- To find the Cartesian equation of a curve give parametrically you eliminate the parameter t between the parametic equations.
- The are under a graph is given by ∫y dx. By the chain rule ∫y dx = ∫y dx/dt dt.
1 of 9
The Binomial Expansion
2 of 9
- You can find the gradient of a curve given in parametric coordinates
dy/dx = dy/dt ÷ dx/dt
- Implicit differentiation
When f(y) is differentiated with respect to x it becomes f'(y)dy/dx.
A product term such as f(x) . g(y) is differentiated by the product rule and becomes
f(x) . g'(y)dy/dx + g(y) . f'(x)
- y = a^x dy/dx = a^x lna
3 of 9
- Vectors that are equal have the same magnitude and the same direction.
- The modulus is another name for its magnitide
Vector a is written as |a|
- The modulus or magnitude of xi + yj is √x² + y²
- The distance between the points (x₁, y₁, z₁) and (x₂, y₂, z₂) is
√(x₁-x₂)² + (y₁-y₂)² + (z₁-z₂)²
- The scalar product of two vectors a and b is written as a.b and defined by a.b = |a||b| cosθ where θ is the angle between a and b.
- cosAOB = a.b
- If two vectors are perpindicular the angle between them is 90
because cos90° = 0 then a.b = |a||b| cos 90° = 0
4 of 9
5 of 9
Trigonometric Identities and Standard Patterns
6 of 9
Substitution and Integration by Parts
7 of 9
Trapezium Rule and Volume of Revolution
8 of 9
Separating the Variables
9 of 9