O-Level Additional Math

[CoffeeCat]

midnightspark:

Hi,


Just asking some sec 2 maths questions, please help


1)
A rectangle of sides x cm and y cm has an area of 72 cm2. Another rectangle of sides (x+1.5) and (y-4)cm has the same area. Find the values of x and y.

2)
When 5 is added to both the numerator and denominator of a fraction, the result becomes 1/2. When 1 is subtracted from both the numerator and the denominator, the fraction becomes 1/5. Find the fraction.

3)
The scale of map X is 1: x and the scale of map Y is 1:y. If the same distance is represented as 5cm on map X and 7.5cm on map Y, calculate the ratio x:y.

Thanks.

For qns 2, use algebra.
let the original fraction be x/y.
(x+5)/(y+5) = 1/2
cross multiplying, 2x + 10 = y+ 5
2x + 5 = y
(x-1)/ (y-1) = 1/5
5x - 5 = y - 1
......

For qns 1
xy = 72
(x+1.5)(y-4) = 72
let y= (72/x) and substitute . You will get a quadratic equation after multiplying the whole equation by x.

For qns 3,
5x = 7.5y
x/y = 7.5/5 = ...

hmmm too busy to give you full solutions. hope this helps.

[midnightspark]

CoffeeCat:

midnightspark:

Hi,


Just asking some sec 2 maths questions, please help


1)
A rectangle of sides x cm and y cm has an area of 72 cm2. Another rectangle of sides (x+1.5) and (y-4)cm has the same area. Find the values of x and y.

2)
When 5 is added to both the numerator and denominator of a fraction, the result becomes 1/2. When 1 is subtracted from both the numerator and the denominator, the fraction becomes 1/5. Find the fraction.

3)
The scale of map X is 1: x and the scale of map Y is 1:y. If the same distance is represented as 5cm on map X and 7.5cm on map Y, calculate the ratio x:y.

Thanks.

For qns 2, use algebra.
let the original fraction be x/y.
(x+5)/(y+5) = 1/2
cross multiplying, 2x + 10 = y+ 5
2x + 5 = y
(x-1)/ (y-1) = 1/5
5x - 5 = y - 1
......

For qns 1
xy = 72
(x+1.5)(y-4) = 72
let y= (72/x) and substitute . You will get a quadratic equation after multiplying the whole equation by x.

For qns 3,
5x = 7.5y
x/y = 7.5/5 = ...

hmmm too busy to give you full solutions. hope this helps.

Thanks for the solution!

[SKT]

Hi,


LCM of A&B is 4x², B&C is 12x³, A&C is 6x³. Find all possible expressions C.

[CoffeeCat]

SKT:

Hi,


LCM of A&B is 4x², B&C is 12x³, A&C is 6x³. Find all possible expressions C.

lol this is like a deductive puzzle.
Remember the concept of lcm is about choosing the highest index of prime factor.
lcm (A & B) = 4 x ^2 --- [1]
lcm (B & C) = 12 x^3 --- [2]
lcm (A & C) = 6 x^3 --- [3]

From [1] and any of [2] or [3] you can tell C must have x^3.
From [3] & [1] you can tell A has only factor 2 and not 4. B is the one with 4.
From [3] & [2] you can tell C must have factor 3 and possibly 2 but not 4.
Therefore possible expressions of C are
x^3, 3x^3, 6x^3.

[SKT]

CoffeeCat:

SKT:

Hi,


LCM of A&B is 4x², B&C is 12x³, A&C is 6x³. Find all possible expressions C.

lol this is like a deductive puzzle.
Remember the concept of lcm is about choosing the highest index of prime factor.
lcm (A & B) = 4 x ^2 --- [1]
lcm (B & C) = 12 x^3 --- [2]
lcm (A & C) = 6 x^3 --- [3]

From [1] and any of [2] or [3] you can tell C must have x^3.
From [3] & [1] you can tell A has only factor 2 and not 4. B is the one with 4.
From [3] & [2] you can tell C must have factor 3 and possibly 2 but not 4.
Therefore possible expressions of C are
x^3, 3x^3, 6x^3.

Thank you CoffeCat.

[OK Lor]

Hi Sir,


What is the least possible value of
(a^2 + 9)^(1/2) + [(b-a)^2 + 4 ]^(1/2) + [(8-b)^2 + 16]^(1/2)
for real numbers a and b?

Thanks.

[liketoeat]

Hi Guanhui,


Please help me with the following:

If B = {a, {a}, b, {b}, {c}, d}, state whether each of the following is true or false.

(a) {a} is a subset of B

(b) {{a}} is a subset of B

{a, {a,c}, d} is a subset of B

Thank you

[k1ndan]

What is the last digit for 3^2010?


^: to the power of

Thanks

[fromnuaa]

answer: 1


3x3=9
9x9=81
1x1=1

k1ndan:

What is the last digit for 3^2010?

^: to the power of

Thanks

[k1ndan]

fromnuaa:

answer: 1


3x3=9
9x9=81
1x1=1

k1ndan:

What is the last digit for 3^2010?

^: to the power of

Thanks

Hi,

Thanks for the answer, but can you elaborate more on how you get the answer. Look complicated to me.

Thanks.