Cambridge Prelim MX1 Textbook Marathon/Q&A (4 Viewers)

[InteGrand]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Months. Not years.

You did not cater for the fact that interest is being compounded monthly in doing 1.135



Edit: I will give you a bit of the benefit of the doubt though - the question didn't explicitly say interest was compounded monthly either.

If it just says monthly repayments, then it means compounded monthly too (unless told otherwise).

 

[appleibeats]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

So in general if question have monthly repayments and they give interest rates per annum should you reckon that it is compounded monthly ??

Or is it just these questions are ambiguous??

Edit: Dont worry IG answered the Question

 

[leehuan]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

If it just says monthly repayments, then it means compounded monthly too (unless told otherwise).

You could have questions where the repayments are per month but the compounding is annually. (Albeit it's a bit counter-logical because then you'd just have 12M which is why I've never seen it before.)

So in general if question have monthly repayments and they give interest rates per annum should you reckon that it is compounded monthly ??

Or is it just these questions are ambiguous??

In general the former

But it was most certainly ambiguous

 

[InteGrand]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

So in general if question have monthly repayments and they give interest rates per annum should you reckon that it is compounded monthly ??

Yes.

The "rate per annum" given needs to be divided by the appropriate number (in this case 12) to get the per-period interest rate.

I don't think it's actually ambiguous, it's just that these conventions aren't usually taught or emphasised properly in class, which can thus cause confusion among students.

 

[InteGrand]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

You could have questions where the repayments are per month but the compounding is annually. (Albeit it's a bit counter-logical because then you'd just have 12M which is why I've never seen it before.)

Yeah that's why I said "unless told otherwise".

I.e. If nothing else is said, the convention is what was required for this Q. (so in this case compounded monthly, and in general compounded per period of payment, which could be quarterly, semi-annually, or anything).

 

[dlau]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Could someone please help me with question 14 (e). It's from ex 7B


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[Drongoski]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

For (e): a = 6 or -6

vertex is V(a/2, -a²/4)

y = x² - ax = x(x-a) = 0 at x = 0, a

.: axis of symmetry is: x = (0+a)/2 = a/2

at x = a/2, y = -a²/4

Hence the co-ords of the vertex

Here you find the gradient of the tangent = 0

So the tangent is a horizontal line: y = -a²/4 = - 9

so that a = 6 or -6


or

Since f(x) is a concave-up parabola, the tangent at the vertex is horizontal, so that this tangent has equation: y = -9

 

[dlau]

Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

For (e): a = 6 or -6

Thank you.

 

[dlau]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Help with q27 please.


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[InteGrand]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Help with q27 please.


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[AfroNerd]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

So im not quite sure how to do questions b,c & d, and just out of curiosity how would you find how many 4 digit numbers are even.

 

[leehuan]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

So im not quite sure how to do questions b,c & d, and just out of curiosity how would you find how many 4 digit numbers are even.

View attachment 33328

If you want even 4 digit numbers:

The last digit must be 2, 4, 6, 8 or 0. 5 options
The first digit can't be a 0. 9 options
The second and third digit can be anything.

Your answer: 9 x 10² x 5
___________
I think this is how to do it.


The number is greater than 4000: The first number cannot be a 3.

Case 1: First number is a 4
Remaining digits are 3, 4, 5, 6
There are 4! ways of arranging them.

Case 2: First number is a 5 or a 6. (Note: 2 favourable cases here.)
Remaining digits are 3, 4, 4, ?
There are 4!/2! ways of arranging them.

Answer: 4! + 2*4!/2!

 

[Linh_N]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I keep getting 5/26 for part (C). Can anyone explain how to work out the question?

 

[davidgoes4wce]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I keep getting 5/26 for part (C). Can anyone explain how to work out the question?

 

[HeroicPandas]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

@davidgoes4wce: Out of curiosity, what font is used for the first row of the table and "Total combinations"?

 

[AfroNerd]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

If you want even 4 digit numbers:

The last digit must be 2, 4, 6, 8 or 0. 5 options
The first digit can't be a 0. 9 options
The second and third digit can be anything.

Your answer: 9 x 10² x 5
___________
I think this is how to do it.


The number is greater than 4000: The first number cannot be a 3.

Case 1: First number is a 4
Remaining digits are 3, 4, 5, 6
There are 4! ways of arranging them.

Case 2: First number is a 5 or a 6. (Note: 2 favourable cases here.)
Remaining digits are 3, 4, 4, ?
There are 4!/2! ways of arranging them.

Answer: 4! + 2*4!/2!

I don't understand how the answer wouldn't be 60 for b) since there are 5 numbers that can form 5 digits, which are greater than 4000. And the question doesn't say how many digits the number over 4000 can be.

However, I understand ur working for a 4 digit number greater than 4000

 

[leehuan]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I don't understand how the answer wouldn't be 60 for b) since there are 5 numbers that can form 5 digits, which are greater than 4000. And the question doesn't say how many digits the number over 4000 can be.

However, I understand ur working for a 4 digit number greater than 4000

Because maths in focus sucks.

That's a typo for 40000 and 50000 for b) and c) respectively.

 

[AfroNerd]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Because maths in focus sucks.

That's a typo for 40000 and 50000 for b) and c) respectively.

Ah so u were working it out for 40000 and not 4000?

 

[leehuan]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Ah so u were working it out for 40000 and not 4000?

Yes.

 

[AfroNerd]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Yes.

Okay tyvm I understand now. I was originally looking in the year 11 3u Cambridge book for permutations and combinations but couldn't find it.