Unit 2 Flashcards
How do you find the roots of a quadratic
Factorise
Complete the square
Use quadratic formula
What is the quadratic formula
x = -b +- √b²-4ac
2a
What is the discriminant formula
b²-4ac
If b²-4ac>0…
The roots are real and unequal/distinct
If b²-4ac=0…
The roots are real and equal/repeated root
If b²-4ac<0…
There are no real roots
y=a(x+p)²+q
How to extract axis of symmetry
x=-p
y=a(x+p)²+q
How to extract turning point
(-p,q)
How to determine how many roots a parabola has
Use discriminant formula
b²-4ac
How to sketch a parabola with one or two roots
Factorise or use quadratic formula to find x axis intercepts
Use x=0 to find y axis intercepts
Find turning point, halfway in between x coordinates
How to sketch a parabola with no real roots
Find y axis intercept with x=0
Find turning point by completing the square
Formula for the equation of a parabola
y=k(x-a)(x-b)
How to find the equation of a parabola
Sub in x coordinates to a&b in equation
Sub in y coordinates
Rearrange to find k
Write out equation
How to solve a quadratic inequality
State whether concave up or down
Factorise to find where cuts the x axis
Draw graph to find where x is on parabola
State values of x
How to find the point of contact of a tangent
Make equations equal
Rearrange
Factorise for x value
Sub x value into equation of line
How to find points of intersection of curves
Make equations equal
Factorise for x coordinates
Sub into equation of line for y coordinates
Equation to determine equation of curve
y=k(x-a)(x-b)(x-c)
How to determine equation of curve
Sub roots into equation
Sub coordinates of point into equation
Rearrange to find k
Write out equation
How to integrate
Plus one to indice
Divide number by indice
Write +c on end
How to find a definite integral
Integrate
Sub in each limit and take them away from the other
How to calculate the shaded area of a graph
Use definite integration with the two x roots
How to find the area between curves
Work out points of intersection by making equations equal and factorising
Integrate upper curve - lower curve
Sub in limits
Sin
180 - x
Tan
180 + x
Cos
360 - x
Eg.
3tan(3x-20)=5
tan (3x-20) = 5/3
3x-20 = tan-1 (5/3)
=59
3x-20 = 59 or 239 or 419 or 599 or 779 or 959
3x = 79 or 259 or 439 or 619 or 799 or 979
x = 26.3 or 86.3 or 146.3 or 206.3 or 266.3 or 326.3
Trig identities
tanx = sinx/cosx
sin²x + cos²x = 1
How to find the equation of a circle
Sub in centre point and radius to equation
(x-a)² + (y-b)² = r²
If (p-a)²+(q-b)²< r²…
The point lies within the circle
If (p-a)²+(q-b)²= r²…
The point lies on the circumference of the circle
If (p-a)²+(q-b)²>r²
The point lies outwith the circle
How to find the centre of a circle from the equation
State what 2g and 2f are equal to
Rearrange
State coordinates with (-g,-f)
How to find line’s points of intersection in a circle
Sub equation of line into equation of circle
Solve to find x coordinates
Sub into equation of line for y coordinates
How to prove a line is a tangent to a circle
Sub equation of line into equation of circle
Solve to find x coordinates
If there is only one x coordinate, the line is a tangent
How to find the equation of a tangent to a circle
Find point of intersection which lies on the circle
Find centre of circle
Find gradient of line with centre of circle and tangent point
Find perpendicular gradient
Write equation
If d > r1 + r2…
The circles do not touch
If d = r1 + r2…
The circles touch externally
r1 - r2 < d < r1 + r2
The circles meet at two distinct points
If d = r1 - r2…
The circles touch internally
If d < r1 - r2…
The circles do not touch
