Pure Flashcards
When using parametric equations, what is the domain and range of f(x)?
Domain- the range of x= f(t)
Range- the range of y= f(t)
How do you differentiate parametric equations?
Dy/dx = dy/dt X dt/dx
How do you integrate parametric equations?
Area= f y X dx/dt dt
When integrating by parts, how do you determine which part is U, and which is dv/dx?
U is LATE
longs
Algebra
Trig
Exponentials
How do you integrate lnx?
Use integration by parts
lnx X 1
U= lnx
Dv/dx= 1
How do you prove that tanx integrated is ln(secx) + c
Tanx = sinx/cosx
Integrate by recognition (-cosx differentiates to sinx)
= -ln(cosx) + c
= ln(secx) +c
How can you proove that cotx integrated is ln(sinx)
Use integration by recognition
Cotx= cosx/sinx
cosx integrated is sinx
When using the trapezium rule to estimate area, how many strips are there compared to values of x and y?
If there are n strips, there are n+1 values for x and y
Simplify sin2x
2sinxcosx
What are the three ways to Simplify cos2x?
cos^2x - sin^2x
1- 2sin^2x
Cos^x -1
Simplify tan2x
2tanx / (1-tan^2x)
How do you differentiate trig from first principles?
Use small angle approximations for h
What is a rational number?
A number that can be defined by a/b
Where a and b are integers
What is a natural number
A positive integer
What are the two types of functions- do they have inverse functions?
One to one function- has inverse
Many to one- does not have inverse
How can you tell is an expression is a function or not?
Not a function when the domain can map ro more than one range
What is the equatipn for arc length in radians?
0r
What is the equatipn for area of a sector in radians?
0r^2 / 2
Using angles in all four quadrats, in which quadrats are each trig values positive?
1quadrat- all
2quadrat- sin
3quadrat- tan
4quadrat- cos
What is the relatipnship between the graphs lnx and e^x?
Reflection in the line y=x
Equation for area of a triangle
Area = 1/2 absinC
Cosine rule for length of a triangle
a* = b* + c* - 2bccosA
Equation for distance between two points
D= d=√((x2 – x1)² + (y2 – y1)²)
How do you identofy a root?
Graph must be continuous
Must be a sign change around the interval
How can you identify a stationary point?
Where dy/dx is zero
Or when there is a sign change on the interval (gradient goes from decreasing to increasing)
What is a gradient?
A number that describes the steepness of a curve at a particular point
What is a gradient function?
A formula that allows you to find the gradient of a formula at any given point on a curve
What are two ways to prove/ disprove a statement
Proof by exhaustion, proof by counter example
State the two equations linking tanx cotx secx and cosecx
1+ tanx = secx
1+ cotx = cosecx
