O-Level Additional Math

[Jtutor]

Rhyll:

Hi jtutor,

I was looking at the math question ,
Do you mind explain how to know the power for 2 and 3.
is it by testing eg. 2^2 x 3^2 is a perfect square as well as perfect cube, then follow by guessing the power.

Hi Rhyll,

Yes this question involves some \"guess & check\" technique.

To have a perfect cube, the power for 2 and 3 must be either 3, 6, 9, etc (multiples of 3). To have a perfect square, the power must be either 2, 4, 6, etc (multiples of 2).

Examples of perfect squares: 2^2 x 3^2, 2^2 x 3^4
Examples of perfect cubes: 2^3 x 3^3, 2^3 x 3^6
(Pls note that the powers for 2 and 3 need not be the same.)

Cheers!
Jtutor

[2DMommy]

Please help with these :


1) Look at the ( ) digit. If it is a ( ) or a ( ) , then original number is divisible by 5.

2)Look at the number formed by the ( ) digits only. If this number is divisible by 8, then the original number is divisible by 8.

3) ( ) up the digits in the ( ) positions. Then ( ) up the digits in the ( ) positions. If the difference between the two is ( ) or ( ), then the original number is divisible by 11.

[YumYum]

Hi, can anyone pls help with this Qn:


Give the reduced fraction representation of -2.05232323232323…

Thanks 

[YumYum]

quekcc:

YumYum:

Hi, can anyone pls help with this Qn:


Give the reduced fraction representation of -2.05232323232323......

Thanks 

Let y = 0.05232323....
then 100y = 5.23232323....
and 10000y = 523.232323...
-> 9900y = 523 - 5 = 518
so y = 518/9900 = 259/4950

Ans -2.0523232323 = -2 259/4950 or -10159/4950.

Thanks for the detailed explanation 

[lost boy]

Hi, can someone help me answer these two Secondary 3 Questions…


1. A motorist started driving from Point G to Point H which is 188km apart. he travelled 30km at an average speed of x km/hr for the first part of the journey. The average speed increased by 12km/hr for the rest of the journey. Given that he took 1.5hrs to complete his journey, find the speed for the first part of the journey, giving your answer corrected to three significant figures.

2. A housewife planned to buy 430 worth of vegetables at x cents/kg.

(E) Write down an expression, in terms of x, for the number of kg she planned to buy.

(F) She found that the price of vegetables had decreased by 6 cents/kg. write down an expression in terms of x for the number of kg she can buy for $30 now.

(G) Given that she actually bought 5 5/9kg more than she had planned, form an equation in x and show that it reduces to x^2 - 6x - 3240 =0.

(H) Solve the above equation and use your answer to find the number of kg of vegetables she bought after the price had decreased.

Thank you.

P.S. : Please show the working for the respective questions.

[jieheng]

lost boy:

Hi, can someone help me answer these two Secondary 3 Questions...


1. A motorist started driving from Point G to Point H which is 188km apart. he travelled 30km at an average speed of x km/hr for the first part of the journey. The average speed increased by 12km/hr for the rest of the journey. Given that he took 1.5hrs to complete his journey, find the speed for the first part of the journey, giving your answer corrected to three significant figures.

P.S. : Please show the working for the respective questions.

Time = Distance / Speed

Time taken for the first part of the journey = 30 / x

Time taken for the rest of the journey = (188-30) / (x+12) = 158 / (x+12)

30/x + 158/(x+12) = 1.5
[ 30(x+12) + 158x] / [x(x+12)] = 3/2
(188x + 360 ) / (x^2 + 12x) = 3/2
376x + 720 =3x^2 + 36x
3x^2 - 340x - 720 = 0

x = {340 ± square_root [ (-340)^2 - 4 (3)(-720)] } / 6
= (340 ± 352.48 ) / 6

x = 115 or x = -2.08 (rej)

Ans : The speed of the first part of the journey is 115 km/h

[jieheng]

lost boy:

2. A housewife planned to buy $30 worth of vegetables at x cents/kg.

(E) Write down an expression, in terms of x, for the number of kg she planned to buy.

(F) She found that the price of vegetables had decreased by 6 cents/kg. write down an expression in terms of x for the number of kg she can buy for $30 now.

(G) Given that she actually bought 5 5/9kg more than she had planned, form an equation in x and show that it reduces to x^2 - 6x - 3240 =0.

(H) Solve the above equation and use your answer to find the number of kg of vegetables she bought after the price had decreased.

Thank you.

P.S. : Please show the working for the respective questions.

$30 = 3000 cents

E) the number of kg she planned to buy = 3000 / x

F) the number of kg she can buy for $30 now = 3000 / (x-6)

5 5/9kg = 50 / 9 kg

G)

3000/(x-6) - 3000/x = 50/9
[3000x-3000(x-6)] / [x(x-6)] = 50/9
18000 / (x^2 - 6x) = 50/9
360 / (x^2 - 6x) = 1/9
x^2 - 6x = 3240
x^2 - 6x - 3240 = 0 (Shown)

H)

x^2 - 6x - 3240 = 0
(x-60)(x+54) = 0
x = 60 or x = -54 (rej)

the number of kg of vegetables she bought after the price had decreased
= 3000 / (x-6)
= 3000 / (60-6)
=3000 / 54
=55.6 (Ans)

[lost boy]

Thank you for your help Jieheng.

[Michaelia0816]

Need help with this Sec 1 Factor and Multiple Question:


3 faulty light bulbs which flickers a intervals of 6,45 and x minutes respectively. If all of them flickers at the same time at 3 minutes interval, find the smallest possible value of x?

Sources:
From Pasir Ris Sec School Paper

[Skyed]

Michaelia0816:

Need help with this Sec 1 Factor and Multiple Question:


3 faulty light bulbs which flickers a intervals of 6,45 and x minutes respectively. If all of them flickers at the same time at 3 minutes interval, find the smallest possible value of x?

Sources:
From Pasir Ris Sec School Paper

Do you mean \"flickers at intervels of 6,45 and x SECONDS respectively\"? Because otherwise the question doesn't make sense.