O-Level Additional Math

[blitz]

URGENT


Need help to solve this.

If X^2+Y^2=8 and (X+Y)=5 Find the value of 4XY

and

Given that (a/3)=Square root of ((b+1)/(b-1))
express b in terms of a
Find b if a=7

Thank you in advance.

[FrekiWang]

blitz:

URGENT


Need help to solve this.

If X^2+Y^2=8 and (X+Y)=5 Find the value of 4XY

and

Given that (a/3)=Square root of ((b+1)/(b-1))
express b in terms of a
Find b if a=7

Thank you in advance.

Both questions are very standard, you may have to revise your work carefully since you have difficulties in them.
1.
X+Y=5
(X+Y)^2=25
X^2+2XY+Y^2=25
given X^2+Y^2=8
2XY=25-8=17
4XY=34
(I do not like the question as X and Y are not real numbers)

2.
Square both sides, we have
a^2 / 9 = (b+1) / (b-1)
Cross multiplying them, we have
(a^2)b - (a^2) = 9b + 9
(a^2 - 9)b = 9 + a^2
b = (9+a^2) / (a^2 - 9)
if a=7,
b=(9+49)/(49-9)=58/40=29/20 (or 1.45)

[blitz]

Thanks FrekiWang

[Andrew Lee]

liketoeat:

Thanks FrekiWang, it's a sec 1 qn.

Hi, can help me solve this question:

a. 7(x+3)-(4x-5)=5-(3x+6)

The HCF of two numbers is 1 and the LCM of these numbers is 91, what are the numbers? :roll:

b.(12y-4)/6 = (7y-4)/5

The product of the ages of a group of teenagers (13-19 yr old) is 4590 yrs, Find --
(i) the numbers of teenagers in the group :roll:
(ii) the sum of their ages :roll:

[Andrew Lee]

liketoeat:

Thanks FrekiWang, it's a sec 1 qn.

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[HeSheMe]

Andrew Lee:

liketoeat:

Thanks FrekiWang, it's a sec 1 qn.

Hi, can help me solve this question:

a. 7(x+3)-(4x-5)=5-(3x+6)

The HCF of two numbers is 1 and the LCM of these numbers is 91, what are the numbers? :roll:

b.(12y-4)/6 = (7y-4)/5

The product of the ages of a group of teenagers (13-19 yr old) is 4590 yrs, Find --
(i) the numbers of teenagers in the group :roll:
(ii) the sum of their ages :roll:

a. 7(x+3)-(4x-5) = 5-(3x+6)
7x+21-(4x-5) = 5-3x-6
7x+21-4x+5 = 5-3x-6
3x+26 = -1-3x
3x+3x = -1-26
6x = -27
x = -27/6

The two numbers are 1 and 91.

Highest common factor = 1
Lowest common multiple = 91 (1x91)

b. (12y-4)/6 = (7y-4)/5
(6y-2)/3 = (7y-4)/5
5(6y-2) = 3(7y-4)
30y-10 = 21y-12
30y-21y = -12+10
9y = -2
y = -2/9

[HappieNewbie123]

Hi,

just curious, what sec one teach? (in maths lah!)

[bluesky63]

hi, can anyone help to solve this question for my daughter, it is o level A Maths question from acs


determine the values of p for which the line y = x - 2p is a tangent to the curve x^2+y^2 = 16p


Thanks

[BlurBerry]

This question appeared in my son’s Sec1 EOY paper. I’m stumped. Can anyone help? Thanks in advance.


One of the famous Arithmetic and algebraic paradoxes show the proof of 2=1

Proof of 2=1:
Assume that
a = b
Multiplying both sides by a,
a^2 = ab
Subtracting b^2 from both sides,
a^2 - b^2 = ab - b^2
Factoring both sides,
(a + b)(a - b) = b(a - b)
Dividing both sides by (a - b),
a + b = b

If now we take a = b = 1, we conclude that 2 = 1.

Analyse the above solution and explain the conceptual error that leads to the above paradox of 2 = 1.

[BlurBerry]

This question appeared in my son’s Sec1 EOY paper. I’m stumped. Can anyone help? Thanks in advance.


One of the famous Arithmetic and algebraic paradoxes show the proof of 2=1

Proof of 2=1:
Assume that
a = b
Multiplying both sides by a,
a^2 = ab
Subtracting b^2 from both sides,
a^2 - b^2 = ab - b^2
Factoring both sides,
(a + b)(a - b) = b(a - b)
Dividing both sides by (a - b),
a + b = b

If now we take a = b = 1, we conclude that 2 = 1.

Analyse the above solution and explain the conceptual error that leads to the above paradox of 2 = 1.