FP1

Question 1

What is an argand diagram used to display?

Answer 1

Real and imaginary parts of complex numbers

Question 2

What is Z* if Z=a+bi

Answer 2

Z*=a-bi

Question 3

What is the name for Z*

Answer 3

The complex conjugate

Question 4

express (2+2i)/(1-3i) in the form a+bi where a and b are values to be found

Answer 4

-2/5+4/5i

Question 5

How many different roots does a cubic have?
A, 1 real 2 imaginary
B, 2 real 1 imaginary
C, 3 real 0 imaginary
D, 0 real 3 imaginary
E, 2 real 0 imaginary
F, 0 real 2 imaginary

Answer 5

Either A,C or E depending on the function

Question 6

What is this notation called=

r∠θ

Answer 6

Mod-Arg form of a complex number [Modulus argument form)

Question 7

What is on the horizontal axis of an argand diagram?

Answer 7

Real component

Question 8

What is on the vertical axis of an argand diagram

Answer 8

Imaginary component

Question 9

How would you go about finding a root of f(x) where a>x>b using interval bisection?

Answer 9

m1=(a+b)/2.
f(m1)>0 then replace b with m1.
and visa versa

Question 10

What is the formula for linear interpolation?

Answer 10

(y - y0)/(x - x0) = (y1 - y0)(x1 - x0)
Solving for y gives:
y = y0 + (y1-y0)(x - x0)(x1-x0)

Question 11

What is the principle of the Newton-Rhapson process?

Answer 11

Finds the root of the equation by finding the intersection of the x-axis and the tangent of the graph of f(x) at (x0, f(x0)).

Question 12

What is the formula for the Newton-Rhapson process?

Answer 12

x1=x0-f(x)/f’(x)

Question 13

What is the equation of the directrix for y^2=4ax?

Answer 13

x=-a

Question 14

What are the coordinates of the focus for y^2=4ax?

Answer 14

(a,0)

Question 15

What is the gradient function for y^2=4ax?

Answer 15

a/sqrt(ax)

Question 16

What are the first three identity matrices (1x1) (2x2) (3x3)

Answer 16

(1)

/10\
\01/

/100\
|010|
\001/

Question 17

What is the general form for a rotation of a 2x2 matrix at angle θ?

Answer 17

/ cos θ -sin θ \

R = \ sin θ cos θ /

Question 18

What is the size of the product of the matrices (MxN) (AxB)

Answer 18

(MxB)

Question 19

what is the size of the sum of the matrices (MxN) + (AxB)

Answer 19

(MxN) and (AxB) as you can only add matrices of equal dimensions

Question 20

What is the general form for the discriminant?

Answer 20

ad-bc

Question 21

What makes a matrix singular?

Answer 21

Discriminant=0

Question 22

how do you find the inverse of a matrix?

Answer 22

Swap signs of a and d, Swap locations of b and c. multiply by 1/discriminant

Question 23

how do you multiply a matrix by the scalar x?

Answer 23

ax bx

cx dx

Question 24

What is the general notation for sum x?

Answer 24

xn

Question 25

What is the general notation for sum r?

Answer 25

n/2(n+1)

Question 26

What is the general notation for sum r^2

Answer 26

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

Question 27

What is the general notation for sum r^3

Answer 27

n/4(n+1)^2 (sum r squared)

Question 28

What are the 4 base steps for mathematical induction?

Answer 28

1. Prove true for N=1 [true for N=1]
2. Assume true for N=K
3. Prove True for N=K+1 [which implies true for N=K+1]
4. Finishing statement [As result is true for 1 n= this implies true for all positive integers and so result is true by induction] (optional Q.E.D for style points)

Question 29

what is the general parametric equation for a rectangular hyperbola?

Answer 29

x=ct y=c/t at the point P(ct,c/t)

Question 30

What is the general Cartesian equation for a rectangular hyperbola?

Answer 30

xy=c^2 at the point P(a,b)

Question 31

What is the general cartesian formula for a parabola?

Answer 31

y^2=4ax

Question 32

What is the general parametric formula for a parabola?

Answer 32

x=at^2

y=2at