A-level Further Maths: Advanced Concepts
Strengthen your mathematical expertise in advanced topics like matrices, vectors, and complex numbers to prepare thoroughly for A-levels and STEM studies.
Strengthen your mathematical expertise in advanced topics like matrices, vectors, and complex numbers to prepare thoroughly for A-levels and STEM studies.
Dive into advanced mathematical concepts with this comprehensive course from Imperial College London, designed for Year 12 students pursuing A-level Further Mathematics. This course covers critical topics such as complex numbers, matrices, roots of polynomial equations, and vectors, providing a solid foundation for A-level exams and future STEM degrees. Through eight intensive modules, you'll develop essential skills in mathematical fluency, critical thinking, and problem-solving. From exploring the Argand diagram to mastering vector equations of planes, this course bridges the gap between A-level study and university-level mathematics, preparing you for academic excellence and future career success in STEM fields.
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What you'll learn
Understand and manipulate complex numbers, including their modulus and argument
Use matrices for linear transformations and solve systems of linear equations
Analyze roots of polynomial equations and their relationship to coefficients
Apply series, partial fractions, and the method of differences to solve problems
Use vectors to define and work with lines and planes in 2D and 3D space
Develop problem-solving skills for unfamiliar mathematical scenarios
Skills you'll gain
This course includes:
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Graded assignments, exams
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Limited Access access
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There are 8 modules in this course
This course offers an in-depth exploration of advanced mathematical concepts crucial for A-level Further Mathematics and preparation for STEM degrees. It covers a wide range of topics including complex numbers, matrices, roots of polynomial equations, series, and vectors. The course emphasizes not just theoretical understanding but also practical problem-solving skills, encouraging students to develop fluency, confidence, and deep reasoning abilities. Through eight comprehensive modules, students will learn to work with complex numbers on the Argand diagram, use matrices for linear transformations, analyze roots of polynomial equations, and apply vectors to solve geometrical problems. The course also introduces advanced algebraic techniques such as partial fractions and the method of differences. Throughout, students are encouraged to think critically, construct mathematical arguments, and understand how these concepts fit into the broader mathematical landscape, preparing them for both A-level exams and future studies in mathematics, engineering, and sciences.
Complex Numbers 1: An Introduction to Complex Numbers
Module 1
Matrices 1: An Introduction to Matrices
Module 2
Further Algebra and Functions 1: Roots of Polynomial Equations
Module 3
Complex Numbers 2: Modulus-Argument form and Loci
Module 4
Matrices 2: Determinants and Inverse Matrices
Module 5
Further Algebra and Functions 2: Series, Partial Fractions and the Method of Differences
Module 6
Vectors 1: The Scalar (dot) Product and Vector Equations of Lines
Module 7
Vectors 2: The Vector Equations of a Plane and Geometrical Problems with Lines and Planes
Module 8
Fee Structure
Instructors
8 Courses
Mathematics Education and Outreach Expert at Imperial College London
Philip Ramsden serves as Director of Cross-Curricular Mathematics Education and Principal Teaching Fellow at Imperial College London, where he has made significant contributions to mathematics education and outreach since 1993. His teaching spans multiple departments including Mathematics, Physics, and Aeronautics, while leading major initiatives in widening participation and mathematics education. He directs the mAths programme, an extensive outreach initiative targeting Year 12 and 13 students from underrepresented backgrounds pursuing A grades at A-level, and coordinates the monthly "Maths Circle" masterclasses in partnership with the Royal Institution
8 Courses
Mathematics Education and Problem-Solving Expert at MEI
Phil Chaffé serves as a national coordinator for the Advanced Mathematics Support Programme, a UK government-funded initiative promoting post-16 mathematics education, bringing extensive experience from his previous roles in schools and universities. His current work focuses on coordinating projects across England that prepare students for advanced study at top universities, with particular emphasis on developing problem-solving skills necessary for university admissions examinations. As a respected figure in mathematics education, he has gained recognition for his engaging presentations on diverse topics including evolutionary biology mathematics, music mathematics, and recursive universe concepts, making complex mathematical ideas accessible to students. His expertise spans both theoretical mathematics and its practical applications, demonstrated through his work in developing enrichment programs and delivering masterclasses that bridge the gap between secondary education and university-level mathematics. His contributions to mathematics education extend beyond traditional classroom teaching to include innovative approaches that inspire students to explore advanced mathematical concepts and their real-world applications.
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