorrow and wrecks me for saying that)

I'm not sure how much of this you need to know; because there is a whole set of rules in place to handle all sorts of different circumstances and finding obtuse angles. Note that for you, it will be far more common to be using the sine/cosine rules to find obtuse angles, not the trig ratios! I'll ask Steph to stop by tomorrow and perhaps shed some light on this for us

[kmorritt]

Hey there!! So I'm going to confer with our General Lecturer on this, because I believe this is something that's a tad beyond the scope of the General course. It's in there, but right on the edge, because the syllabus asks you to:

- Establish the ratios for obtuse angles using a calculator
- Determine the sign of the ratios for obtuse angles

At no stage are you asked to specifically find obtuse angles, so this is borderline

In any case, let me lend a hand with the first of those questions!



So we've got a negative angle here, uh oh! This doesn't make sense in this scenario, and as Rui correctly says, we fix this by adding 180 degrees to the angle. So:



You don't need to understand why it works, you just need to understand THAT it works (unless Steph comes along tomorrow and wrecks me for saying that)

I'm not sure how much of this you need to know; because there is a whole set of rules in place to handle all sorts of different circumstances and finding obtuse angles. Note that for you, it will be far more common to be using the sine/cosine rules to find obtuse angles, not the trig ratios! I'll ask Steph to stop by tomorrow and perhaps shed some light on this for us

Hi Daliaradosevic and Jamon,
Thank you so much this does help me work out the question. I know its not a big part of the syllabus and abit beyond general maths, thats why I was suprised I found a question on it.
Youre working out is very clear and easy to understand Jamon, thank you.
When I originally tried to do it I was confused as to why if im finding an obtuse angle, the number wasnt bigger than 180, but now i understand to add 180.
Thanks again

[stephanieazzopardi]

Hi Daliaradosevic and Jamon,
Thank you so much this does help me work out the question. I know its not a big part of the syllabus and abit beyond general maths, thats why I was suprised I found a question on it.
Youre working out is very clear and easy to understand Jamon, thank you.
When I originally tried to do it I was confused as to why if im finding an obtuse angle, the number wasnt bigger than 180, but now i understand to add 180.
Thanks again

Hi kmorritt, was going to post a 'General Math' friendly explanation, but it seems that you understand their explanations so I'm very glad Please keep asking questions if need be, and good luck!