Verified Certificate

Supported by the following organizations

This is to certify that Hardik Karan successfully completed and received a passing grade in ALFM001: A-level Further Mathematics for Year 12 - Course 1: Complex Numbers, Matrices, Roots of Polynomial Equations and Vectors a course of study offered by ImperialX, an online learning initiative of Imperial College London.

Noted by

Philip Ramsden

Philip Ramsden

Dr Imperial College London

Phil Chaffe

Phil Chaffe

Mr Mathematics in Education and Industry

About edX

edX offers interactive online classes and MOOCs from the world’s best universities, including MIT, Harvard, Berkeley, University of Texas, and many others. edX is a mission driven initiative created by founding partners Harvard and MIT.

About edX Verified Certificates

An edX Verified Certificate signifies that the learner has agreed to abide by the edX honor code and completed all of the required tasks of this course under its guidelines, as well as having their photo ID checked to verify their identity.