O-Level Additional Math

[Michaelia0816]

Michaelia0816:

I have common test tmr, can help me with this challenging questions:


1.Given that the HCF of 30,100 and x is 10 and x is not equal to 10, find 3 possible values of x less than 150.

2. Given that the LCM of 5,14 and y is 140, find 3 possible of y.

3.Find the smallest positive integer n for which perfect cube 2750n is a whole number.

4. Rashid had sweets of 3 different flavours. There were 99 strawberry flavoured, 42 orange flavoured and 141 lemon flavoured sweets. He packed an equal number of each flavour into small packet but 1 strawberry and 1 lemon flavoured sweets were left out.

(a) (i) What was the maximum number of packets?
(ii) How many sweets were there in each small packets?

(b) If all sweets were included,
(i) what was the maximum number of packets
(Ii) how many sweets were there in each packet

Pls help with Q3 and 4, I had completed Q1 and 2

[jieheng]

[quote="Michaelia0816"]I have common test tmr, can help me with this challenging questions:


1.Given that the HCF of 30,100 and x is 10 and x is not equal to 10, find 3 possible values of x less than 150.

2. Given that the LCM of 5,14 and y is 140, find 3 possible of y.


1)

HCF = 10 =25

30 = 235

100 = 2²5²

X must include 25 and other prime numbers 2,3,5,7,11,13

Possible values of x less than 150 are 20 , 40 , 50 , 60 , 70 , 80 , 90 , 110 , 120 , 130 , 140


2)

LCM = 140 = 2²57

5

14 = 27

y must include 2² and prime numbers 5 , 7 and 5*7

Possible values of y = 4 , 20 , 28 , 140

[Michaelia0816]

Ty so much , ty

[Michaelia0816]

I need help with the Q3 and 4 pls

[jieheng]

Michaelia0816:

I have common test tmr, can help me with this challenging questions:


3.Find the smallest positive integer n for which perfect cube 2750n is a whole number.

3)

2750 = 2*5^3*11

To be perfect cube , the index of the prime no must be multiple of 3

n = 2^2*11^2 = 484

[jieheng]

Michaelia0816:

4. Rashid had sweets of 3 different flavours. There were 99 strawberry flavoured, 42 orange flavoured and 141 lemon flavoured sweets. He packed an equal number of each flavour into small packet but 1 strawberry and 1 lemon flavoured sweets were left out.
(a) (i) What was the maximum number of packets?
(ii) How many sweets were there in each small packets?

(b) If all sweets were included,
(i) what was the maximum number of packets
(Ii) how many sweets were there in each packet

4)

Strawberry 98 = 2*7*7
Orange 42 = 2*7*3
Lemon 140 = 2*7*10

HCF = 2*7 =14

a)
i) the max no of packets = 14

ii) No of sweets in each small packets = 7+3+10 = 20

For part b , you can try yourself

[Michaelia0816]

4. Rashid had sweets of 3 different flavours. There were 99 strawberry flavoured, 42 orange flavoured and 141 lemon flavoured sweets. He packed an equal number of each flavour into small packet but 1 strawberry and 1 lemon flavoured sweets were left out.


(a) (i) What was the maximum number of packets?
(ii) How many sweets were there in each small packets?

(b) If all sweets were included,
(i) what was the maximum number of packets
(Ii) how many sweets were there in each packet

Help me!

[jieheng]

Michaelia0816:

4. Rashid had sweets of 3 different flavours. There were 99 strawberry flavoured, 42 orange flavoured and 141 lemon flavoured sweets. He packed an equal number of each flavour into small packet but 1 strawberry and 1 lemon flavoured sweets were left out.


(a) (i) What was the maximum number of packets?
(ii) How many sweets were there in each small packets?

(b) If all sweets were included,
(i) what was the maximum number of packets
(Ii) how many sweets were there in each packet

Help me!

4)

Strawberry 98 = 2*7*7
Orange 42 = 2*7*3
Lemon 140 = 2*7*10

HCF = 2*7 =14

a)
i) the max no of packets = 14

ii) No of sweets in each small packets = 7+3+10 = 20


Strawberry 99 = 3^2*11
Orange 42 = 2*3*7
Lemon 141 = 3*47

HCF =3

b)

i) the max no of packets = 3

ii) No of sweets in each small packets = 3*11+2*7+47 = 94

[jieheng]

quekcc:

jieheng:

[quote=\"Michaelia0816\"]4. Rashid had sweets of 3 different flavours. There were 99 strawberry flavoured, 42 orange flavoured and 141 lemon flavoured sweets. He packed an equal number of each flavour into small packet but 1 strawberry and 1 lemon flavoured sweets were left out.


(a) (i) What was the maximum number of packets?
(ii) How many sweets were there in each small packets?

(b) If all sweets were included,
(i) what was the maximum number of packets
(Ii) how many sweets were there in each packet

Help me!

4)

Strawberry 98 = 2*7*7
Orange 42 = 2*7*3
Lemon 140 = 2*7*10

HCF = 2*7 =14

a)
i) the max no of packets = 7+3+10 = 20

ii) No of sweets in each small packets = 14

Strawberry 99 = 3^2*11
Orange 42 = 2*3*7
Lemon 141 = 3*47

HCF =3

b)

i) the max no of packets = 3*11+2*7+47 = 94

ii) No of sweets in each small packets = 3

Hi, your answer for (i) and (ii) should exchange.

The HCF will give you the max number of packets for both cases.

a) i) max no of packets = 2 x 7 = 14
ii) no sweets in each small packet = 7 + 3 + 10 = 20
b) i) max no of packets 3
ii) no sweets in each small packet = 3 x 11 + 2 x 7 + 47 = 94[/quote]Hi ,

You are right . Thanks for pointing out the error.

[LOL123]

pls help me


The function f is defined by f(x)=1-2x.
(a) Find the range of f corresponding to the domain -1≤x<3
(b) Find the domain of f corresponding to the range 0≤f(x)<5

thanks