Algebra
If z is multiplied by i, how does it move around the Argand Plane?
It rotates 90 degrees anti-clockwise
Translate the following so that it is equal to the graph of y=sin(theta)
y = cos(theta)
y=cos(theta-pi/2)
State the quotient rule
quotient rule
What is resultant force equal to?
Fnet = ma
How much data lies within 2 standard deviations
around 95%
What is the domain of the Argument of a complex number
-pi to pi
State the formula for calculating the distance between two points
s = SQRT[ (x2-x1)^2 + (y2-y1)^2 ]
Fully describe the conditions for a stationary point of inflection
Where second derivative changes from positive-negative, and equals zero
(chart goes from concave up to concave down or vice versa)
State the formula for a dot product
Define a Type 1 error
fail to reject null hypothesis when it is false
Give the formula for a circle in the complex plane
|z| = r
What is the domain and range of the function y=cos^-1 (x)
DOM: -1,1
RAN: 0, pi
State the fundamental theorem of calculus
Integral from x0 to x1 of f(x)dx = F(x1) - F(x0)
= [a.b(hat)].b(hat)
How do we calculate the E(aX+b) and Var(aX+b) where X is a random variable?
= aE(X) + b
a^2*Var(X)
State de Moivre's Theorem
z^n = r^n * cis(n*theta)
Complete the following identity:
cot^2(x) +1 =
= cosec^2(x)
What is the formula for the volume of a solid of revolution rotated about the x axis
integral from y1 to y2 of pi*x^2 dy units cubed
1 - law of inertia
2 - f=ma
3 - action/reaction pairs
Give the formula for a 95% confidence interval)
(x-Z*s/SQRT(n)),(x+Z*s/SQRT(n))
What does the following give:
theta/2 * radius^2
Area of a sector
Complete the following identity:
tan(2x) =
= 2tan(x)/(1-tan^2(x)
State the four different DE expressions of acceleration
= d^x/dt^2 = dv/dt = v*dv/dt = d/dx(1/2*v^2)
How can we prove that three points are collinear?
If AB = kBC
Explain the influence of sample size on the shape and location of the distribution of a sample mean
sample size = lower sd and tighter grouping
mean - no effect