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