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Level 2 Further Mathematics AQA
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Level 2 Further Mathematics AQA
free revision notes.
Level 2 Further Mathematics AQA
– Topics
Algebra
n-th Terms of Quadratic Sequences
n-th Terms of Linear Sequences
Using n-th Terms of Linear Sequences
Algebraic Proof
Index Laws
Solution of Linear and Quadratic Inequalities
Algebraic Solution of Linear Equations in 3 Unknowns
Algebraic and Graphical Solution of Simultaneous Equations in 2 Unknowns
Solution of Linear and Quadratic Equations
Interpretation of Graphs
Drawing and Sketching of Functions
Completing the Square
Use of the Factor Theorem for Rational Values of the Variable for Polynomials
Manipulation of Formulae and Expressions
Manipulating of Rational Expressions
Factorising
Expand (a + b)^n for Positive Integer n
Expanding Brackets and Collecting Like Terms
Inverse Functions
Composite Functions
Domain and Range of a Function
Definition of a Function
The Basic Processes of Algebra
Calculus
Sketch or Interpret a Curve with Known Maximum and Minimum Points
Using Calculus to Find Maxima and Minima in Simple Problems
Use of Differentiation to Find Maxima and Minima Points on a Curve
Understand and Use the Notation d^2y / dx^2
Differentiation: Increasing and Decreasing Functions
The Equation of a Tangent and Normal at any Point on a Curve
Differentiation of kx^n
Differentiation: Gradient Function
Coordinate Geometry (2 Dimensions Only)
The Equation of a Tangent at a Point on a Circle
The Coordinate Geometry of Circles: (x - a)^2 + (y - b)^2 = r^2
The Coordinate Geometry of Circles: x^2 + y^2 = r^2
The Straight Line: Equation of a Circle
The Coordinate Geometry of Circles
Draw a Straight Line from Given Information
The Equation of a Straight Line (y = mx + c)
Use Ratio to Find the Coordinates of a Point on a Line Given the Coordinates of 2 Other Points
The Straight Line: Use Pythagoras' Theorem to Calculate Distance between 2 Points
Know the Relationship between the Gradients of Parallel and Perpendicular Lines
The Straight Line: Know and Use the Definition of a Gradient
Geometry
Solution of Simple Trigonometric Equations in Given Intervals
Know and use tanθ = sinθ / cosθ = and sin^2 θ + cos^2 θ = 1
Knowledge and use of 30-60-90 and 45-45-90 Triangles
Using the Definitions sin θ, cos θ and tan θ
Sketch and Use Graphs y=sin x, y=cos x, y=tan x
Pythagoras' Theorem
Trigonometry in Triangles
Geometric Proof
Matrix Transformations
Combination of Transformations
Transformations of the Unit Square in the x - y Plane
The Identity Matrix
Multiplication of Matrices
Number
Manipulation of Surds, including Rationalising the Denominator
The Product Rule for Counting
Use of Numbers