O-Level Additional Math

[bran36]

Hi, as the exams are near, I'm preparing for my papers. However, while doing my assessment book, there's this question I do not understand.

It's an inequality question. I don't understand why must the sign change. Perhaps anyone can enlighten me? Many thanks!!

My work:
http://i44.tinypic.com/2gxfqdv.jpg

The Answer:
http://i44.tinypic.com/35irdbp.jpg

[mum_sugoku]

bran36:

Hi, as the exams are near, I'm preparing for my papers. However, while doing my assessment book, there's this question I do not understand.

It's an inequality question. I don't understand why must the sign change. Perhaps anyone can enlighten me? Many thanks!!

My work:
http://i44.tinypic.com/2gxfqdv.jpg

The Answer:
http://i44.tinypic.com/35irdbp.jpg

(Actually it's quite hard to explain without using drawings but let me try )

First of all, the eqn you have is a quadratic eqn (ie eqn in the form of ax^2 + bx + c) which, if you were to draw a graph of the eqn, it's either a U shape curve (if a is +ve), or an inverted U (if a is -ve).

Next, if we look at your eqn x^2 -4x +3 >=0, or (x-3)(x-1)>=0
since a (ie coef of x^2) is = +ve, it's a U shape curve which cuts the x-axis (ie y=0) at x=3 and x=1

What it means is that when x is between 1 and 3 (ie 1<x<3) the curve falls below the x-axis (ie eqn is -ve), and when x is <1 and when x is >3, the curve rises above the x-axis (ie eqn is +ve).

Hence for eqn to be >= 0 (ie +ve), x<1 or x>3.

If you can't understand the above explanation, alternatively, just bear in mind that for quadratic inequality eqn, say (x-3)(x-1)>0, ans is always either in the form

1<x<3, or

x<1, or x>3

To find out which is the correct ans, one way is to pick a number between 1 and 3, say x=2, and insert into the eqn, and you'll get (2-3)(2-1) = -1, which is <0. Since question ask for >=0, correct ans has to be the second one, ie x<1 or x>3.

[bran36]

mum_sugoku:

bran36:

Hi, as the exams are near, I'm preparing for my papers. However, while doing my assessment book, there's this question I do not understand.

It's an inequality question. I don't understand why must the sign change. Perhaps anyone can enlighten me? Many thanks!!

My work:
http://i44.tinypic.com/2gxfqdv.jpg

The Answer:
http://i44.tinypic.com/35irdbp.jpg

(Actually it's quite hard to explain without using drawings but let me try )

First of all, the eqn you have is a quadratic eqn (ie eqn in the form of ax^2 + bx + c) which, if you were to draw a graph of the eqn, it's either a U shape curve (if a is +ve), or an inverted U (if a is -ve).

Next, if we look at your eqn x^2 -4x +3 >=0, or (x-3)(x-1)>=0
since a (ie coef of x^2) is = +ve, it's a U shape curve which cuts the x-axis (ie y=0) at x=3 and x=1

What it means is that when x is between 1 and 3 (ie 1<x<3) the curve falls below the x-axis (ie eqn is -ve), and when x is <1 and when x is >3, the curve rises above the x-axis (ie eqn is +ve).

Hence for eqn to be >= 0 (ie +ve), x<1 or x>3.

If you can't understand the above explanation, alternatively, just bear in mind that for quadratic inequality eqn, say (x-3)(x-1)>0, ans is always either in the form

1<x<3, or

x<1, or x>3

To find out which is the correct ans, one way is to pick a number between 1 and 3, say x=2, and insert into the eqn, and you'll get (2-3)(2-1) = -1, which is <0. Since question ask for >=0, correct ans has to be the second one, ie x<1 or x>3.

Hi thanks a lot for your help! However, how do you which value of x is > or <? I don't really understand this part. Thanks again!

[mum_sugoku]

bran36:

Hi thanks a lot for your help! However, how do you which value of x is > or <? I don't really understand this part. Thanks again!

Just bear in mind that for a quadratic inequality eqn, (range of) x is either (1) in between the smaller no. and bigger no., or (2) x is less than the smaller no. or more than the bigger no.,

for eg, the eqn (x+3)(x-5) >0, ans must be either

(1) -3<x<5 (x in between -3 and 5) or
(2) x<-3; x>5. (x less than -3 or more than 5)

(PS. you cannot have something like x>-3; x>5 because if x>5 then of cos x must be >-3, likewise you also cannot have something like x<-3; x<5 since if x<-3 then of cos x must be <5)

Presuming that (sign of) x^2 is +ve, then

if question asks for \">0\" (eg (x+3)(x-5)>0), always choose (2). And if question asks for \"<0\" (eg (x+3)(x-5)<0), always choose (1). (The reason has already been given in the 1st part of my previous post )

[htn]

Hi, need help for the following:


A) 1/(x+2)-1/(2x+4)=3/2

B) 1/(x-1)+1/6=5/12


C) 7/(2x+4)-2/(3x+6)=3/4


TIA

[Kafer]

John spwes ia x m/s.

Mary speed ia y m/s
If john starts 2 sec later, he will take 8 secs to catch up with mary.
If john starts to run only when mary is 8m ahea 5 sec to catch up with her.
Form two eqn in x an y.

[greenflora]

Hi, can anyone help with this question?


The scale of map X is 1 : x and the scale of map Y is 4 : y.
If the actual area of a park is represented by 10cm^2 and 2.5cm^2 on maps X and Y respectively, find x : y in its simplest form.

[JadeDry]

Hello,


I would appreciate help with the following question:

Find the values of x and y-

((2/3)x) - ((3/5)y) - 4 = ((1/20)x) - y + (17/30) = 2x - y - (18 + (14/15))

I would greatly appreciate a step-by-step answer.

Thanks in advance.

[JadeDry]

Hello again, I have one more question with which I would appreciate some assistance.


Find the values of x and y-

((2/7)x) + ((3/4)y) - 4 = ((3/5)x) - ((2/7)y) - 44 = ((7/15)x) + y - (3 + (1/3))

I would greatly appreciate a step-by-step answer as before.

Thanks in advance.

[red rose]

Would appreciate help for these 2 Qs.


1) The polynomial 3x^2-9x+2 has the same remainder when divided by x-p or by x+4q, where p is not equal to -4q. Find the value of p-4q.
2) When a polynomial f(x) is divided by x+1 and x+2, the remainders are 3 and 5 respectively. Find the remainder when f(x) is divided by x^2+3x+2.

Thanks!