Cambridge Prelim MX1 Textbook Marathon/Q&A (1 Viewer)

pikachu975

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

Q 7 (b) EX 9A

I just wondering has there been a mistake in this answer of the 3U Year 11 textbook?

ii) ==> PA² + PB² + PC² = 3x² + 3y² - 14x - 6y + 78 = 77

==> 3x² + 3y² - 14x - 6y = -1

==> x² + y² - 14x/3 - 2y = -1/3

Grouping, (x² - 14x/3) + (y² - 2y) = -1/3

==> (x² - 14x/3 + 49/9) + (y² - 2y + 1) = -1/3 + 49/9 + 1

==> (x - 7/3)² + (y - 1)² = 55/9

The back of the book has the answer as (2,1) for centre and radius of
You didn't give us point A B and C

jathu123

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

Q 7 (b) EX 9A

I just wondering has there been a mistake in this answer of the 3U Year 11 textbook?

ii) ==> PA² + PB² + PC² = 3x² + 3y² - 14x - 6y + 78 = 77

==> 3x² + 3y² - 14x - 6y = -1

==> x² + y² - 14x/3 - 2y = -1/3

Grouping, (x² - 14x/3) + (y² - 2y) = -1/3

==> (x² - 14x/3 + 49/9) + (y² - 2y + 1) = -1/3 + 49/9 + 1

==> (x - 7/3)² + (y - 1)² = 55/9

The back of the book has the answer as (2,1) for centre and radius of
You made a small silly mistake, the point B has coordinates (0,-4). So PB^2 would be x^2+(y+4)^2

davidgoes4wce

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

OK I decided to redo Q 7 a and 7b from EX 9A

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trea99

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

Hi, need help with Exercise 8H Page 311 Extension Question 27.
If alpha and beta are the roots of x^2 = 5x - 8. Find (a)^1/3 + (b)^1/3 without finding the roots.
Tried cubing (a^1/3 + b^1/3) but got stuck.
Any help would be appreciated.

Also, with Extension question 26 (same page),
If the equations mx^2 + 2x +1 =0 and x^2 + 2x +m = 0 have a common root, find the possible values of m and the value of the common root in each case. I let first equation be p(x) and the second be f(x) and the common root be alpha.
If alpha is the common root p(a) = f(a) = 0 and hence you get,
a^2(m-1) + (1-m) = 0, and that the common root a is x=-1 when m = 1
I had no idea how to get the second common root of the two equations (its x = 1 when m = -3),
So I used product of roots of the above equation a^2(m-1) + (1-m) = 0 as a quadratic is a, and the product of roots is thus -1
Hence I found the other root to be x = -1 and subbing x = -1 into any of the given functions p(x), f(x) and letting it equal 0 I then got m = -3.
Is there a way to find the 2nd m value prior to finding the 2nd common root?
(because this is what the question seems to imply find m then find the common root)
Sorry for long post couldn't find anything on either of the questions
Thanks!

Drongoski

Well-Known Member
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Hi, need help with Exercise 8H Page 311 Extension Question 27.
If alpha and beta are the roots of x^2 = 5x - 8. Find (a)^1/3 + (b)^1/3 without finding the roots.
Tried cubing (a^1/3 + b^1/3) but got stuck.
Any help would be appreciated.

Ok - to save time I will use a and b for alpha and beta.

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• trea99

trea99

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

Yes, I got that part lol.
But what would you do to get a^(1/3) + b^(1/3) from a+b = 5 and ab = 8
What I tried was,
(a^(1/3) + b^(1/3))^3 and got a + 3a^(2/3)b^(1/3) + 3a^(1/3)b^(1/3) + b
Tried doing something with the 3a^(2/3)b^(1/3) + 3a^(1/3)b^(2/3) but ended up getting more a^(1/3) + b^(1/3) terms when I tried factorising by taking out powers of ab
Or would cubing a^(1/3) + b^(1/3) be useless for this question?

trea99

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

Thank you so much Drongoski

Well-Known Member
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Thank you so much You were so close to finishing. Never done this type of question before.

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davidgoes4wce

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

EX7D Q 9 (b) is there a mistake with the answer?

davidgoes4wce

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

One of the angles I believe to be right (the 71 34') and the other I believe to be wrong. Would love it , if somebody could confirm.

Seeing that the two points of intersection are at x=2, -3

I then substituted this back into the derivative which is dy/dx=2x-1=tan

Drongoski

Well-Known Member
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

The 2 angles in degrees: 71.565 and 98.13

being: inverse tan (3) and 180 - inverse tan (7)

Maybe my calculator is exceptionally accurate.

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davidgoes4wce

Well-Known Member
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

I had an attempt at the question and I can't quite get it

davidgoes4wce

Well-Known Member
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

My reasoning as to why I subtract 180 from 81'52' is that the tan theta value is a value of negative 7, which lies somewhere in the 2nd quadrant of the ASTC diagram.

lypoon

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

Anyone know how to do 12B Question 16? thanks.

integral95

Well-Known Member
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Anyone know how to do 12B Question 16? thanks.
Post it up, not everyone has the book.

studyingg

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

Exercise 6J q11b

Every two hours, half of a particular medical isotope decays. If there was originally 20g, how much remains after a day (to two significant figures)?

Thanks!

integral95

Well-Known Member
Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread