[Subterranean and Homesick]

I did the best I could with the title; I really don't know what this type of problem is called. I just had a crack at two C1 practice papers. I got near enough full marks bar these two questions:



and



I simply don't know how to answer these questions. In the second question, I got the mark on 7a) by expanding the bracket and doing a simultaneous equation. I don't know where to go from here. In the first question, I haven't got any marks at all. I've tried to find this topic in my revision guide but I can't, what is the name of the topic?

How will I solve these? is it something to do with ?

I saw from looking at the mark scheme that you can solve the last stage of the question by factorising, but how to you know what to do with the inequality sign?

Thanks in advance for your help

[Necro Defain]

If the equation has real roots, you know b^2-4ac>=0 for any quadratic ax^2 + bx + c = f(x). Use that to find the inequality. For (b), factorise the expression, and consider that for two factors to be less than zero, one must be negative while the other must be positive

[Glutamic Acid]

The discriminant!

Suppose one has a quadratic of the form ax^2 + bx + c = 0. If the discriminant, "b^2 - 4ac" > 0 then the equation has distinct real roots, if b^2 - 4ac = 0 then the equation has a repeated root, and if b^2 - 4ac < 0 then the equation has no real roots (this can be intuitively deduced by considering the quadratic formula). The term "real roots" includes both distinct roots and a repeated root, so b^2 - 4ac >= 0.

In your first question, a = k + 1, b = 12 and c = k - 4.

[Necro Defain]

For the other one, when the curves intersect, you know the two equations are equal, use that to find the expression in (a) [equate the two y values basically]

[The Muon]

If a quadratic has real roots then

So for the first bit you just need to but a, b and c in the equation above, expand, and rearrange.

For the inequalities bit see this thread

Finally if a line and a curve intersect at two distinct points the equation you find which gives the x coordinates will have two real solutions so

[hazzypants]

you do b squared - 4ac.

for the first question it is 12x^2-4x(k+1)x(k-4)

which gets you to 160-4k^2+12k

then simplify to get 40-k^2+3k

which is the same as k^2-3k-40 less than or equal to 0.

then factorize to (k+5)(k-8)

k= -5 and +8 and draw a graph.. think this is right!

[hazzypants]

so when x is greater or equal to 8, or less than or equal to -5 and possible values of k.

is that what the mark scheme says?

[.:excel4100%:.]

Second Question:

a) Intersection means when 'y's of two equations are the same so
x^2 +7= k(3x+1)
x^2 +7=3kx + k
x^2 -3kx + 7 - k =0

b) Two distinct points suggests different real roots....Roots=Discriminant
b^2-4ac>0
(-3k)^2 - 4(1)(7-k)>0
9k^2 + 4k - 28 >0

c) (9k - 14)(k + 2) > 0 Cr. values: k= 14/9 or -2
Draw a graph...Solutions: k<-2 or k>14/9

It's a typical last or second-to-last question so practice..

Good luck on friday

[Subterranean and Homesick]

Thanks for all your help, I'm going to have a crack at solving them - could someone have a look to see if this is right?

7)a) for this eqn, a = (k+1), b = 12, c = (k-4)

0 = 12^2 - (4(k+1)(k-4))

0 = 144 - (4k^2 + 4k -16k -16)

0 = 144 - 4k^2 -4k +16k + 16

0 = 144 -4k^2 + 12k +16

0 =< -4k^2 + 12k + 160

move everything to other side and divide by four to give...



b) to find values of k, factorise k^2 - 3k - 40

= (k+5)(k-8)

0 >= (k+5)(k-8)

8 >= k >= -5

-----

7a) simultaneous equation... I knew how to do this before

b) b^2 - 4ac > 0 (two distinct roots)

4^2 - 4(9)(-28) = 16 + 1008 = 1024

1024 > 0, so C and L must intersect and two distinct points.

c)

= (9k-14)(k+2)

= (k-14/9)(k+2)

= 14/9 >= k >= -2

Is that all correct?

[Daniel Freedman]

Originally Posted by Glutamic Acid

The discriminant!

I know of someone that would tap that.

[Tallon]

I got k<-2 or k>14/9

[Subterranean and Homesick]

I've just practised a question like this...

I got the equation at the end as

This is definitely right, I checked it in the mark scheme.

Anyway, I worked this out by moving to the other side/adding and subtracting as and

therefore, I ended up with just , because the first term is meaningless. But this is WRONG according to the mark scheme, I'm supposed to have ended up with . How do I get there? This is basic algebra, I should know better..

[Subterranean and Homesick]

anyone? ^

[.:excel4100%:.]

Originally Posted by Subterranean and Homesick

I've just practised a question like this...

I got the equation at the end as

This is definitely right, I checked it in the mark scheme.

Anyway, I worked this out by moving to the other side/adding and subtracting as and

therefore, I ended up with just , because the first term is meaningless. But this is WRONG according to the mark scheme, I'm supposed to have ended up with . How do I get there? This is basic algebra, I should know better..

For this type of question you should sketch the u-shaped curve and mark the points where they intersect with the x-axis (roots), for clarification.

When the equation is f(k) <=0 then its the part of the u curve under the x-axis, which in your case is 1/2 <= k <= 2.

For this question it's better to sketch a small u shaped curve and mark the roots.

If the question asks for f(x) < 0 then it's under the x-axis which should be something like, e.g. 2 < x < 3/2...

However if the question asks for f(x) > 0, then it's over the x-axis and should be something like, (for the same example), x<2 and x>3/2.

Good luck tomorrow mate

[Fatima0065]

Hello, i don't know how to do harder simultaneous equations- canomeone help me?
1) 2x/3 +y=16, x+y/4=14
2)x/3+x/2=5, x+y= 5
Also ,how do i do these: a^2b/cd^3 * c^2d/ab^3
thanks

[steve2005]

Originally Posted by Fatima0065

Hello, i don't know how to do harder simultaneous equations- canomeone help me?
1) 2x/3 +y=16, x+y/4=14
2)x/3+x/2=5, x+y= 5
Also ,how do i do these: a^2b/cd^3 * c^2d/ab^3
thanks

The first thing with Q1 is to get rid of the fractions. Multiply the first by 3 to get 2x + 3y =48 , multiply the second by 4. Then the equations will look much better and it should be obvious what to do.

[Fatima0065]

Thankyou so much, i haven't tried it yet and erm how do i do the algebra one at teh bottom. by the way thanks again oh yh o i do the same for the second simultneuos equation?

[Fatima0065]

Hello steve, how are you? im sorry to bother you again but is it possible for you to help me with these questions a step by step guide on how to get the answer.
A parabola passes through three points. find the equation
(-2,0) (3,0) (0,-30)

How to find the greates and least value when completing the square

Surds in Pythagros's thereom:
hypotenuse is 5 root 2
1 side is 3cm whats the lengthof the other side

How do i change change y=mx +c into ax+by+c=0 for these:

1) find the equation of the line passing through (-3,-2) parallel to the line 5x+10y-8=0. Give your answer in ax+by+c=0
2)find the equation passing through (2,-3) perpendicular to 6x-2y-13=0. Give your answer in ax+by+c=0
3) Find the equation of the distance joining the points (-8,5) (2,-4). Give your answer in ax+by+c=0

thanks a lot, youve been an amzing help, ur a life saver