O-Level Additional Math

[MathIzzzFun]

S-H:

Hi MathIzzzfun,


Thank you so much for your answer and notes on circles. Can you please explain to me why when the pt(6,1) lies outside the circle, the value is positive and when it lies inside it, the value is negative?

There is one more question that I cannot solve too, can u pls help me again, so sorry to trouble you again.

The question is :-

Find the possible equations of the circle which touches both coordinate axes and passes through (2,1).

Thank you very much.

The equation of circle centred on (a,b) with a radius r is:

(x-a)² + (x-b)² = r²

for any point (a1,b1) inside the circle
(a1-a)² + (b1-b)² = r1² < r²

so the expression

(a1-a)² + (b1-b)² - r² < 0

similarly for any point (a2,b2) outside the circle
(a2-a)² + (b2-b)² = r2² > r²

so the expression

(a2-a)² + (b2-b)² - r² > 0

cheers.

[S-H]

Thank you very much!! MathIzzzFun. :thankyou:

[pinky88]

Hi all, pls help on the following 2 qns:


1) If x & y are positive integers which satisfy x² - 8x - 1001y² = 0, what is
the smallest possible value of x + y?

2a) If y = |x| + |x + 1| + |x - 1|, find the minimum value of y.

b) Find the area, in square units, enclosed by the figure whose boundary
points satisfy |x|+ |y|=4

TIA.

[lost boy]

Pls help me to slove sec 3 emath


Factorise each of the following completely.
a) ab^2 - 16a
b) (x^4 - x^2) + (x^2 - 1)
c) m - n - 1 + mn

Thanks! !

[kiasu_student]

Hi there, although I am still not required to know cubic equations until few years time, but I am too kiasu, can ask for any simplified formula or must I use inequalities and quadratic formula?

[jieheng]

lost boy:

Pls help me to slove sec 3 emath


Factorise each of the following completely.
a) ab^2 - 16a
b) (x^4 - x^2) + (x^2 - 1)
c) m - n - 1 + mn

Thanks! !

a)

ab^2 - 16a
= a(b^2 - 16)
=a(b^2 - 4^2)
=a(b+4)(b-4)

b)

(x^4 - x^2) + (x^2 - 1)
=x^2 (x^2 - 1) + (x^2 - 1)
=(x^2 + 1)(x^2 - 1)
=(x^2 + 1)(x + 1)(x - 1)

c)

m - n - 1 + mn
=m(1 + n) - (n + 1)
=(m - 1) (n + 1)

[lost boy]

Thank u jieheng can u pls help me another ques


Solve the simultaneous equations.

2x - 5y= 12
3x - 2y = 7

Thanks

[jieheng]

lost boy:

Thank u jieheng can u pls help me another ques


Solve the simultaneous equations.

2x - 5y= 12
3x - 2y = 7

Thanks

2x - 5y= 12 -----(1)
3x - 2y = 7 -----(2)

(1) x3 , 6x - 15y = 36 => 6x = 36 + 15y

(2) x2 , 6x - 4y = 14 => 6x = 14 + 4y

36 + 15y = 14 + 4y
11y = - 22
y = -2

6x = 14 + 4y
6x = 14 + 4(-2)
x= 1

[lost boy]

Thank you Jieheng.

[lost boy]

Pls help me to solve sec 3 a math


Use suitable substituitions to solve each of the following equations.

a) 5^x + 5 = 30(5^x-1)

b) 9^x + 10(3^x) = 3^x+2 + 12

Thanks