Conquer
The
Academy
Welcome
back
Skip to content
Conquer
YOUR A LEVELS
Subjects
C
Cambridge
E
Pearson Edexcel
AQA
AQA
OCR
OCR
Competitive
Study space
Mistake Bank
AI Marking
Log in
Create free account
Study space
Mistake Bank
AI Marking
Subjects
C
Cambridge
E
Pearson Edexcel
AQA
AQA
OCR
OCR
Competitive
Log in
Create free account
Course navigation
Mathematics
Revision Notes
Pure Mathematics 3
Mathematics · Cambridge 9709
Pure Mathematics 3
10 chapters · 113 lessons
Collection
Pure Mathematics 1
Pure Mathematics 2
Pure Mathematics 3
Mechanics
Probability & Statistics 1
Probability & Statistics 2
Expand all
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
14 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
6 lessons
First Derivatives of eˣ and ln x
Composite Exponential Functions
Composite Logarithmic Functions
Trigonometric Derivatives
Inverse-tangent Derivative
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
11 lessons · 6 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
1 lesson
Definite Integrals and Area
04
Recognising Advanced Forms
2 lessons
Inverse-tangent integrals and mixed numerators
Recognising derivative over function
05
Transforming Integrals
3 lessons
Integration using a given substitution
Integrating after partial fractions
Integration by parts
06
Choosing and Applying Methods
1 lesson
Choosing an Integration Method
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
07
Vectors
9 lessons · 3 topic areas
01
Vector Foundations
4 lessons
Vector language and operations
Displacement vectors from points
Position vectors and constructing points
Magnitude and unit vectors
02
Scalar Product and Geometry
1 lesson
Scalar product and vector angles
03
Vector Lines
4 lessons
Vector equation of a line
Angle between two lines
Parallel, intersecting and skew lines
Foot of a perpendicular from a point
Practise this chapter
08
Further Algebra
5 lessons · 2 topic areas
01
Partial Fractions
2 lessons
Equal-degree fractions before partial fractions
Choosing and solving partial fractions
02
Binomial Series
3 lessons
Binomial series for rational powers
Adapting a binomial series and its validity
Partial fractions with binomial series
09
Differential equations
7 lessons · 3 topic areas
01
Meaning and Solving
3 lessons
What a differential equation means
Solving a separable differential equation
Complete solutions and integration choices
02
Forming Models
2 lessons
Forming an equation from a rate statement
Linked rates and net-rate models
03
Growth and Interpretation
2 lessons
Growth, decay and limiting values
Interpreting a differential-equation model
Practise this chapter
10
Complex numbers
7 lessons · 3 topic areas
01
Complex Foundations
2 lessons
Imaginary numbers and Cartesian form
Complex arithmetic and the conjugate
02
Argand Geometry and Form
2 lessons
Argand diagrams, modulus and argument
Polar form, multiplication and division
03
Equations and Loci
3 lessons
Complex roots and equations
Standard loci in the complex plane
Locus intersections and extreme values
Practise this chapter
All subjects
Mathematics
AS & A Level · 9709
Course overview
Study resources
Revision Notes
Practice Questions
Topical Past Paper Questions
Exam Skills
Past Papers
Mock Exams
Exam Guide
Browse all practice
Saved resources
Study space
Search resources