Advanced Precalculus: Geometry, Trigonometry and Exponentials

Take your precalculus knowledge to the next level

This course is the second of two precalculus courses from the University of Padova, providing you with the advanced mathematical skills required to complete a first course in calculus.

You’ll get to grips with more challenging precalculus topics: plane and solid geometry; logarithms and exponentials; equalities and inequalities; and trigonometric functions and identities.

By the end of this course you’ll have gained the skills to support further mathematical studies.

This course is for anyone who wants to brush up on their basic mathematical skills, particularly students in the last year of high school, or at the beginning of undergraduate studies, who intend to take a first course in calculus.

Ideally, you’ll have already taken the first course - Precalculus: the Mathematics of Numbers, Functions and Equations or be familiar with the topics covered in it, and have a basic knowledge of high school mathematics.

• Exponential and logarithmic functions
• Course presentation
• Exponential functions
• The Euler number
• Functions and their inverses
• Logarithms
• It's quiz time
• Test yourself
• Trigonometry
• Trigonometry by triangles
• Trigonometry by the unit circle
• Graphs of trigonometric functions
• Trigonometric identities
• Harmonic motion
• The function arctan
• More inverse trig functions, and a few others
• It's quiz time
• Test yourself
• Geometry
• Geometry of the plane: points, segments, lines
• Distance and circles
• Ellipses
• Parabolas and hyperbolas
• Level curves of quadratic functions
• Lengths, areas, and volumes
• It's quiz time
• Test yourself
• From equations to spirals
• Equations with exponentials and logarithms
• Growth and decay problems
• Trigonometric equations
• Inequalities with logarithms and exponentials
• Trigonometric inequalities
• Polar coordinates
• It's quiz time
• Test yourself
• Final step and revision test