O-Level Additional Math

[Happylady]

Can someone help me with this Q…Tks in adv:)

A motorist took t hrs to travel from Town P to Town Q with an avg speed of x km/h.
(a) Write down an expression in terms of x and t, for the distance between P and Q.

On his return journey frm Town Q to Town P, he travelled faster by 15 km/h and his
Travelling time was shortened by 20%.
(b) using tis info, write down another expression in terms of x and t, for distance between P and Q.
Hence, form an equation and solve for x.
(Taken frm Victoria SA 2, Y2010)

[dazzlego]

BeContented:

Hi.

DS going sec 1 next year.
Like to know if SMO is similar to the Sec Sch Maths? Thanks.

SMO (Singapore Maths Olympiad) is the competition for secondary school students.
The syllabus is including school stuffs and some topics so-called 'olympiad topics' that will not be learned at school at all.
I forget whether it's going to be learned at JC level or not. Bcoz I learned too many things already and forget where and when did I learned all that :boogie:

[dazzlego]

JadeDry:

Thanks for the help jieheng!


If you could help me with another question, I would appreciate it.

There is a hemisphere with a radius of 4cm. Some liquid is poured into the hemisphere to a depth of x cm. Show that the volume of the liquid is more than ( x cubed / 64) of the volume of the hemisphere.

Thanks in advance!

Hi JadeDry,

Are u still waiting there?
I'll just give u a hint to get the idea how to prove this question.
Draw a hemisphere with radius of 4 cm and a hemisphere with radius of x cm. Draw it like you put the bowl with radius x cm inside the bowl with radius of 4 cm.

Hope it helps :rahrah:

[BeContented]

dazzlego:

BeContented:

Hi.

DS going sec 1 next year.
Like to know if SMO is similar to the Sec Sch Maths? Thanks.

SMO (Singapore Maths Olympiad) is the competition for secondary school students.
The syllabus is including school stuffs and some topics so-called 'olympiad topics' that will not be learned at school at all.
I forget whether it's going to be learned at JC level or not. Bcoz I learned too many things already and forget where and when did I learned all that :boogie:

Haha. That's good to hear, having the ability to learn more is always a blessing Thank you.

[lotto]

red rose:

Hi! Would appreciate help with 2 Trig Qs. Solve:


1. cot(2y+10°)=-0.5

2. 2 sin y + 1 = 3/cosec^2 y

Thanks!

Hi red rose,

First question is quite straight-forward.
First u need to know that tan (2y+10) = -2
since tan is negative, it must be located in IV
2y + 10 = 360 - tan-1(-2)
From here, u can continue yourself
Hope it helps

Second question is abit complicated. Please check my work if there is any mistakes.
2 sin y + 1 = 3 sin^2 2y
2 sin y + 1 = 3 sin 2y sin 2y
2 sin y + 1 = 3 (2 sin y cos y) (2 sin y cos y)
2 sin y + 1 = 12 sin^2 y cos^2 y
2 sin y + 1 = 12 sin^2 y (1 - sin^2 y)
2 sin y + 1 = 12 sin^2 y - 12 sin^4 y
12 sin^4 y - 12 sin^2 y + 2 sin y + 1 = 0
Let x= sin y
12 x^4 - 12 x^2 + 2 x + 1 = 0
U can factorize it and get 4 value of x which will lead u to 4 value of y.
I am not sure about it. There must be wrong somewhere. Or maybe we need to try another substitution.

[dazzlego]

BeContented:

dazzlego:

[quote=\"BeContented\"]Hi.

DS going sec 1 next year.
Like to know if SMO is similar to the Sec Sch Maths? Thanks.

SMO (Singapore Maths Olympiad) is the competition for secondary school students.
The syllabus is including school stuffs and some topics so-called 'olympiad topics' that will not be learned at school at all.
I forget whether it's going to be learned at JC level or not. Bcoz I learned too many things already and forget where and when did I learned all that :boogie:

Haha. That's good to hear, having the ability to learn more is always a blessing Thank you.[/quote]btw did your DS join some competitions in his primary school (NMO, SMOPS, etc)?

[dazzlego]

lotto:

red rose:

Hi! Would appreciate help with 2 Trig Qs. Solve:


1. cot(2y+10°)=-0.5

2. 2 sin y + 1 = 3/cosec^2 y

Thanks!

Second question is abit complicated. Please check my work if there is any mistakes.
2 sin y + 1 = 3 sin^2 2y
2 sin y + 1 = 3 sin 2y sin 2y
2 sin y + 1 = 3 (2 sin y cos y) (2 sin y cos y)
2 sin y + 1 = 12 sin^2 y cos^2 y
2 sin y + 1 = 12 sin^2 y (1 - sin^2 y)
2 sin y + 1 = 12 sin^2 y - 12 sin^4 y
12 sin^4 y - 12 sin^2 y + 2 sin y + 1 = 0
Let x= sin y
12 x^4 - 12 x^2 + 2 x + 1 = 0
U can factorize it and get 4 value of x which will lead u to 4 value of y.
I am not sure about it. There must be wrong somewhere. Or maybe we need to try another substitution.

Hi lotto,
You read the question wrongly!
It is 3 / cosec^2 y not 3 / cosec^2 2y

So it would be as simple as this,
2 sin y + 1 = 3 sin^2 y
Let x= sin y
3x^2 - 2x - 1 = 0
(3x + 1) (x - 1) = 0
x = -1/3 or x = 1
sin y = -1/3 or sin y = 1
y = 360 - sin-1(-1/3) or y = 90

Good job! CHeers :celebrate:

[BeContented]

dazzlego:

BeContented:

[quote=\"dazzlego\"]
SMO (Singapore Maths Olympiad) is the competition for secondary school students.
The syllabus is including school stuffs and some topics so-called 'olympiad topics' that will not be learned at school at all.
I forget whether it's going to be learned at JC level or not. Bcoz I learned too many things already and forget where and when did I learned all that :boogie:

Haha. That's good to hear, having the ability to learn more is always a blessing Thank you.

btw did your DS join some competitions in his primary school (NMO, SMOPS, etc)?[/quote]Yes he did. NMOS, SMOPS, RIPMWC, Mathlympics etc, usually silver.
Actually I asked this question cos a tutor has repeatedly asked DS to take up his sch Maths tuition despite knowing I'm only keen for MO type classes. So I was curious, is SMO really so similar to Sch syllabus? For Pri, it is different. Looks like sec level also different. Looks like i will have to reject firmly. Thanks.

[dazzlego]

Happylady:

Can someone help me with this Q..Tks in adv:)

A motorist took t hrs to travel from Town P to Town Q with an avg speed of x km/h.
(a) Write down an expression in terms of x and t, for the distance between P and Q.

On his return journey frm Town Q to Town P, he travelled faster by 15 km/h and his
Travelling time was shortened by 20%.
(b) using tis info, write down another expression in terms of x and t, for distance between P and Q.
(c) Hence, form an equation and solve for x.
(Taken frm Victoria SA 2, Y2010)

Hi Happylady,

a) U can apply the formula D = S x T
Over here S = x km/h and T = t hours
So D = (xt) km

b) S = (x-15) and T = 0.8t
D = 0.8t (x-15)

c) Since D is the same, xt = 0.8t (x-15)
xt = 0.8xt - 12t
0.2xt = 12t
0.2x = 12
x = 60

My input for you is to treat words (algebra) the same as numbers. Don't get confuse because of the words.
Good luck for the upcoming SA!! If you have any more question, u can ask it again here or u can give me a PM. I would be happy to help :snuggles:

[dazzlego]

BeContented:

Yes he did. NMOS, SMOPS, RIPMWC, Mathlympics etc, usually silver.
Actually I asked this question cos a tutor has repeatedly asked DS to take up his sch Maths tuition despite knowing I'm only keen for MO type classes. So I was curious, is SMO really so similar to Sch syllabus? For Pri, it is different. Looks like sec level also different. Looks like i will have to reject firmly. Thanks.

That's quite an achievement!
Yeah it's always different. Coz olympiad is more on thinking and school is more on solving.
If your DS is doing well in his school then u should put him into olympiad. Who knows he will represent Singapore to World Olympiad
Btw is there any private tutor specialized on MO (secondary level)? I would like to know too if there is.