Mathematics Question Thread

[jamonwindeyer]

For C) ii. I only put my answer as -0.00425 but the BOSTES answer says -0.004252436
Do it matter how many sig figs you put your answer to because the question doesn't really indicate how many sig figs or decimal places to put your answer

Hey! Your answer would definitely be deemed correct - They'd just be providing that to indicate how many places would be likely to appear on your calculator, at a guess?

[Kekemato_BAP]

Can someone explain how sin(x)=sin(π-x)?
On the unity circle and the x-y graph?

[pikachu975]

Yup, the only way I could make it work is that we have an iso. triangle.

You can just angle chase to get the straight angle on the right to be 50 + x + 130 - x and just sub in each option to see which gives 180.

[RuiAce]

You can just angle chase to get the straight angle on the right to be 50 + x + 130 - x and just sub in each option to see which gives 180.

Clarify? Which angles are you chasing?


Also 50+x+130-x is always 180

[michaelalt]

hello ! does anyone know how to do question 18 & 19? its under exponential growth and decay, but I don't know how to do it when no initial value is given.. thank you!

[RuiAce]

hello ! does anyone know how to do question 18 & 19? its under exponential growth and decay, but I don't know how to do it when no initial value is given.. thank you!

Alternatively, we may W.L.O.G. suppose the initial value is 1.

[jamonwindeyer]

hello ! does anyone know how to do question 18 & 19? its under exponential growth and decay, but I don't know how to do it when no initial value is given.. thank you!

Hey, to do this, define an initial amount as \(A_0\). Then you consider the amount at any given time as some multiple of \(A_0\), so for example, 10% more would be \(1.1A_0\). 50% more would be \(1.5A_0\)

Doing it this way, you'll get the \(A_0\) cancelling out in your equations - Give it a go!

[12070]

If you have 4m(m-15)< 0, why does the inequality change so m>0? It makes sense if you logically think about it but how do you know which inequality changes if you couldn't work it out?

[RuiAce]

If you have 4m(m-15)< 0, why does the inequality change so m>0? It makes sense if you logically think about it but how do you know which inequality changes if you couldn't work it out?

[12070]

So when I sketched it I got 0<m<15 because it isn't it basically asking when is the function below the x axis?

[RuiAce]

So when I sketched it I got 0<m<15 because it isn't it basically asking when is the function below the x axis?

Misread the symbol earlier for some reason. Fixing.

[_____]

Going through past trials - I've given the answers so you don't need to work them out. I just don't get why they're right.

1. "Evaluate to 2 significant figures: sin (1/SQRT2)"

I look at this and think of using the sin^-1 button to work out the angle since there's no use of pi and the numbers are found on the sides of the standard 45 degree triangle. So I gave the answer as 45 degrees but it's actually 0.65 (considering it as radians). Does it need to say sin^-1 for it to refer to the sides rather than a radian measure?

2. "A circle has a circumference of 12pi cm. If an angle of pi/3 is subtended at the centre of the circle, find the exact area of the minor segment."

Their answer (having found radius to be 6cm):


Why introduce sine rather than using the radian measure of the angle already given? I think I'm missing something here.

Thanks!

[RuiAce]

Going through past trials - I've given the answers so you don't need to work them out. I just don't get why they're right.

1. "Evaluate to 2 significant figures: sin (1/SQRT2)"

I look at this and think of using the sin^-1 button to work out the angle since there's no use of pi and the numbers are found on the sides of the standard 45 degree triangle. So I gave the answer as 45 degrees but it's actually 0.65 (considering it as radians). Does it need to say sin^-1 for it to refer to the sides rather than a radian measure?

2. "A circle has a circumference of 12pi cm. If an angle of pi/3 is subtended at the centre of the circle, find the exact area of the minor segment."

Their answer (having found radius to be 6cm):
(Image removed from quote.)

Why introduce sine rather than using the radian measure of the angle already given? I think I'm missing something here.

Thanks!

You typed sin and not sin^-1. If it says sin you keep as sin. Of course, you may have typo'd it and actually meant sin^-1

Always assume radians unless specified otherwise. The radian is the standard unit of angular measure in mathematics and degrees just exist because of astronomy. You should never use degrees unless they specify it, or give the circle superscript that hints degrees.

For the second question, they want the area of the minor segment, not sector. Check that you did not attempt to use the wrong formula.

[_____]

You typed sin and not sin^-1. If it says sin you keep as sin. Of course, you may have typo'd it and actually meant sin^-1

Always assume radians unless specified otherwise. The radian is the standard unit of angular measure in mathematics and degrees just exist because of astronomy. You should never use degrees unless they specify it, or give the circle superscript that hints degrees.

For the second question, they want the area of the minor segment, not sector. Check that you did not attempt to use the wrong formula.

Nah I didn't typo it said sin, I was just used to year 11 questions in that format I think. Thanks for clearing that up.

I thought segment == sector, so I was using A = 1/2 r^2 theta. Shouldn't be trusting my school to teach the entire syllabus like that 

[RuiAce]

Nah I didn't typo it said sin, I was just used to year 11 questions in that format I think. Thanks for clearing that up.

I thought segment == sector, so I was using A = 1/2 r^2 theta. Shouldn't be trusting my school to teach the entire syllabus like that 

A segment is not a sector.

A sector looks like what happens when you slice a pizza. A segment is just one random slice. You might be able to find some images on google quite easily.


They can easily ask you for the sine of something that doesn't appear to be an angle. If it says sin and not sin^-1 it's likely it was intended to be that way to trick you.