---
title: "Precalculus guide and practice — NextStep"
description: "What you will learn in Precalculus, common challenges, workload and expectations, flashcards, practice questions and vocabulary."
url: "https://nextstep-transition.spark.site/courses/precalculus"
site: "NextStep"
updated: "2026-11-13"
---

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High school · Math

# Precalculus

Precalculus strengthens function and trigonometry skills that help you make sense of calculus.

[Survival guide](https://nextstep-transition.spark.site/courses/precalculus#guide)[What to expect](https://nextstep-transition.spark.site/courses/precalculus#expect)[Flashcards](https://nextstep-transition.spark.site/courses/precalculus#flashcards)[Practice questions](https://nextstep-transition.spark.site/courses/precalculus#practice)[Vocabulary](https://nextstep-transition.spark.site/courses/precalculus#vocab)

## What you will learn

- Analyze and combine functions.
- Use radians and the unit circle.
- Graph trigonometric functions.
- Solve exponential, logarithmic, and trigonometric equations.
- Model change with several function families.

## Common challenges

- ### Radians

  Radians connect an angle to arc length rather than degrees. Practice familiar angles in both units and check calculator mode.
- ### Trigonometric identities

  An identity is true throughout its allowed domain. Rewrite one side using known identities instead of testing just one angle.
- ### Function notation

  Composition and multiplication mean different things. Write out the inner function before substituting it into the outer one.

## Key concepts

Unit circle

On a circle of radius 1, the point at angle theta has coordinates (cos(theta), sin(theta)).

Radians

Radian measure is arc length divided by radius. A full turn is 2 pi radians.

Periodicity

A periodic function repeats its outputs over a fixed input interval. Sine and cosine repeat every 2 pi radians.

Composition

For f(g(x)), calculate g first and then apply f. Check that the intermediate output is an allowed input.

Inverse functions

An inverse reverses a one-to-one function. Restricting a domain can make an inverse possible.

Average rate of change

The difference in outputs divided by the difference in inputs measures change across an interval.

## How to prepare

- Review factoring and rational expressions.
- Practice graphing quadratic and exponential functions.
- Review right-triangle sine, cosine, and tangent.
- Make a degree-to-radian chart for 0, 30, 45, 60, and 90 degrees.

### Study habits that help

- Sketch the unit circle from memory, then check it.
- Compare a function's equation, table, and graph.
- Label every trigonometry problem with degrees or radians.
- Practice a few algebra problems alongside each new topic.

## What to expect

Typical workload

Moderate

Time outside class

Typically about 4 to 6 hours outside class; your school and starting skills may change this.

Pace

Units often connect algebraic rules, graphs, and applications at a steady pace.

How it is usually graded

Tests, quizzes, problem sets, and sometimes modeling projects commonly contribute to grades.

### Skills that help

- Algebra fluency
- Graph reading
- Exact-value calculations
- Connecting representations

### What teachers usually expect

- Give exact values when asked.
- Check angle units before calculating.
- Explain how a graph supports your answer.

### Before you start

- Typical Algebra 2 skills
- Geometry and right-triangle relationships
- Comfort solving equations and using function notation

These are general descriptions of a typical course. Workload, pace and prerequisites differ by school and instructor, so check with your counselor, advisor or the course catalog.

## Where it can lead

- Engineering
- Physics
- Mathematics
- Economics
- Computer science

## Flashcards

Card 1 of 10

## Practice questions

Question 1 of 6

Convert 60 degrees to radians.

pi/6pi/2pi/32 pi/3

## Vocabulary

Amplitude

Half the distance between the maximum and minimum of a sinusoidal graph.

Period

The smallest positive input shift over which a periodic function repeats.

Radian

The angle unit for which an arc of one radius has measure 1.

Identity

An equation true for every input where both sides are defined.

One-to-one

Describes a function in which different inputs give different outputs.

End behavior

How a function behaves as the input increases or decreases without bound.

Secant line

A line through two points on a graph.

Phase shift

A horizontal shift of a periodic graph.

## Related courses

- [Algebra 2](https://nextstep-transition.spark.site/courses/algebra-2)
- [AP Calculus AB](https://nextstep-transition.spark.site/courses/ap-calculus-ab)
- [Calculus I](https://nextstep-transition.spark.site/courses/calculus-1)

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