Half Term 2 Flashcards
What is the equation for a circle centred at the origin?
x^2 + y^2 = r^2
What is the equation of a circle with centre (a,b)?
(x-a)^2 + (y-b)^2 = r^2
What is the tangent perpendicular to?
The radius
T/F: Any perpendicular bisector to the chord passes through the centre
True
What does it mean when a circle is circumscribing a triangle?
The circle surrounds the triangle with the vertices of the triangle all touching the circumference of the circle
What is the circle that circumscribes a triangle called?
The circumcircle
What is the centre of a circumcircle called?
The circumcentre
What is the hypotenuse of an inscribed triangle also?
The diameter of the circle
What is the differential equation of a function?
f’(x) = (f(x+h) - f(x)) / h
If y = ax^n then dy/dx = ?
anx^(n-1)
n! = ?
n x (n-1) x (n-2) x … x 2 x 1
What is the factorial of n?
The number of ways of arranging n things in a line
nCr = ?
(n!) / r!(n-r)!
What is nCr?
The number of ways of choosing r things from a selection of n things when order doesn’t matter
What is the sine rule?
sinA / a = sinB / b = sinC / c
a / sinA = b / sinB = c / sinC
What is the cosine rule?
a^2 = b^2 + c^2 - 2(bc) x cosA
A = 1/2 x a x b x sinC
What do you use cos, sin or tan of 45?
Use a right-angled isosceles triangle
What do you use to find cos, sin or tan or 30 or 60?
Use an equilateral triangle split down the middle
What is a cast diagram?
Split into four quadrants which dictate what values are positive or negative
What are the two main trigonometric functions?
sinx/cosx = tanx
sin^2x + cos^2x = 1
What is the relationship between sin and cos angles?
sin(x) = cos(90-x)
How do you find other solutions to sin, cos and tan equations?
sin(x) = sin(180 - x)
cos(x) = cos(360 - x)
tan(x) = tan(180 + x)
If y = ax^n then dy/dx = ?
anx^(n - 1)
What does it mean if f’(x) > 0?
The function is increasing for the interval of [a,b]
What does it mean if f’(x) < 0?
The function if decreasing for an interval of [a,b]
What is the notation for second order differentiation?
(d^2 x y) / (d x x^2) or f’’(x)
How can you tell if a stationary point is a min, max or point of inflection?
If f’‘(x) > 0 it is a minimum
If f’‘(x) < 0 it is a maximum
If f’‘(x) = 0 it could be a min, max or point of inflection
What are the rules for mapping the gradient function of an equation?
1. Max/min – > ?
2. Point of inflection –> ?
3. Positive gradient –> ?
4. Negative gradient –> ?
5. Vertical asymptote –> ?
6. Horizontal asymptote –> ?
- Cuts the x-axis
- Touches the x-axis
- Above the x-axis
- Below the x-axis
- Vertical asymptote
- Horizontal asymptote at y = 0
