# Additional Maths

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- Created by: A.B.
- Created on: 27-03-13 20:11

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- Additional Maths
- Algebra
- 1 (Recapping)
- Linear Expressions
- Quadratic Expressions
- To Solve
- Factorise
- Quadratic Formula
- Complete the Square
- Halve b then square it and add it on inside the brackets. Minus this number after +c. Factorise the values inside the bracket. Rearrange to solve, giving 2 values due to the square root.

- To Solve
- Simultaneous Equations
- Substitution
- When y is subject (or other unknown).

- Elimination
- Add or subtract to eliminate variables
- Substitute into first equation.

- When y is not the subject.

- Add or subtract to eliminate variables

- Substitution

- 2
- Linear Inequalities
- Do the same to both sides.
- Open circles show that the number is not included
- Closed circles show the number is included
- Quadratic Inequalities
- Sketch a graph
- Draw a table showing values of x
- Terms MUST be collected to one side

- Algebraic Fractions
- When multiplying, only multiply the numerator

- Simplifying expressions containing square roots
- Rationalise the denominator

- Linear Inequalities
- 3 (polynomials)
- Factor Theroem
- If (x-a) is a factor of f(x) then f(a)=0.
- Can be found through division of polynomials.

- If (x-a) is a factor of f(x) then f(a)=0.
- Remainder Theorem
- f(a) is the remainder when f(x) is divided by (x-a)

- Factor Theroem
- 4 (Bionomials)
- Bionomial Distribution
- In probability...
- The probability of a successful outcome is 'p'
- The probability that the outcome is a failure is 'q'
- There are 'n' trials
- The number of successes is 'X'

- In probability...

- Bionomial Distribution

- 1 (Recapping)
- Co-ordinate Geometry
- 1 (Straight lines and circles)
- To find the distance between a and b
- Use Pythagoras

- Circles
- With centre (h,k) and radius r
- When the centre is at the origin (0,0) (Simplified version of other).

- With centre (h,k) and radius r
- The co-ordinates of the point of intersection of two lines are found by solving their equations simultaneously.

- To find the distance between a and b
- 2 (Inequalities)
- Represent boundaries that are < or > as a dotted line whereas if they are also equal to as a solid line.
- Region where inequalities satisfied simultaneously called the feasible region.
- Objective function is the quantity wanted to be maximised or minimised (e.g. profit)
- Will lie at, or near to the vertex of the feasible region.

- 1 (Straight lines and circles)
- Trigonometry
- 1 (Review)
- SOHCAHTOA,for right angled triangles.
- For angle theta, in right angled triangle
- For triangle ABC
- Sine rule
- Cosine rule
- Area

- Sine rule
- Sin theta and Cos theta can only take values between 1 and -1

- 2 (Applications)
- In 3D
- Plane = flat surface
- 2 lines may meet, be parallel or be skew
- Untitled

- In 3D

- 1 (Review)
- Calculus
- Differentation
- Used to find whether point is maximum, minimum or point of inflection.

- Integration
- Used to find area under graph
- Definite
- Indefinite

- Kinetmatics
- SUVAT
- Variables
- Acceleration = a, Initial velocity = u, at time =t, velocity = v and displacement = s.

- Equations
- For General Motion

- Variables

- SUVAT

- Differentation

- Algebra

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