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Flashcards in FP1 Deck (32):
1

Sum of roots
alpha + beta

-b/a

2

Product of roots
Alpha X beta

c/a

3

For new roots α^2 and β^2, what are a b and c

α^2 + β^2 = (α+β)^2 - 2αβ = (-b/a)^2 -2(c/a)
α^2β^2 = (αβ)^2 = (c/a)^2

4

New roots mα and mβ. What is equation?

Replace x in original equation by y/m and simplify

5

Σr from 1 to n

1/2n(n+1)

6

Σr^2 from 1 to n

1/6n(n+1)(2n+1)

7

Σr^3 from 1 to n

1/4n^2(n+1)^2

8

Identity matrix

(1 0)
(0 1)

9

How to transform point (x,y) by matrix (ab|cd)

M(x|y) = (ab|cd)(x|y)

10

Reflection matrix in y=X

(0 1)
(1 0)

11

Reflection in y=tanθx

(cos2θ sin2θ)
(sin2θ -cos2θ)

12

Rotation anti-clockwise matrix

(cosθ -sinθ)
(sinθ cosθ)

13

How to find vertical asymptote of rational function

What makes denominator 0

14

How to find horizontal asymptote of rational function

cancel constants and see what happens as x tends to infinity

15

If denominator of a quadratic rational function doesn't have real roots

The curve will not have a vertical asymptote

16

How to find stationary points of rational function

Make curve = k and solve, putting in form b^2-4ac =0

17

General formula for a parabola

y^2=4ax

18

General formula for a ellipse

x^2/a^2 +y^2/b^2 =1

19

General formula for a hyperbola

x^2/a^2 - y^2/b^2 =1

20

What is a rectangular hyperbola and general formula

Asymptotes at 90°

xy=c^2

21

i^2

-1

22

Complex conjugated

z=x+iy
z*=x-iy

23

Differentiating from first principles

Using chord AP with A(x1,y1) and P(x+h,y2) as h tends to 0

24

Two things which make an integral improper

- infinity or negative infinity in limits
- integral undefined at a limit or between them IE. Crosses an asymptote

25

General solution for cosθ

θ= 360n° +/- α
θ= 2nπ +/- α

26

General solution for sinθ

θ= 180n° +(-1)^n α
θ= nπ +(-1)^n α

27

General solution for tanθ

θ= 180n° + α
θ= nπ + α

28

Interval bisection

If a root lies between f(a) and f(b), try x=a+b/2. Sign determines which side root is closer to. Repeat until desired accuracy

29

Linear interpolation

Using similar triangles to compare x/y ratios and find estimation for the root

30

Newton raphson method

If α is an approximation of a root of f(x)=0, hen a better approximation is given using α-f(α)/f'(α)

31

Euler formula for step by step solution to differential equations

Yn+1 ~Yn + hf(xn)

32

How to prove something has a linear correlation

Get in the form
logy = loga +nlogx