Can ANYONE help me with these maths questions?

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ytlucci
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Im gonna break down in a second, is there anyone who can help take me through these, or at least a couple of them?
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futurematters
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Q11. My thoughts are...
A:B is 2:5 and C: D is 3:1, C and D share twice as much money, so their ratio will be doubled, thus A:B:C: Dis 2:5:6:2

Q12. Draw the triangle labelling the sides opposite, hyp and adj. QR is op, PQ hyp, PR adj. The length of QR is 0.6 and the length of PQ is 1. To find the size of the angle it'll be sin -1 or 0.6/1 to give an answer of 36.9 degrees.

Q16. Substitute 2 in and then substitute 3 in to the formula given. One will give you a positive answer, the other negative. The change of sign shows a solution lies between the two.

For part b rearrange to get x^3 = 3x^2 + 3 and then cube root both sides.

Hope I've helped a little bit, hard to explain
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youknownothing7
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For the first one:
To make it easier, turn them into real numbers. To decide how much money Carl and Donna should share, you want to find a number that can be divided by both 7 (2 + 5, the parts you need to divide Anna and Bill's money into), 2 (because it's exactly double Anna and Bill's amount of money) and 4 (3 + 1, the parts you need to divide Carl and Donna's money into). The lowest number is 28.

So say Carl and Donna have £28, and Anna and Bill have £14 (exactly half). Do you know how to work it out from there?

What are these problems for?
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ytlucci
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(Original post by youknownothing7)
For the first one:
To make it easier, turn them into real numbers. To decide how much money Carl and Donna should share, you want to find a number that can be divided by both 7 (2 + 5, the parts you need to divide Anna and Bill's money into), 2 (because it's exactly double Anna and Bill's amount of money) and 4 (3 + 1, the parts you need to divide Carl and Donna's money into). The lowest number is 28.

So say Carl and Donna have £28, and Anna and Bill have £14 (exactly half). Do you know how to work it out from there?

What are these problems for?
I understand what you've taken me through, but I don't know how to continue it. Would I have to divide 28 by 2 and 5 or something?
These are practice questions I'm doing for improvement but I cant find the mark scheme anywhere for these questions, lol.
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youknownothing7
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(Original post by lucci77)
I understand what you've taken me through, but I don't know how to continue it. Would I have to divide 28 by 2 and 5 or something?
These are practice questions I'm doing for improvement but I cant find the mark scheme anywhere for these questions, lol.
Determined to self-improve, good on you

Carl and Donna share the £28 in a ratio of 3:1, as we're told in the question, so how much do they get each?
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MystG123
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q14) I got 720. This is not my strongest point but my logic was:

on Monday, he had 10 different options to choose from
on Tuesday, he has already picked one so he has 9 different options to choose from
on Wednesday, he has 8 different options to choose from

so I did 10x9x8 = 720 because I assumed he could pick the different options in a random order
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ytlucci
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(Original post by youknownothing7)
Determined to self-improve, good on you

Carl and Donna share the £28 in a ratio of 3:1, as we're told in the question, so how much do they get each?
21:7, right?
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youknownothing7
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For the second question, sin is opposite divided by hypotenuse.
Opposite QPR is QR. The hypotenuse (the longest side) is PQ. So sinQPR is QR divided by PQ.

Assign a random number to be PR (5 would be a convenient one). QR will be 60% of that, and you can use Pythagoras to work out PQ.
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youknownothing7
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(Original post by lucci77)
21:7, right?
Yep. And how much will Anna and Bill have?
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ytlucci
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(Original post by youknownothing7)
Yep. And how much will Anna and Bill have?
4:10 ))))
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youknownothing7
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(Original post by lucci77)
4:10 ))))
Yep, so the ratio is 4 : 10 : 7 : 21

I went through the second question above and MystG123 has explained the third one very well.

The last one is an incredibly dull question imo. For a), make the whole equation equal to y and imagine plotting it on a graph. When x=2, y will equal -1. When x=3, y will equal 3. So at some point between them, the curve must pass through a point where y = 0.

Can you do b?

(Is this GCSE or A Level stuff? I struggle to remember)
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ManLike007
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(Original post by lucci77)
Im gonna break down in a second, is there anyone who can help take me through these, or at least a couple of them?
Just to add on from what futurematters has said in Q16a,

Here's the reason why there's a change in signs. Have a look at the diagram below,

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Suppose this f(x) = sin(\frac{1}{2}x) graph. You can see the root lies in between x=6 and x=7.

But how do we prove this?

Substitute in the values and you'll see the sign change.

f(6) = 0.1411..
f(7) = -0.3507..

So f(6)>0 and f(7)<0. Look at the diagram, you have a positive y value at x=6 and a negative y value at x=7 therefore there is a root between x=6 and x=7 because this is where the curve crosses the x axis.

Also adding onto Part b from the user I mentioned,

You need to obtain the equation x=\sqrt[3]{3x^{2}-3}, you can work backwards so cube the whole equation to obtain x^{3}=3x^{2}-3 so you can see that you want to make x^{3} the subject first then cube root the whole equation to make x the subject as required.
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Zoqua
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(Original post by futurematters)
Q11. My thoughts are...
A:B is 2:5 and C: D is 3:1, C and D share twice as much money, so their ratio will be doubled, thus A:B:C: Dis 2:5:6:2

Q12. Draw the triangle labelling the sides opposite, hyp and adj. QR is op, PQ hyp, PR adj. The length of QR is 0.6 and the length of PQ is 1. To find the size of the angle it'll be sin -1 or 0.6/1 to give an answer of 36.9 degrees.

Q16. Substitute 2 in and then substitute 3 in to the formula given. One will give you a positive answer, the other negative. The change of sign shows a solution lies between the two.

For part b rearrange to get x^3 = 3x^2 + 3 and then cube root both sides.

Hope I've helped a little bit, hard to explain

This is basically it.
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ytlucci
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(Original post by youknownothing7)
Yep, so the ratio is 4 : 10 : 7 : 21

I went through the second question above and MystG123 has explained the third one very well.

The last one is an incredibly dull question imo. For a), make the whole equation equal to y and imagine plotting it on a graph. When x=2, y will equal -1. When x=3, y will equal 3. So at some point between them, the curve must pass through a point where y = 0.

Can you do b?

(Is this GCSE or A Level stuff? I struggle to remember)
Its GCSE, I can do b I got the mark scheme off of my teacher today and most of my answers were correct ))
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JanNotYourMan
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is question 12) 31 degrees???
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JanNotYourMan
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would you do inverse sin for question 12???
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JanNotYourMan
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does anybody have the mark scheme for this paper? if so could they attach it or send the link pls. tyy xx
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youknownothing7
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(Original post by JanNotYourMan)
would you do inverse sin for question 12???
No, it only asks you for what sinQPR is, not QPR itself, so there’s no need to do inverse sin.Remember also that sin is OPPOSITE over hypotenuse, not adjacent. I get 0.514 to 3 significant figures.
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len11
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16.b. X^3= 3X^2-3 take all other terms to other side
Take cube roots on both sides
You will get your answer right
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JanNotYourMan
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(Original post by youknownothing7)
No, it only asks you for what sinQPR is, not QPR itself, so there’s no need to do inverse sin.Remember also that sin is OPPOSITE over hypotenuse, not adjacent. I get 0.514 to 3 significant figures.
oh okay. Thank you soo much xx
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