Precalculus for High School Students

Categories: Math
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About Course

Precalculus: Inquiry, Functions, and Preparation for Calculus

Explore why precalculus works. Connect algebra, geometry, trigonometry, and motion through questions, diagrams, and complete explanations.

This independent Computing4All course supports students taking OnRamps Discovery Precalculus. Its eight units follow the topic areas in UT Austin’s public OnRamps overview. Prerequisites are Algebra II and Geometry.

32 lessons · 256 worked practice exercises · 8 unit investigations · 16 quizzes with 160 explained questions.

How to study

  1. Try each opening question before reading the explanation. Draw a picture or make a table when a formula is unclear.
  2. Work through examples with pencil and paper. Record units, domains, and assumptions.
  3. Attempt all eight practice problems in each lesson, then open the worked solutions.
  4. Explain the unit investigation to a partner, compare approaches, and write your own argument.
  5. Take both practice quizzes. Study every explanation and retry as needed. Keep an error journal with the mistaken idea and its correction.

Use exact fractions and radicals unless an approximation is requested. Calculators and graphing tools help explore and check. Confirm the angle mode before using trigonometric functions.

These are independent support materials, not official UT Austin or OnRamps assignments, exams, or grading policies. Follow your teacher’s current syllabus for pacing and assessment requirements.

What Will You Learn?

  • Construct mathematical arguments, test conjectures, and use counterexamples.
  • Analyze functions through domains, graphs, transformations, composition, and inverses.
  • Connect circles, parabolas, ellipses, and hyperbolas with geometric definitions.
  • Use matrices to solve systems and build mathematical models.
  • Solve exponential and logarithmic equations and interpret growth and decay.
  • Connect trigonometric ratios, the unit circle, graphs, identities, and periodic motion.
  • Explore limits, continuity, and instantaneous rates of change.
  • Use vectors, parametric equations, polar coordinates, and complex-number rotations.
  • Work with sequences, series, binomial coefficients, convergence, and induction.

Course Content

Unit 0: Thinking Like a Mathematician
Make claims precise, use counterexamples and proofs, and connect representations with meaningful units.

Unit 1: Functions, Rates, and Patterns
Read graphs and domains, transform and compose functions, find inverses, and distinguish rational holes from asymptotes.

Unit 2: Algebra and Geometry
Derive conics from distance definitions, use their equations, and organize model-fitting systems with matrices.

Unit 3: Exponential and Logarithmic Functions
Connect multiplicative change with exponential models, use inverse logarithms, and solve growth and decay problems.

Unit 4: Trigonometry
Connect triangles, radians, circles, graphs, identities, inverse functions, and periodic motion.

Unit 5: Limits and Rates of Change
Use nearby behavior to interpret limits, test continuity, and build instantaneous rates from difference quotients.

Unit 6: Other Coordinate Systems
Describe direction and motion with vectors, parameterizations, polar coordinates, and complex-number rotations.

Unit 7: Sequences, Series, and Induction
Describe discrete patterns, calculate finite and infinite sums, explain binomial coefficients, and prove claims by induction.

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