O-Level Additional Math

[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

[mathtuition88]

the above method is very nice.

[mathtuition88]

Does your child need practice on Expansion and Factorisation, especially the more challenging questions? It is a key technique that needs to be honed for the O Levels.


Practice Hwa Chong Institution Expansion and Factorisation (Sec 2, IP) here.

http://mathtuition88.wordpress.com/2013/05/07/sec-2-ip-hci-revision-1-expansion-and-factorisation/

[PiggyLalala]

Need help to solve the following question.

Log (base 9) a = log (base 12) b =log (base 16) (a+b), find the value of a/b.
TIA

[mathtuition88]

PiggyLalala:

Need help to solve the following question.

Log (base 9) a = log (base 12) b =log (base 16) (a+b), find the value of a/b.
TIA

Dear Sir/Mdm,

Please see my answer at http://mathtuition88.com/2013/05/12/o-level-logarithm-question-challenging/

Best wishes.

[PiggyLalala]

mathtuition88:

PiggyLalala:

Need help to solve the following question.

Log (base 9) a = log (base 12) b =log (base 16) (a+b), find the value of a/b.
TIA

Dear Sir/Mdm,

Please see my answer at http://mathtuition88.com/2013/05/12/o-level-logarithm-question-challenging/

Best wishes.

:thankyou: very much for the solution. Was using the wrong approach- change of base n made a big mess... haha..

I did not think of letting y = the log expression n change it into its exponential form.

Thank you so much.