# AQA Level 2 Further Maths

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

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@A____J
i might post the stuff about further here so others can view it
kk thank you sm x
Original post by A____J
kk thank you sm x

yw! if you have any questions feel free to ask
calculs an matrixes?
could u like explain a lil ty xx
Original post by illegallylexi
Anyone else taking this paper? I haven’t seen a discussion for it anywhere

Yep.
I was just looking for a discussion. Thanks
Original post by A____J
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
Original post by illegallylexi
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.

omggg tysmmm im literally taking down notes rnn
Original post by A____J
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

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
Original post by A____J
omggg tysmmm im literally taking down notes rnn

you’re welcomeee :3

i’ll sort the matrices after i’ve eaten
(edited 1 year ago)
Original post by illegallylexi
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
Original post by lesgo21
you smart

thank youuuu! i try
Original post by illegallylexi
you’re welcomeee :3

i’ll sort the matrices after i’ve eaten

np x u deserve the complimets lol
shush no i don’t all i did was solve a question
Original post by illegallylexi
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

copied it down now i just gotta make sense of it lol
Original post by illegallylexi
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
Original post by A____J
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
Original post by illegallylexi
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
Original post by A____J
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

based on the crappy online tests it’s about 140 but shush, and i can’t eat yet as it hasn’t been cooked but i’ll type the matrix rubbish out then (i don’t like them very much)