FP1

Question 1

Sum of roots

alpha + beta

Answer 1

-b/a

Question 2

Product of roots

Alpha X beta

Answer 2

c/a

Question 3

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

Answer 3

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

α^2β^2 = (αβ)^2 = (c/a)^2

Question 4

New roots mα and mβ. What is equation?

Answer 4

Replace x in original equation by y/m and simplify

Question 5

Σr from 1 to n

Answer 5

1/2n(n+1)

Question 6

Σr^2 from 1 to n

Answer 6

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

Question 7

Σr^3 from 1 to n

Answer 7

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

Question 8

Identity matrix

Answer 8

(1 0)

0 1

Question 9

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

Answer 9

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

Question 10

Reflection matrix in y=X

Answer 10

(0 1)

1 0

Question 11

Reflection in y=tanθx

Answer 11

(cos2θ sin2θ)

sin2θ -cos2θ

Question 12

Rotation anti-clockwise matrix

Answer 12

(cosθ -sinθ)

sinθ cosθ

Question 13

How to find vertical asymptote of rational function

Answer 13

What makes denominator 0

Question 14

How to find horizontal asymptote of rational function

Answer 14

cancel constants and see what happens as x tends to infinity

Question 15

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

Answer 15

The curve will not have a vertical asymptote

Question 16

How to find stationary points of rational function

Answer 16

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

Question 17

General formula for a parabola

Answer 17

y^2=4ax

Question 18

General formula for a ellipse

Answer 18

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

Question 19

General formula for a hyperbola

Answer 19

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

Question 20

What is a rectangular hyperbola and general formula

Answer 20

Asymptotes at 90°

xy=c^2

Question 21

i^2

Answer 21

-1

Question 22

Complex conjugated

Answer 22

z=x+iy

z*=x-iy

Question 23

Differentiating from first principles

Answer 23

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

Question 24

Two things which make an integral improper

Answer 24

• infinity or negative infinity in limits

- integral undefined at a limit or between them IE. Crosses an asymptote

Question 25

General solution for cosθ

Answer 25

``` θ= 360n° +/- α θ= 2nπ +/- α ```

Question 26

General solution for sinθ

Answer 26

``` θ= 180n° +(-1)^n α θ= nπ +(-1)^n α ```

Question 27

General solution for tanθ

Answer 27

``` θ= 180n° + α θ= nπ + α ```

Question 28

Interval bisection

Answer 28

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

Question 29

Linear interpolation

Answer 29

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

Question 30

Newton raphson method

Answer 30

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

Question 31

Euler formula for step by step solution to differential equations

Answer 31

Yn+1 ~Yn + hf(xn)

Question 32

How to prove something has a linear correlation

Answer 32

Get in the form | logy = loga +nlogx