O-Level Additional Math

[liketoeat]

Hi, I need help with the following Qn…


A motorist travelled the first part of his journey at an average speed of 56 km/h. He the increases his speed to 64 km/h for the rest of his journey. If he travels 130 km in 2 hours and 15 minutes, find the distance he travelled for the first part of the journey.

Thanks.

[FrekiWang]

Herbie:

if 600= 2*2*2*3*5*5. Find the smallest value of k such tat 600k is a perfect square. Can help to solve it?

600=2^3 * 3^1 * 5^2

For a perfect square, all the prime factors must have an EVEN power.

Therefore we need to mutiply 600 by another 2 and 3.

so k=2 * 3 =6

This type of question is standard and the approach is standard too.

[FrekiWang]

liketoeat:

Hi, I need help with the following Qn..


A motorist travelled the first part of his journey at an average speed of 56 km/h. He the increases his speed to 64 km/h for the rest of his journey. If he travels 130 km in 2 hours and 15 minutes, find the distance he travelled for the first part of the journey.

Thanks.

primary? secondary?

Let assume it is a secondary question first, then we can solve it by using an equation.
2hour15mins=2.25hour(15mins=1/4hour)
Let the time of the first part be t hours, then the time of the second part will be (2.25-t) hours.
Here we have
56t+64(2.25-t)=130
Solve, we get t=1.75
Therefore the distance travelled in the first part = 56 x 1.75 = 98km.

If it is a primary question,
Assumed he travelled 2.25hours at a speed of 56km/h
Distance he would have travelled = 56 x 2.25 = 126km
He actually travels 4km more than 126km because he has increased the speed somewhere. In each hour, he could travel 64-56=8km more, which means he need to travel 4/8=0.5hour at the new speed to increase his distance travelled to 130km.

So time taken for the first part of the journey is 2.25-0.5=1.75
56 x 1.75=98km.

[liketoeat]

Thanks FrekiWang, it’s a sec 1 qn.

[k1ndan]

Given that 6/V -15V = 24, find the values of 5V + 2/V.

[FrekiWang]

k1ndan:

Given that 6/V -15V = 24, find the values of 5V + 2/V.

6/V-15V=24
2/V-5V=8
Square both sides
(2/V-5V)=64
(2/V)^2 - 2(2/V)(5V) + (5V)^2 = 64
so (2/V)^2 + (5V)^2 = 84
so (2/V)^2 + 2(2/V)(5V)+(5V)^2=104
(2/V+5V)^2=104
2/V+5V=+/-sqrt(104)

[red rose]

Would appreciate help with the following Qs:


1) Arrange the following numbers in ascending order: 2^3333, 3^2222, 6^1111, 9^555
2) Which is bigger, 3^3^3^3 or 4^4^4
3) Solve (x^2-5x+5)^x+2000 = 1

Thanks in advance!

[FrekiWang]

red rose:

Would appreciate help with the following Qs:


1) Arrange the following numbers in ascending order: 2^3333, 3^2222, 6^1111, 9^555
2) Which is bigger, 3^3^3^3 or 4^4^4
3) Solve (x^2-5x+5)^x+2000 = 1

Thanks in advance!

If you are referring to these basic olympiad questions, I guess it is useless to know only the solution, you may need more systematic way of learning them.

1)
2^3333 = (2^3)^1111=8^1111
3^2222=(3^2)^1111=9^1111
9^555=(3^2)^555=3^1110
therefore 3^2222>2^3333>6^1111>9^555

2) Assuming there is no bracket(without any bracket the upper indice will be evaluated first)
3^3^3^3=3^3^9=3^(3 x 3^8)=9^(3^8)
4^4^4=4^(4^4)

since 9>4 and 3^8=9^4>4^4, 3^3^3^3>4^4^4

3) I assume you are asking (x^2-5x+5)^(x+2000)=1
There are three possibilities:
a) x+2000=0 and x^2-5x+5>0
x=-2000, check x^2-5x+5 is positive when x=-2000
b) x^2-5x+5=1
solve this simple quadratic equation we have x=-1 or x=-4
c) x^2-5x+5=-1 and x+2000 is even
solve this simple quadratic equation we have x=-2 or x=-3
reject x=-3 and (-3)+2000 is odd.

Therefore x=-2000, -1,-2 or -4.

[heutistmeintag]

Need help on Sec 3 A maths Trigo question:

Given that cosec A + cot A = 3, evaluate cosec A - cot A and cos A.

Thanks in advance!

[FrekiWang]

heutistmeintag:

Need help on Sec 3 A maths Trigo question:

Given that cosec A + cot A = 3, evaluate cosec A - cot A and cos A.

Thanks in advance!

Sorry I feel lazy to solve it in a standard approach.
1/sinA + cosA/sinA = 3
1 + cosA = 3sinA ...(1)
Let cosecA - cotA = k
1/sinA - cosA/sinA = k
1 - cosA = ksinA ...(2)
(1)*(2) we have,
1 - (cosA)^2 = 3k(sinA)^2
(sinA)^2 = 3k(sinA)^2
3k = 1
k = 1/3 (this is the value of cosecA - cotA)

subst k = 1/3 into (2), we have
1 - cosA = 1/3sinA ... (3)
(1) - (3)*9, we have
(1+cosA) - 9(1-cosA) = 0
-8 + 10cosA = 0
cosA = 0.8