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
Try for free
Study space
Mistake Bank
AI Marking
Subjects
C
Cambridge
E
Pearson Edexcel
AQA
AQA
OCR
OCR
Competitive
Try for free
Log in
Create free account
Course navigation
Further Mathematics
Revision Notes
Further Pure Mathematics 1
Further Mathematics · Cambridge 9231
Further Pure Mathematics 1
7 chapters · 81 lessons
Collection
Further Pure Mathematics 1
Further Pure Mathematics 2
Further Mechanics
Further Probability & Statistics
Expand all
01
Roots of Polynomial Equations
11 lessons · 4 topic areas
01
Roots and coefficients
3 lessons
Roots, factors and multiplicity
Deriving quadratic root relations
Cubic and quartic root relations
02
Expressions in roots
2 lessons
Evaluating expressions in roots
Power sums from the original equation
03
New equations
5 lessons
Shifting and scaling roots
Reciprocal root transformations
Equations for squared roots
Equations for cubed roots
Combined roots and chapter review
04
Reference
1 lesson
Formula and method reference
Practise this chapter
02
Rational Functions
11 lessons · 4 topic areas
01
Rational graphs
4 lessons
Domains, intercepts and excluded points
Horizontal asymptotes and first sketches
Stationary points and quadratic denominators
Oblique asymptotes and parameters
02
Range and inequalities
2 lessons
The range of a rational function
Solving rational inequalities
03
Graph transformations
4 lessons
Reciprocal graphs
Output modulus and input modulus
Modulus graphs: asymptotes and solutions
Graphs of y² = f(x)
04
Review
1 lesson
Rational functions: review and method reference
03
Summation of Series
8 lessons · 3 topic areas
01
Finite sums
4 lessons
Sigma notation and linear sums
Sums of squares and cubes
Polynomial and patterned sums
Changing summation limits
02
Differences and limits
3 lessons
The method of differences
Recognising more complex differences
Convergence, remainders and bounds
03
Review
1 lesson
Summation of series: method selection
Practise this chapter
04
Matrices 1
14 lessons · 4 topic areas
01
Matrix algebra
6 lessons
Matrix entries and operations
Matrix multiplication
Inverse matrices of order 2
Determinants
Inverse matrices of order 3
Matrix equations and inverse products
02
Plane transformations
5 lessons
Matrices and point images
Stretches, enlargements and shears
Rotations and reflections
Combining matrix transformations
Area scale factors
03
Invariant points and lines
2 lessons
Invariant points
Invariant lines
04
Review
1 lesson
Matrices 1: mixed problems
05
Polar coordinates
14 lessons · 3 topic areas
01
Coordinates and curves
8 lessons
Polar coordinates and points
Polar and Cartesian equations
Tracing polar curves
Symmetry and cardioids
Petal curves
Spirals
Intersections of polar curves
Greatest distances
02
Areas
5 lessons
Areas from polar sectors
Areas of petals
Areas between curves
Common regions
Unfamiliar polar integrals
03
Review
1 lesson
Polar coordinates review
Practise this chapter
06
Vectors
15 lessons · 5 topic areas
01
Vector products
3 lessons
Vectors and projection
The vector product
Areas using vectors
02
Lines and planes
4 lessons
Lines and their intersections
Point-to-line distance
Equations of planes
Plane forms and construction
03
Intersections and angles
3 lessons
Line-plane intersections
Intersection of two planes
Angles with lines and planes
04
Distances and perpendiculars
3 lessons
Point-to-plane distance
Distance between skew lines
Common perpendiculars
05
Review
2 lessons
Vectors — Formula Summary
Vectors review
Practise this chapter
07
Proof by induction
8 lessons · 1 topic areas
01
Proof by induction
8 lessons
Why induction works
Proving sums
Proving recurrence formulas
Proving bounds
Proving derivative patterns
Proving matrix powers
Proving divisibility
Induction review
Practise this chapter
All subjects
Further Mathematics
AS & A Level · 9231
Course overview
Study resources
Revision Notes
Practice Questions
Topical Past Paper Questions
Past Papers
Mock Exams
Exam Guide
Browse all practice
Saved resources
Study space
Search resources