Project Maths HL and OL help thread

DavTaru

Been looking through this forum for a long time now and i thought it would be a good idea for people who are stuck on maths questions to get solutions and be talked through them by others, if they are willing to help

I'll start it off; i've been stuck on this question for a long time now and hopefully somebody can help me with it!

"The future value F, of an investment is given by the formula f=p(1+i)^t, where P is the present value of the investment, i is the annual rate of interest and t is the time in years. A sum of money P, is invested into a post office account.use logarithms to find the time taken for the investment to double in value if the annual rate of interest is
i)5%
ii)7%
iii)10%

Active maths 4 book 1 page 152

Thanks

Peregrine

I was going to start something like this but I never got around to it.

But unfortunately Dav, I can't help you My teacher haven't done logs with us yet and so I can only do basic things on them.

I'd be happy to help anyone with Algebra(not Logs, Indices or Proofs), Area and Volume, Complex Numbers, Co-Ordinate Geometry, Trig and a few other chapters.

Oh and I use Text and Tests 4, 5, 6 and 7.

yoho139

(I don't know your level, so this may seem a bit condescending as I'll be breaking it all down, which aids understanding - the whole point of Project Maths after all)

Alright, the formula takes the form given, F=P(1+i[latex]$)^t$[/latex]. Breaking down and understanding it will help you figure out the answer so I'll do that first.

F is obviously what you'll have left. P is the sum you put in at first, those two are simple enough. (i+1) is the rate at which the investment will increase. Suppose you have a rate of 5%, at the end of the first year, you'll have 105% of what you started with. The following year, you'll have 105% of what you started that year with.

You'll notice that this means for each year, you multiply it by 1.05. This gives you the ^t part, as you'll multiply it by 1.05 t times.

For the actual answer:
Your investment is to double. This means your final sum, f, should be twice your initial sum, p.
Subbing in 2p for f, .05 for i and leaving t as t, then cancelling terms, we get:
2=[latex]$(1.05)^t$[/latex]

Now, since the variable we're solving for, t, is an exponent, we need to use logs. Getting the log of both sides, we get:
log(2)=log([latex]$1.05^t)$[/latex]

Applying the laws of logs, we get:
log(2)=t(log(1.05))
t=[latex]\frac{log(2)}{log(1.05)}[/latex]
t=14.2067 years

Usually we round up in these cases, but it varies.
You'll notice at the end, the general form is:
t=log(2)/log(1+i)

which will help you solve the others faster.

Tell me if you need anything clarified.

Peregrine

yoho139 wrote: »

(this thing needs superscript...)

Agreed.

But here's some useful alt codes for maths:

Press Alt + these codes.

Alt 248 °
Alt 241 ±

Superscript:
Alt 253 ²
Alt 252 ³
Alt 166 ª

Fractions
Alt 172 ¼
Alt 171 ½
Alt 243 ¾

I hope they work, they've worked for me.

yoho139

Cheers. the one problem with that is that some browsers/devices won't have those symbols included, so the entire meaning can be lost when they're replaced with placeholder symbols.

DavTaru

yoho139 wrote: »

(I don't know your level, so this may seem a bit condescending as I'll be breaking it all down, which aids understanding - the whole point of Project Maths after all)

Alright, the formula takes the form given, F=P(1+i)^t . Breaking down and understanding it will help you figure out the answer so I'll do that first.

F is obviously what you'll have left. P is the sum you put in at first, those two are simple enough. (i+1) is the rate at which the investment will increase. Suppose you have a rate of 5%, at the end of the first year, you'll have 105% of what you started with. The following year, you'll have 105% of what you started that year with.

You'll notice that this means for each year, you multiply it by 1.05. This gives you the ^t part, as you'll multiply it by 1.05 t times.

For the actual answer:
Your investment is to double. This means your final sum, f, should be twice your initial sum, p.
Subbing in 2p for f, .05 for i and leaving t as t, then cancelling terms, we get:
2=(1.05)^t

Now, since the variable we're solving for, t, is an exponent, we need to use logs. Getting the log of both sides, we get:
log(2)=log(1.05^t)

Applying the laws of logs, we get:
log(2)=t(log(1.05))
t=log(2)/log(1.05)
t=14.2067 years

Usually we round up in these cases, but it varies.
You'll notice at the end, the general form is:
t=log(2)/log(1+i)

which will help you solve the others faster.

Tell me if you need anything clarified. (this thing needs superscript...)

Thank you! Im in higher level at the moment.

yoho139

There's a lot of variation within HL, is all. When I explain stuff to classmates, I can adjust the detail based on what I know of their level of understanding... Can't really do the same here.

equivariant

Nimrod 7 wrote: »

Agreed.

But here's some useful alt codes for maths:

Press Alt + these codes.

Alt 248 °
Alt 241 ±

Superscript:
Alt 253 ²
Alt 252 ³
Alt 166 ª

Fractions
Alt 172 ¼
Alt 171 ½
Alt 243 ¾

I hope they work, they've worked for me.

Don't want to derail, but boards supports the latex tag. So, for example, you can easily put something like

[latex]\frac{2^{2^{4}}}{\sqrt{\int_{0}^1t^2 dt}} [/latex]

in your posts. It's a little more effort to type (not much more mind) but it makes it easy for others to parse your mathematical posts. To see what I entered to get that, just click the quote button and you should be able to see the latex

yoho139

Thanks, I've fixed the post. One problem, though - if I stick (1+i) in the latex tag, it gets rid of the +. I tried escaping it with \, but that didn't work either.

Kiki652

Hello I am new here and I need some help with my co-ordinate geometry: The line.
I am doing dividing a line segment in a given ratio a:b Internal and external division.
I am struggling with 3 questions.
1.A is a point on the y-axis and E is a point on the x-axis D(2,1) divides [ae] internally in the ratio 4:1. Find co-ordinates of A and E.
2. A(8,-6) and B (5,-2) are two points. In what ratio does the line 6x-8y-71=0 divide [ab]?
3. A(x,y) B(0,1) and C(-2,2) are three points. C divides [ab] externally in the ratio 5:1
i) find the ratio /AB/ : /BC/
ii) Find the value of x and the value of y.
If there is anybody that could explain this it would be great Thanks.

Peregrine

Kiki652 wrote: »

1.A is a point on the y-axis and E is a point on the x-axis D(2,1) divides [ae] internally in the ratio 4:1. Find co-ordinates of A and E.

Is A (0, 5) and E (2.5, 0)?

Kiki652

The back of the book agrees with you

yoho139

The first question is just a formula, pg 18 (last one) of your log book (formulae and tables book, or whatever you call it). As A is on the y axis, one of the x coordinates is 0. As B is on the x axis, the other y coordinate is 0.

For 2, use the slope formula and y-[latex]y_1[/latex]=m(x-[latex]x_1[/latex]) to find the equation of the line [AE]. With that equation, perform a simultaneous equation with the equation given to find the point of intersection of the two lines, then use the distance from that point to the two given points, then find the ratio of those two.

3 (i) External division means that for a set of collinear (in a line) points A-B-C, where C externally divides [AB] in a ratio m:n, the ratio |AC|:|AB| = m:n. This means that |BC| has to be |AC|-|AB|. You should be able to get it from there.
(ii) There's a number of ways to do it, but the easiest is probably translation. As you know the ratio of the distances, you can use that to translate B and find A.

Good luck!

Peregrine

Yeah, just use the internal divisor formula like yoho said.

Since the ratio is 4:1 or h:k, h = 4 and k = 1.

X1 is 0 because A is on the y axis and Y2 is 0 because E is on the x axis.

When you fill those in to the formula, you will get a co ordinate with two unknowns, X2 and Y1, but you know it's equal to (2, 1). So whatever value you got for x is equal to 2 and the value for y is equal to 1.

Example:
(x, y) = (2, 1)
x = 2, y=1
(10m, 2t) = (20, 4)
m = 2, t = 2

Kiki652

Thank you so much

lollipop95mal

Anybody have the solutions to this sum:

2x-3+4x (the x-3 is suppossed to be above the 2 in smaller writing)

16
---- = 2x+y (x+y is also in smaller writing)
2x

Answers must be -3 and 10

skippy1977

Idea is to use the rules of indices to break down the initial equations so that you have the same 'big' number each side. Then let the powers equal each other.