Solving by factoring
Factor, then set each factor to zero. x² − 5x + 6 = 0 gives (x − 2)(x − 3) = 0, so x = 2 or x = 3.
Try it: Solve x² − 7x + 12 = 0.
Show answer
x = 3 or x = 4.
Grade 11
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
Quadratic Functions
The quadratic formula
x = (−b ± √(b² − 4ac)) ÷ 2a. For x² + 2x − 3 = 0, the discriminant is 16, so x = 1 or x = −3.
Try it: Is the discriminant positive, zero, or negative when a quadratic has two real solutions?
Show answer
Positive.
Exponential and Logarithmic Functions
Exponential growth
y = a(1 + r)ᵗ. $100 growing 5% a year for 2 years becomes 100 × 1.05² = $110.25.
Try it: $200 grows 10% a year for 2 years. What is the final amount?
Show answer
$242, because 200 × 1.1² = 242.
Logarithms
log_b x = y means bʸ = x. So log₂ 8 = 3 because 2³ = 8.
Try it: Evaluate log₁₀ 1000.
Show answer
3.
Geography
Geography and Westward Expansion
Manifest destiny and the West
In the 1800s, many Americans believed the nation should spread across the continent. Trails like the Oregon Trail carried settlers west.
Try it: What was the goal of travelers on the Oregon Trail?
Show answer
To reach the Oregon country in the Pacific Northwest.
Transportation and growth
The first transcontinental railroad was completed in 1869, cutting travel across the country from months to days.
Try it: In what year was the first transcontinental railroad completed?
Show answer
1869.
Migration in the United States
The Great Migration
Beginning around 1916, millions of African Americans moved from the rural South to cities in the North, Midwest, and West seeking jobs and fewer restrictions.
Try it: Name one reason people joined the Great Migration.
Show answer
Jobs, or escaping segregation and violence.
The Dust Bowl
In the 1930s, drought and poor farming practices turned Plains farmland into dust storms, pushing many families to leave, many toward California.
Try it: What caused the Dust Bowl?
Show answer
Drought combined with farming practices that left soil exposed.
Language Arts
American Literature
Literary movements
Romanticism stresses emotion and nature, Realism shows ordinary life, and Modernism breaks with tradition and experiments with form.
Try it: Which movement focuses on ordinary life as it really is?
Show answer
Realism.
Tone, mood, and irony
Tone is the author's attitude. Mood is the feeling readers get. Irony is a contrast between expectation and reality.
Try it: What is situational irony?
Show answer
When the outcome is the opposite of what is expected.
Writing
Persuasive argument
Strong arguments address counterclaims fairly and use rhetorical devices like parallelism, repetition, and strong evidence.
Try it: Name one rhetorical device.
Show answer
Repetition, parallelism, or a rhetorical question.
Analyzing historical texts
To analyze a speech or document, identify the author, audience, purpose, and the techniques used to persuade.
Try it: What questions help you analyze a speech?
Show answer
Who wrote it, who it is for, why, and how it persuades.