Precalculus essentials
Explore advanced functions, trigonometry, complex numbers, vectors, matrices, conic sections, and series while strengthening algebraic reasoning and problem-solving skills. Analyze transformations, limits, continuity, and rational models, and apply precalculus concepts to graphical, geometric, and real-world contexts that prepare students for higher-level mathematics.
9 units147 videos15 hours
Learn it live with a class on Puzzicle · Teachers: use it with your class
Unit 1: Composite and inverse functions
Composing functions
Invertible functions
Unit 2: Trigonometry
Trigonometric identities on the unit circle
Inverse trigonometric functions
Law of sines
Law of cosines
Sinusoidal equations
Sinusoidal models
Angle addition identities
Trig angle addition identities ✓ Check-ins11:07
Using the cosine angle addition identity ✓ Check-ins5:14
Using the cosine double-angle identity ✓ Check-ins3:28
Proof of the sine angle addition identity ✓ Check-ins8:26
Proof of the cosine angle addition identity ✓ Check-ins6:02
Proof of the tangent angle sum and difference identities ✓ Check-ins6:55
Unit 3: Complex numbers
The complex plane
Distance and midpoint of complex numbers
Complex conjugates and dividing complex numbers
Identities with complex numbers
Modulus (absolute value) and argument (angle) of complex numbers
Graphically multiplying complex numbers
Unit 4: Rational functions
End behavior of rational functions
Discontinuities of rational functions
Modeling with rational functions
Analyzing structure word problem: pet store (1 of 2) ✓ Check-ins5:54
Analyzing structure word problem: pet store (2 of 2) ✓ Check-ins2:44
Combining mixtures example ✓ Check-ins5:48
Rational equations word problem: combined rates ✓ Check-ins5:26
Rational equations word problem: combined rates (example 2) ✓ Check-ins6:00
Rational equations word problem: eliminating solutions ✓ Check-ins7:59
Reasoning about unknown variables ✓ Check-ins6:07
Reasoning about unknown variables: divisibility ✓ Check-ins3:38
Structure in rational expression ✓ Check-ins4:41
Unit 5: Conic sections
Introduction to conic sections
Center and radii of an ellipse
Foci of an ellipse
Introduction to hyperbolas
Foci of a hyperbola
Hyperbolas not centered at the origin
Unit 6: Vectors
Vectors introduction
Vector components
Magnitude of vectors
Scalar multiplication
Vector addition
Vector components from magnitude and direction
Adding vectors in magnitude and direction form
Unit 7: Matrices
Introduction to matrices
Multiplying matrices by scalars
Adding and subtracting matrices
Matrices as transformations of the plane
Matrices as transformations of the plane ✓ Check-ins8:12
Working with matrices as transformations of the plane ✓ Check-ins4:15
Intro to determinant notation and computation ✓ Check-ins3:26
Interpreting determinants in terms of area ✓ Check-ins4:19
Finding area of figure after transformation using determinant ✓ Check-ins2:07
Proof: Matrix determinant gives area of image of unit square under mapping ✓ Check-ins4:19
Multiplying matrices by matrices
Properties of matrix multiplication
Defined matrix operations ✓ Check-ins3:32
Intro to identity matrix ✓ Check-ins7:59
Dimensions of identity matrix ✓ Check-ins3:44
Is matrix multiplication commutative? ✓ Check-ins7:32
Associative property of matrix multiplication ✓ Check-ins8:37
Zero matrix & matrix multiplication ✓ Check-ins4:42
Using properties of matrix operations ✓ Check-ins3:30
Using identity & zero matrices ✓ Check-ins3:58
Introduction to matrix inverses
Finding inverses of 2x2 matrices
Unit 8: Series
Geometric series
Geometric series (with summation notation)
Understanding summation notation ✓ Check-ins4:27
Geometric series with sigma notation ✓ Check-ins4:28
Worked example: finite geometric series (sigma notation) ✓ Check-ins2:48
Finite geometric series word problem: social media ✓ Check-ins8:03
Finite geometric series word problem: mortgage ✓ Check-ins17:36
The binomial theorem
Arithmetic series
Arithmetic series intro ✓ Check-ins3:56
Arithmetic series formula ✓ Check-ins7:47
Worked example: arithmetic series (sigma notation) ✓ Check-ins7:02
Worked example: arithmetic series (sum expression) ✓ Check-ins6:47
Worked example: arithmetic series (recursive formula) ✓ Check-ins5:21
Proof of finite arithmetic series formula ✓ Check-ins3:32
Unit 9: Limits and continuity
Defining limits and using limit notation
Exploring types of discontinuities
Defining continuity at a point
Confirming continuity over an interval
Removing discontinuities
Working with the intermediate value theorem
Learn this with a class
With a class on Puzzicle this course runs as a timetable of live study parties: your batch watches together and answers the check-ins, sometimes with a teacher leading.
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