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Mathematics
Revision Notes
Pure Mathematics 2
Mathematics · Cambridge 9709
Pure Mathematics 2
6 chapters · 79 lessons
Collection
Pure Mathematics 1
Pure Mathematics 2
Pure Mathematics 3
Mechanics
Probability & Statistics 1
Probability & Statistics 2
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01
Algebra
17 lessons · 4 topic areas
01
Modulus
5 lessons
Modulus as Distance and Equations
Modulus Equations with Restrictions
Equations with Two Moduli
Graphs and Modulus Intersections
Transforming Modulus Graphs and Ranges
02
Modulus Inequalities
4 lessons
Modulus Inequalities
Modulus Inequalities with a Variable Side
Comparing Two Moduli
Sums of Moduli
03
Polynomial Division
3 lessons
Polynomial Division
Division by Non-monic Linear Polynomials
Division by Quadratic Polynomials
04
Factors and Remainders
5 lessons
Factor and Remainder Theorems
Finding Unknown Polynomial Coefficients
Solving Polynomial Equations
Quadratic Factors and Unknown Roots
Polynomial Equations with Changed Inputs
Practise this chapter
02
Logarithmic and exponential functions
19 lessons · 4 topic areas
01
Meaning and Graphs
4 lessons
What a Logarithm Means
Natural Logarithms and Calculator Keys
Exponential and Logarithmic Graphs
Shifted Functions and Their Inverses
02
Logarithm Laws and Equations
6 lessons
The Logarithm Laws
Combining and Expanding Logarithms
Solving Logarithmic Equations
Quadratic Logarithmic Equations
Unknown Bases and Nested Logarithms
Simultaneous Logarithmic Equations
03
Exponential Equations and Inequalities
5 lessons
Solving Exponential Equations
Equations with Repeated Powers
Exponential Inequalities
Exponential Models and Thresholds
Exponential Graph Intersections
04
Linearising Relationships
4 lessons
Linearising Power Models
Linearising Exponential Models
Choosing Transformed Axes
Fitting Models to Logarithmic Data
03
Trigonometry
20 lessons · 4 topic areas
01
Reciprocal Functions
5 lessons
Reciprocal Trig Ratios
Reciprocal Trig Graphs
Transforming Reciprocal Trig Graphs
Solving Reciprocal Trig Equations
Pythagorean Trig Equations
02
Compound and Double Angles
6 lessons
Compound-angle Formulae
Exact Values with Compound Angles
Equations with Compound Angles
Double-angle Formulae
Half-angle Values
Equations with Double Angles
03
Identities and Equations
3 lessons
Further Trig Identities
Multiple-angle Identities
Using Identities in Equations
04
R-form
6 lessons
R-form
Choosing Sine or Cosine R-form
Solving R-form Equations
Ranges and Extrema of R-form
Squared and Reciprocal R-form
Hidden R-form
Practise this chapter
04
Differentiation
13 lessons · 4 topic areas
01
Choosing and Combining Rules
3 lessons
Choosing a Differentiation Rule
Using the Product Rule
Using the Quotient Rule
02
Exponential, Logarithmic and Trigonometric Derivatives
5 lessons
First Derivatives of eˣ and ln x
Composite Exponential Functions
Composite Logarithmic Functions
Trigonometric Derivatives
Mixed Rules and Stationary Points
03
Implicit Curves
2 lessons
What Implicit Differentiation Means
Implicit Curve Gradients
04
Parametric Curves
3 lessons
What Parametric Differentiation Means
Parametric Tangents and Normals
Parametric Special Tangents and Direction
Practise this chapter
05
Integration
6 lessons · 3 topic areas
01
Direct Antiderivatives
3 lessons
Integration as reverse differentiation
Integrating a reciprocal linear function
Integrating sin, cos and sec²
02
Trigonometric Rewriting
1 lesson
Integrating sin² and cos²
03
Definite Integrals and Area
2 lessons
Definite Integrals and Area
The trapezium rule
Practise this chapter
06
Numerical Solution of Equations
4 lessons · 3 topic areas
01
Locating Roots
1 lesson
Locating a root
02
Fixed-Point Iteration
2 lessons
From an equation to an iteration
Running and confirming an iteration
03
Applying Numerical Methods
1 lesson
Using iteration in a longer problem
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Mathematics
AS & A Level · 9709
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