CAPE Pure Mathematics Unit 1
Develop the algebra, geometry and calculus foundation required for advanced mathematics and university study.
Algebra, geometry and calculus in one structured programme
Unit 1 strengthens proof, functions, trigonometry, coordinate geometry, vectors and introductory calculus through worked examples and exam-style questions.
Learn, practise and improve
Students receive structured teaching and digital support throughout the programme.
Free CAPE Pure Mathematics Unit 1 Video Course
Study all 27 lessons in order. Open a module and select each separate video lesson.
Algebra, Proofs & FunctionsLessons 1–13+
CAPE Unit 1 Pure Mathematics – Remainder and Factor Theorem
CAPE Unit 1 Pure Mathematics – Logic and Reasoning I
CAPE Unit 1 Pure Mathematics – Logic and Reasoning II
CAPE Unit 1 Pure Mathematics – Field Axioms and Methods of Proof
CAPE Unit 1 Pure Mathematics – Proof by Mathematical Induction I
CAPE Unit 1 Pure Mathematics – Proof by Mathematical Induction II
CAPE Unit 1 Pure Mathematics – Indices and Surds
CAPE Unit 1 Pure Mathematics – Logarithms
CAPE Unit 1 Pure Mathematics – Modelling and Sketching Graphs
CAPE Unit 1 Pure Mathematics – Functions I
CAPE Unit 1 Pure Mathematics – Functions II : Inverse of a Function and Composite Functions
CAPE Unit 1 Pure Mathematics – Functions III : Modulus of a Function
CAPE Unit 1 Pure Mathematics – Cubic Equations
Trigonometry, Geometry & VectorsLessons 14–22+
CAPE Unit 1 Pure Mathematics – Trigonometry I
CAPE Unit 1 Pure Mathematics – Trigonometry II
CAPE Unit 1 Pure Mathematics – Trigonometry III
CAPE Unit 1 Pure Mathematics – Trigonometry IV
CAPE Unit 1 Pure Mathematics – Co-ordinate Geometry I
CAPE Unit 1 Pure Mathematics – Co-ordinate Geometry II
CAPE Unit 1 Pure Mathematics – Co-ordinate Geometry III
CAPE Unit 1 Pure Mathematics – Vectors I
CAPE Unit 1 Pure Mathematics – Vectors II
Limits & CalculusLessons 23–27+
CAPE Unit 1 Pure Mathematics – Limits I
CAPE Unit 1 Pure Mathematics – Limits II
CAPE Unit 1 Pure Mathematics – Differentiation I
CAPE Unit 1 Pure Mathematics – Differentiation II
CAPE Unit 1 Pure Mathematics – Integration
The lessons follow the order of the official ARETE YouTube playlist.
View original playlist ↗What students will study
Topics are grouped into clear modules so students can build understanding progressively.
Basic Algebra & Functions
- Logic and mathematical reasoning
- Real number systems and proof
- Equations, inequalities, indices and logarithms
- Functions, graphs and polynomial equations
Plane Geometry
- Trigonometric functions and identities
- Coordinate geometry
- Vectors
- Geometric modelling and problem-solving
Calculus I
- Limits and continuity
- Differentiation and applications
- Integration and areas
- Volumes and introductory differential equations
Support from lesson to examination
Diagnostic support
Identify weak areas and set clear learning priorities.
Exam practice
Develop method, accuracy, timing and question selection.
ARETE+ access
Review notes, quizzes and learning materials from any device.
Guidance
Get feedback and help with difficult concepts and calculations.
Ready to begin Pure Mathematics Unit 1?
Apply online or message the office to confirm the current timetable and available spaces.