Method - Definite interval

Method - Area under a curve

Method - Area between a curve and a line 
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Method- Classifying the stationary points 

Method - The Quick Way

Eg function= y=axⁿ
Derivative = n x ax^n-1
Method- Finding the tangent to a curve 

Method - Finding the normal to a curve

Key information
If the solution is negative, the point lies inside the circle.
If the solution is equal to 0, the point lies on the circle.
If the solution is positive, the point lies outside the circle.
Method - Circle and line intersect

Key information
When they intersect twice, there will  be two sets of coordinates
Where there is one point of intersection ( a tangent), there is one set of coordinates
Method - No points of intersection

Method - Do Circles meet?
Find distance between centres (length of line)
Find radius of both circles
Key Information
No points of intersection = C₁C₂ > r₁ + r₂
Two points of intersection =C₁C₂ < r₁ + r₂
Circles tough externally =C₁C₂ = r₁ + r₂
Circles touch internally= C₁C₂ = r₁ - r₂
Orthogonal Circles =d² = r₁² +  r₂²
(If the tangents are perpendicular at point of intersection they are said to be orthogonal)

Method - Finding Intersections

Method - Determining the number of solutions
Rearrange one of the equations so that it equals x or y
Substitue changed equation into other
Simplify and put into form ax² + bx + c = 0
Use b² - 4ac

Key Information
b² - 4ac > 0 Lines intersect at two points
b² - 4ac = Lines intersect at one point
b² - 4ac < 0 Lines do not intersect

 

Method - Intersections

Key Information
Questions may be worded like ' lines l₁ and l₂ intersect at point C. Show C has coordinates (x,y)
Method  - Axis Intersection

Key Information
When the line crosses they y axis, x=0
When the line crosses the x axis, y=0
Method - Angles between two lines

Method - Quadratic graphs

3 States
b² - 4ac > 0 Two real roots
b² - 4ac = 0  One real root
b² - 4ac < 0 No real roots