Maths (Paper 1)

[diwash]

May/june 09 Qno 10(III)
http://www.xtremepapers.me/CIE/International A And AS Level/9709 - Mathematics/9709_s09_qp_1.pdf
and Oct/nov 07 Qno11 (iv)
http://www.xtremepapers.me/CIE/International A And AS Level/9709 - Mathematics/9709_w07_qp_1.pdf
are simmilai questions asking the value of A

In may june 2009 question f(x)= 2(x-3)^2 - 5
i thought for the line of symmetry X -3 = 0 ....X=3 ....the maximum value of A is 3....but ms says its 6

However in oct/nov 07 question f(x)=2(x-2)^2 + 3
the same process gets the right answer....A=2

Can any one explain me with this....?

 

[ahmed t]

for s09
at X=0 Y=13
u want another point on the line where Y=13 so it can be symetric so u replace 13 as Y in the equation and solve for X u will get 0 and 6, here:
2X^2 -12X +13=13
2X^2 -12X=0
taking X as common factor
X(2X-12)=0
X=0 or 2X=12,X=6
hope it helps

 

[Saturation]

Hello!
1) State the value of A for which the graph of y = f(x) has a line of symmetry.

When you look at the domain, it shows 0 =< x =< A
So when you work out the vertex of the parabola, you get x= 3
Now, if you were to put A=3, what you're actually doing is "limiting" the graph from x=0, to x= 3, which means it's not going to be a parabola! it'll look like half a parabola ( which doesn't have a line of symmetry). Therefore, if by using A=3, you're limiting the curve to half a parabola, then if you double it, you should get a full parabola, which will have a LINE of symmetry at X=3!
Thus the domain should be:
0 =< x =< 6 , with A = 6 , and a line of symmetry with X=3

2) State the largest value of A for which g has an inverse.

Firstly, for a function to have an inverse it must be a one to one function, which means ( double check on this please!), if you draw a horizontal line anywhere on the graph paper, it should intercept the graph only at one point. In the case of a parabola, a horizontal line will intercept it at two points. So, to get an inverse of the function, we need to restrcit the domain so that only one half of the parabola will exist. For this we use the vertex of the graph, which is at X= 2. Therefore, from x=< 2, the parabola will be "halved", and thus be a one to one function, and will have an inverse!

Hope you were able to understand this! ( it's hard to explain in a forum post!)

 

[diwash]

Thanks ....i got it....