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Quizzes > High School Quizzes > Social Studies

Unit 4 APUSH Practice Quiz

Ace AP World History & APUSH Exams Today

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Colorful paper art promoting a high school math practice quiz, Unit 2 3 Showdown.

What is the solution to the equation 2x + 3 = 11?
x = 5
x = 8
x = 4
x = 2
Subtracting 3 from 11 yields 8, and dividing by 2 gives x = 4. This is a basic linear equation solved with simple arithmetic.
What is the slope of the line given by the equation y = 3x - 2?
3
-2
0
1
The equation is in the slope-intercept form y = mx + b where m represents the slope. Here, m is 3, so the slope is 3.
What is the simplified form of the expression 4(2x)?
6x
4x
8x
2x
Multiplying 4 by 2x gives 8x. This problem uses the distributive property to simplify the expression.
If f(x) = x + 4, what is the value of f(3)?
7
9
8
6
Substitute 3 into f(x) = x + 4 to get 3 + 4 = 7. The question tests basic function evaluation.
Which of the following represents a slope that is perpendicular to a line with a slope of 1/2?
2
-2
1/2
-1/2
Perpendicular lines have slopes that are negative reciprocals. The negative reciprocal of 1/2 is -2, making it the correct answer.
Solve for x: 3(x - 2) = 2x + 1.
x = 8
x = 7
x = 5
x = 6
Expanding 3(x - 2) gives 3x - 6, so the equation becomes 3x - 6 = 2x + 1. Solving for x results in x = 7.
Solve the system of equations: 2x + y = 7 and x - y = 1.
x = 3, y = 1
x = 4, y = -1
x = 8/3, y = 5/3
x = 2, y = 3
Solving x - y = 1 yields y = x - 1. Substituting into 2x + (x - 1) = 7 gives 3x = 8, so x = 8/3 and y = 5/3.
What is the vertex of the parabola represented by the equation y = x² - 4x + 3?
(2, -1)
(0, 3)
(2, 1)
(-2, 11)
The x-coordinate of the vertex is given by -b/(2a). For the equation y = x² - 4x + 3, this computes to 2, and substituting back gives y = -1, so the vertex is (2, -1).
Solve the quadratic equation: x² - 5x + 6 = 0.
x = 2 and x = 3
x = -2 and x = -3
x = 2 only
x = 3 only
The quadratic factors as (x - 2)(x - 3) = 0, which yields the solutions x = 2 and x = 3. Factoring is a common method for solving quadratic equations.
What is the value of log₝₀(100)?
10
100
1
2
Since 10² equals 100, the logarithm log₝₀(100) is 2. This question tests understanding of basic logarithmic concepts.
Simplify the expression (2x³)².
2x❶
4x❵
4x❶
2x❵
When squaring (2x³), square the coefficient to obtain 4 and multiply the exponent by 2 to get x❶, resulting in 4x❶. This demonstrates the power of a product rule.
Which of the following functions exhibits a constant rate of change?
Logarithmic
Linear
Exponential
Quadratic
A linear function has a constant rate of change, represented by its slope. This property differentiates it from non-linear functions.
What is the slope-intercept form of the line that passes through (0, -3) with a slope of 4?
y = -4x + 3
y = 4x + 3
y = -4x - 3
y = 4x - 3
Given the y-intercept at (0, -3) and a slope of 4, the slope-intercept form is y = 4x - 3. This directly applies the formula y = mx + b.
Factor completely: 6x² + 11x + 3.
(2x + 3)(3x + 1)
(2x + 1)(3x + 3)
(3x + 3)(2x + 1)
(x + 3)(6x + 1)
Factoring 6x² + 11x + 3 yields (2x + 3)(3x + 1) when using methods to split the middle term. Expanding these factors reproduces the original quadratic.
Solve for x: (x - 1)/(x + 2) = 2/3.
x = 6
x = 8
x = 5
x = 7
Cross-multiplying gives 3(x - 1) = 2(x + 2), which simplifies to x = 7. This question reinforces solving equations with rational expressions.
For the function f(x) = 2x² - 3x + 1, what is the value of f(3) - f(1)?
8
10
14
12
Evaluating f(3) gives 2(9) - 3(3) + 1 = 10 and f(1) gives 2(1) - 3(1) + 1 = 0, so their difference is 10. This problem combines function evaluation with arithmetic.
Using Vieta's formulas, determine the sum of the roots of the quadratic equation 3x² - 6x + 2 = 0.
2
-2
6
-6
Vieta's formulas state that the sum of the roots is -b/a. For 3x² - 6x + 2 = 0, the sum is -(-6)/3, which simplifies to 2.
A function f is defined as f(x) = 1/(x - 2). What is the domain of this function?
x < 2
x > 2
All real numbers except x = 2
All real numbers
The function is undefined when the denominator is zero. Since x - 2 equals zero when x = 2, the domain excludes this value.
For the function g(x) = √(5 - 2x), what is the domain?
All real numbers
x ≤ 5/2
x ≥ 5/2
x < 5/2
The expression under the square root must be non-negative: 5 - 2x ≥ 0. Solving this inequality gives x ≤ 5/2.
Solve for x in the inequality 2(x - 3) > 4x - 10.
x ≤ 2
x > 2
x ≥ 2
x < 2
Expanding the inequality leads to 2x - 6 > 4x - 10, which simplifies to x < 2 after isolating the variable. This tests skills in solving linear inequalities.
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Study Outcomes

  1. Understand key mathematical concepts presented in Units 2 and 3.
  2. Analyze problem-solving strategies for complex math problems.
  3. Apply learned techniques to solve a variety of practice questions.
  4. Evaluate performance to identify strengths and areas for improvement.
  5. Synthesize multiple steps to approach and resolve challenging problems.

AP World History & APUSH Unit Tests Cheat Sheet

  1. Henry Clay's American System - Think of it as America's first growth hack: a trio of internal improvements, protective tariffs, and a strong national bank all aimed at turbocharging the economy and uniting the nation under one financial roof. Clay wanted fancy roads and canals, American-made goods, and a reliable currency to keep things flowing smoothly. Ready to nerd out on some 19th‑century infrastructure and finance? Barron's AP US History Notes: Period 4
  2. Missouri Compromise of 1820 - Picture a high‑stakes balance beam: admit Missouri as a slave state and Maine as a free state, then draw the 36°30′ line to decide which side new territories will land on. This was early America's way of saying, "Let's keep the peace," even if it only papered over deeper disagreements. It's a dramatic tale of politics, power, and geography all rolled into one. Barron's AP US History Notes: Period 4
  3. Monroe Doctrine, 1823 - Warning shots across the Atlantic: no new European colonies in the Western Hemisphere and a bold claim that America's backyard is off‑limits to outside powers. It was the U.S. striking a power pose on the global stage, saying "hands off" to imperial ambitions. This policy laid the groundwork for future U.S. influence in the region. Barron's AP US History Notes: Period 4
  4. Market Revolution Technologies - The cotton gin juiced the fiber game, interchangeable parts made factory work the new norm, and canals and railroads turned America into a giant logistics network. These innovations transformed everyday life from horse‑and‑buggy static to lightning‑fast trade and travel. Welcome to the era when gadgets and gizmos made modern America possible! Barron's AP US History Notes: Period 4
  5. Social Changes & Cult of Domesticity - The Market Revolution didn't just change machines; it reshaped families. A growing middle class emerged, with the "Cult of Domesticity" championing home as a female haven and men as breadwinners. It set the stage for future debates on gender roles and societal expectations. Barron's AP US History Notes: Period 4
  6. Expansion of Democracy - Voting went from property‑owning elites to a broader slice of white men, the Panic of 1819 shook confidence, and new voter groups found their voice. This political roller coaster made elections more dynamic and parties more competitive. Welcome to the birth of mass democracy in America. Barron's AP US History Notes: Period 4
  7. Andrew Jackson's Presidency - Jackson rewrote the rulebook with the "Tariff of Abominations," a showdown over states' rights, a veto of the Second Bank, and the infamous Indian Removal Act leading to the Trail of Tears. He was a firebrand who reshaped the presidency and polarized the nation. Brace yourself for drama, conflicts, and a larger‑than‑life leader. Barron's AP US History Notes: Period 4
  8. Cultural & Reform Movements - From Emerson's flights of philosophical fancy to Thoreau living off the grid, and from fiery religious revivals to epic battles over temperance, abolition, and women's rights at Seneca Falls. Reformers sparked social change with pens, pulpits, and protests. It's the age where America asked, "Let's make it better!" Barron's AP US History Notes: Period 4
  9. Southern Society Dynamics - Plantations expanded their cotton empires while enslaved people faced brutal conditions, yet carved out communities through music, faith, and resilience. Cultural bonds were a vital lifeline under oppression. This era reveals profound human endurance and the contradictions at the heart of Southern life. Barron's AP US History Notes: Period 4
  10. Nat Turner's Rebellion, 1831 - This uprising sent shockwaves through the South, intensifying fears and triggering harsher slave codes. Turner's revolt became a stark reminder of the deep unrest beneath the plantation façade. It's a poignant, powerful chapter that foreshadowed the coming storm of civil conflict. Barron's AP US History Notes: Period 4
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