Radians and the unit circle
180° equals π radians. To convert degrees to radians, multiply by π/180. 90° = π/2.
Try it: Convert 60° to radians.
Show answer
π/3.
Grade 12
Lessons by subject. Read the lesson, try the question, then check your answer.
Topics follow the Georgia Standards of Excellence, the state's current standards (they replaced the older Common Core Georgia Performance Standards). This is an unofficial study aid, not a Coffee County Schools resource. Your teacher's pacing guide and textbook come first. Official standards: georgiastandards.org.
Math
Precalculus: Functions and Trigonometry
Composition of functions
f(g(x)) means put g(x) inside f. If f(x) = 2x + 1 and g(x) = x², then f(g(3)) = 2(9) + 1 = 19.
Try it: Using the same functions, find g(f(1)).
Show answer
9, because f(1) = 3 and g(3) = 9.
Statistics and Probability
Measures of center and spread
The mean is the average and the median is the middle value. Standard deviation measures how spread out data are. For 2, 4, 6 the mean is 4.
Try it: Find the mean of 3, 5, 10.
Show answer
6.
Independent events
For independent events, P(A and B) = P(A) × P(B). A coin landing heads and a die showing 6: 1/2 × 1/6 = 1/12.
Try it: What is the probability of heads on a coin and a 3 on a die?
Show answer
1/12.
Geography
Government and Geography
The Electoral College
Each state has electors equal to its House seats plus its two senators. There are 538 electors in all (including 3 for the District of Columbia), and a candidate needs 270 to win.
Try it: How many electoral votes does a candidate need to win?
Show answer
270.
Census and apportionment
A census counts the U.S. population every ten years. The 435 House seats are reassigned among the states based on the results.
Try it: How many seats are in the U.S. House of Representatives?
Show answer
435.
Global Connections
Trade and globalization
Globalization connects economies through trade. Imports come into a country and exports leave it.
Try it: Is a car made in Japan and sold in the U.S. an import or an export for the U.S.?
Show answer
An import.
Resources and sustainability
Renewable resources, like solar and wind, replenish naturally. Nonrenewable resources, like coal and oil, do not on a human timescale.
Try it: Is natural gas renewable or nonrenewable?
Show answer
Nonrenewable.
Language Arts
British and World Literature
Satire and irony
Satire uses humor or exaggeration to criticize. Jonathan Swift's A Modest Proposal (1729) is a famous satire that uses an absurd suggestion to criticize attitudes toward the poor.
Try it: What is the purpose of satire?
Show answer
To criticize people or society using humor, irony, or exaggeration.
Comparing themes across texts
Choose a theme, such as power or identity, and show how two texts treat it differently, with evidence from each.
Try it: What should you include when comparing two texts?
Show answer
A shared theme and evidence from both texts.
Writing and Communication
College-ready essays
A strong personal essay uses a specific story, a clear reflection, and an organized structure with a clear voice.
Try it: What makes a personal essay stronger than a list of achievements?
Show answer
A specific story with reflection on what it shows.
Presentations
Speak clearly, make eye contact, use evidence, and prepare for questions. Visuals should support your points, not repeat everything.
Try it: Name one habit of an effective presenter.
Show answer
Eye contact, clear speaking, or evidence-based points.