O-Level Additional Math

[mathtuition88]

Chan09:

Need some help:

Factorise a^3-b^3

Hint is (a-b)^3 and answer is (a-b)(a^2+ab+b^2)

I think:
(a-b)(a-b)(a-b) but then a^2-b^2= (a-b)(a+b)

Hi, usually the standard way to prove that a^3-b^3=(a-b)(a^2+ab+b^2)
is to expand (a-b)(a^2+ab+b^2)=a^3+a^2b+ab^2-a^2b-ab^2-b^3 and cancel out the terms.

Using hint is possible too,
(a-b)^3=a^3-3a^2b+3ab^2-b^3
So, a^3-b^3=(a-b)^3+3a^2b-3ab^2
=(a-b)(a-b)^2+3a^2b-3ab^2
=(a-b)(a^2-2ab+b^2)+(a-b)(3ab)
=(a-b)(a^2+ab+b^2)

Hope it helps!

I have also typed out the solution in LaTeX on my website:
http://mathtuition88.wordpress.com/2013/04/30/factorize-latex-a-b3/

[pinkapple]

Chan09:

Need some help:

Factorise a^3-b^3

Hint is (a-b)^3 and answer is (a-b)(a^2+ab+b^2)

I think:
(a-b)(a-b)(a-b) but then a^2-b^2= (a-b)(a+b)

hi hi.

I think u have a misconception there.

a^3-b^3 is NOT equal to (a-b)^3, which is (a-b)(a-b)(a-b)

just as
a^2-b^2 is NOT equal to (a-b)^2.

for a visual explanation of the two formulas for difference and sum of cubes, see these vidoeos:
http://youtu.be/rGjPJVe8t0I
and http://youtu.be/NZ75wFhmy6o

as for the algebraic proof, think Mr Wu has shown above.

Oh. just realised that the question is asking us to factorise but not to prove. that's why the hint: (a-b)^3

I'll write it out with further explanation if u need more help. hang on...

[pinkapple]

how I do it:

https://www.facebook.com/photo.php?fbid=515384318520921&set=a.499788846747135.1073741829.466376010088419&type=1&relevant_count=1&ref=nf

but Please note that for O levels, you do NOT need to show the working on how u factorise, but you can just memorise and apply the two formulas:

a^3-b^3=(a-b)(a^2+ab+b^2)
a^3+b^3=(a+b)(a^2-ab+b^2)

these are newly introduced in the new syllabus for AMath for exams starting in 2014.

[pinkapple]

there is a method u can use.


don’t really need quadratic equations. but if u know how to solve quadratic equations using ya calculator, u can do the same for cubic equations.

only thing, no marks given if no working shown.

[jeanielai]

Hi

Can anyone help? Need to find a Maths Tutor for my Sec 2 daughter, preferred a 1-to-1 tution. My location is Lengkok Bahru

Thanks

[mathtuition88]

e^(ln x)=x is a useful identity that is needed in both O Level and A Level math.

It is simple, yet when faced with it for the first time it can be puzzling for students.

I have written a short article on: http://mathtuition88.wordpress.com/2013/05/04/why-is-elnx-o-level-math-a-level-math-tuition/
describing two simple ways to understand this formula.

Best wishes.

(it won't appear by itself in a question, but so far I have encountered that it is often needed in the intermediate workings.)

[Haneyi]

A box contains some white and black mugs.

If 3 white mugs are taken out of the box, 2/7 of the remaining mugs in the box are white mugs. If 5 black mugs are removed from the box, 2/3 of the remaining mugs in the box are black mugs.

By forming an algebraic equation, find the number of mugs in the box originally.\t\t

Thank you in advance!

Note: I’m sorry if my question is too easy or seems to be asked without thinking. I tried doing for about 30 minutes but still can’t seem to solve it with algebra.

[pinkapple]

Haneyi:

A box contains some white and black mugs.

If 3 white mugs are taken out of the box, 2/7 of the remaining mugs in the box are white mugs. If 5 black mugs are removed from the box, 2/3 of the remaining mugs in the box are black mugs.

By forming an algebraic equation, find the number of mugs in the box originally.\t\t

Thank you in advance!

Note: I'm sorry if my question is too easy or seems to be asked without thinking. I tried doing for about 30 minutes but still can't seem to solve it with algebra.

HI. is this a Sec 1 or Sec 2 question?

If it's Sec 2 or above, here's the solution: https://www.facebook.com/photo.php?fbid=517213775004642&set=a.500572863335400.1073741830.466376010088419&type=3&src=https%3A%2F%2Ffbcdn-sphotos-c-a.akamaihd.net%2Fhphotos-ak-frc1%2F316389_517213775004642_1830270652_n.jpg&size=633%2C756

If sec1, then u would not have learnt simultaneous equations and I'll have to tackle it another way.

[Haneyi]

pinkapple:

Haneyi:

A box contains some white and black mugs.

If 3 white mugs are taken out of the box, 2/7 of the remaining mugs in the box are white mugs. If 5 black mugs are removed from the box, 2/3 of the remaining mugs in the box are black mugs.

By forming an algebraic equation, find the number of mugs in the box originally.\t\t

Thank you in advance!

Note: I'm sorry if my question is too easy or seems to be asked without thinking. I tried doing for about 30 minutes but still can't seem to solve it with algebra.

HI. is this a Sec 1 or Sec 2 question?

If it's Sec 2 or above, here's the solution: https://www.facebook.com/photo.php?fbid=517213775004642&set=a.500572863335400.1073741830.466376010088419&type=3&src=https%3A%2F%2Ffbcdn-sphotos-c-a.akamaihd.net%2Fhphotos-ak-frc1%2F316389_517213775004642_1830270652_n.jpg&size=633%2C756

If sec1, then u would not have learnt simultaneous equations and I'll have to tackle it another way.

It's a Sec 1 question. ^^

[pinkapple]

Haneyi:

pinkapple:

[quote=\"Haneyi\"]A box contains some white and black mugs.

If 3 white mugs are taken out of the box, 2/7 of the remaining mugs in the box are white mugs. If 5 black mugs are removed from the box, 2/3 of the remaining mugs in the box are black mugs.

By forming an algebraic equation, find the number of mugs in the box originally.\t\t

Thank you in advance!

Note: I'm sorry if my question is too easy or seems to be asked without thinking. I tried doing for about 30 minutes but still can't seem to solve it with algebra.

HI. is this a Sec 1 or Sec 2 question?

If it's Sec 2 or above, here's the solution: https://www.facebook.com/photo.php?fbid=517213775004642&set=a.500572863335400.1073741830.466376010088419&type=3&src=https%3A%2F%2Ffbcdn-sphotos-c-a.akamaihd.net%2Fhphotos-ak-frc1%2F316389_517213775004642_1830270652_n.jpg&size=633%2C756

If sec1, then u would not have learnt simultaneous equations and I'll have to tackle it another way.

It's a Sec 1 question. ^^[/quote]here you go: https://www.facebook.com/photo.php?fbid=517657854960234&set=a.500572863335400.1073741830.466376010088419&type=3&src=https%3A%2F%2Ffbcdn-sphotos-g-a.akamaihd.net%2Fhphotos-ak-prn1%2F944874_517657854960234_454272208_n.jpg&size=819%2C578