Help with C1!

Original post by Rather_Cynical

I have terrible handwriting but made a worked solution.

this is very thorough :smile:

thanks

Reply 22

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i'm having a look through C1 spec and im a bit stuck on this bit. i understand what they mean by ''knowledge of the effect of simple...'' but what does the first paragraph mean? can you give me an example?

Reply 23

fefssdf

they just mean that if they give you a quadratic then you'll be able to sketch it, and that you recognise that the number roots of an equation can be determined by the number of intersections of a graph.

Reply 24

Original post by fefssdf

ok thanks i think i know how to do that. is it something to do with the discriminant, completing the square, then find minimum/max points?

Reply 25

It's already been said, you just need to know how to find key points of F(x) like the points of intersection ect...

You learn the manipulation of functions at GCSE so it shouldn't be too difficult.

Reply 26

discriminant lets to know how many roots their are.

>0 means two roots
= 0 means one root.
<0 means no roots

Completing the square will give you the max or minimum point of a curve. eg. (x-2)^2-9, the minimum point of that curve will be( 2, -9)

Reply 27

Original post by 34908seikj

is this what the paragraph means?

Reply 28

It means you'll be able to sketch curves with simple equations like

x^2, x^3-x^2

, as its restricted to the form

y=f(x)

it seems you won't have to sketch circles (any conic section for that matter), exponentials/log graphs, implicit functions. Basically things that you did at GCSE.

Reply 29

Rather_Cynical

If we had a graph of a quadratic that intersects the x-axis at the points x = 1 and x = -6, you need to be able to figure out that it means

f(x) = (x + 6)(x - 1) = x²+ 5x - 6

If one of the brackets is solved as zero, then f(x) = zero.

The curve is defined as y = f(x) and when it equals zero, you have the x-intercept.

Reply 30

Original post by 34908seikj

Any polynomial with degree n has n roots (multiple roots). But every polynomial (complex coefficients) has at least one root.
The discriminant of a cubic can be less than 0 but does that mean there are no real roots?

(edited 7 years ago)

Reply 31

The top paragraph literally just means that you should know how to use the intersection of points to solve equations. It's as simple as that. Eg. when two curves, or a straight line means a curve and you have worked how say the equations of both, you can find the values for x.

The bottom part of the paragraph is GCSE.

y=aF(x) - means multiply the y values of the function by a
yY=F(x) + a - means move the y values of F(x) up by a units

y=F(x+a) - means add the x vales of F(x) by a, e.g., the minimum point of f(x) was (1,1) then F(x+a), where a = 4, the minimum point will now be 5,1

y=f(ax) - means divide the x values of F(x) by a, similarly if y=F(x/a) then you multiply the values of x by a.

Just remember inside the bracket manipulates the X axis and it's always opposite and that anything outside the bracket manipulates the Y axis and is NOT opposite.

Reply 32

Rather_Cynical

It'll be easiest to show you with an exam paper question, it's harder to talk in abstract if you're not familiar with the concepts as a whole.

Reply 33

Original post by B_9710

Any polynomial with degree n has n roots.
The discriminant of a cubic can be less than 0 but does that mean there are no real roots?

idk, In the context of C1, I don't think you have to find the discriminant of a cubic. I may have passed over it, but I don't remember covering cubics and discriminants. Or at least you could factorise it into a quadratic first.

Reply 34

Original post by 34908seikj

For the following equation

ax^3+bx^2+cx+d

the discriminant is

18abcd-4b^3d+b^2c^2-4ac^3-27a^2d^2

.
This isn't C1 but I'm just responding to what you said about if the discriminant is < or = or > 0.

Reply 35

Original post by B_9710

For the following equation

ax^3+bx^2+cx+d

the discriminant is

18abcd-4b^3d+b^2c^2-4ac^3-27a^2d^2

.
This isn't C1 but I'm just responding to what you said about if the discriminant is < or = or > 0.

Interesting! Though, my knowledge of the discriminant doesn't go past C1 right now, I've taken a small detour onto FP1 instead of C2.

b^2-4ac

Is as far as it goes for me, right now at least.

Reply 36

Original post by 34908seikj

Interesting! Though, my knowledge of the discriminant doesn't go past C1 right now, I've taken a small detour onto FP1 instead of C2.

b^2-4ac

Is as far as it goes for me, right now at least.

It doesn't come up anywhere at A level.

Reply 37

What does this notation mean?

i'm on binomial expansion and came across this, i understand the substitution part, the factorial equation substitution but what does that notation mean? 'n' on top of 'r' . does it mean n take away r? cos thats the pattern i see in the equation

Reply 38