AQA Level 2 Further Maths

kk thank you sm x

Anyone else taking this paper? I haven’t seen a discussion for it anywhere

calculs an matrixes?
could u like explain a lil ty xx

Differentiation

To differentiate, take all terms of an expression or equation, and multiply the coefficient of the term by the power, then decrease it by one. This tells you the rate of change of the function. If dy/dx is positive, the function is increasing. If dy/dx is negative, the function is decreasing.

Tangents and Normals

Tangents have the same gradient as the point on the function they are tangent to, whereas the gradient of normals is the negative reciprocal of the gradient of the point on the function they are normal to (or perpendicular to). The same can be done with circles if you work out the gradient of their radius (change in y/change in x).

Stationary Points

To find the stationary points of a curve, you need to look where dy/dx = 0. This will usually be a quadratic (factorise) or a cubic (factor theorem then factorise) will tell you the x values of the points where there is a stationary point. In order to find the y value, plug the value back into the original function, that’s the coordinate of the stationary point.

In order to find the nature of said stationary point, differentiate again (d^2y/dx^2). Then plug in the x value into that. If the value is negative, the point is a maximum, if the value is positive, the point is a minimum. If the value is zero it’s likely a point of inflection but I've been told to check the first derivative of points either side just to be sure, it works most of the time but just check in case.

Solve the simultaneous equations
xy = 2 and y = 3x + 5
Do not use trial and improvement.
You must show your working


omg how the hek do u do this
it 6 freekin marksss

omggg tysmmm im literally taking down notes rnn

x(3x+5) = 2
3x^2 +5x - 2 = 0
(3x-1)(x+2) = 0
x = 1/3, x = -2

y = 3x+5
y = 1+5 = 6 and y = -6+5 = -1

x = 1/3, y = 6
and x = -2, y = -1

you smart

you’re welcomeee :3

i’ll sort the matrices after i’ve eaten

x(3x+5) = 2
3x^2 +5x - 2 = 0
(3x-1)(x+2) = 0
x = 1/3, x = -2

y = 3x+5
y = 1+5 = 6 and y = -6+5 = -1

x = 1/3, y = 6
and x = -2, y = -1

shush no i don’t all i did was solve a question

YH A FREEKIN 6 MAKRERRRRRR
in fmm
shushh
u are the G.O.A.T, okay? let that sink in ur brain

6 markers are just 5 markers with extra steps, i find them fun most of the time lol

yeah no difference there between 5 and 6 markers, soo simple
face it, u have an IQ of like 372393, okay?
now sh and eat