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Quizzes > High School Quizzes > Mathematics

Unit 2 Progress Check MCQ Practice Quiz

Boost your AP skills with focused practice

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Paper art illustrating trivia for high school algebra students reviewing Unit 5 Mastery Challenge.

What is the value of x in the equation 2x - 5 = 9?
7
2
6
5
Adding 5 to both sides of the equation gives 2x = 14, and dividing by 2 results in x = 7. Therefore, the correct answer is 7.
Solve the equation 3(x + 2) = 15.
3
5
7
4
Dividing both sides by 3 gives x + 2 = 5, and then subtracting 2 yields x = 3. This is the only solution.
Factor the quadratic expression x² + 5x + 6.
(x + 2)(x + 3)
(x - 2)(x - 3)
(x + 1)(x + 6)
(x - 1)(x - 6)
The numbers 2 and 3 multiply to 6 and add up to 5, so the quadratic factors as (x + 2)(x + 3). This is the correct factorization.
Simplify the expression x³ * x².
x❶
x❵
x❹
x
When multiplying powers with the same base, you add the exponents: 3 + 2 = 5. Thus, the simplified expression is x❵.
If f(x) = 2x + 3, what is f(4)?
11
14
7
8
Substituting x = 4 into the function gives 2(4) + 3 = 8 + 3 = 11. Therefore, the correct answer is 11.
Solve the inequality 3x - 4 < 11.
x < 5
x > 5
x ≤ 5
x ≥ 5
Adding 4 to both sides yields 3x < 15, and dividing by 3 gives x < 5. This is the correct solution to the inequality.
Find the solutions of the quadratic equation x² - 5x + 6 = 0.
x = 2 or x = 3
x = -2 or x = -3
x = 1 or x = 6
x = -1 or x = -6
The quadratic factors as (x - 2)(x - 3) = 0, leading to the solutions x = 2 and x = 3. Only this option correctly identifies both roots.
For the linear function y = 2x + 1, what is the y-intercept?
1
2
0
-1
In the slope-intercept form y = mx + b, the constant term b is the y-intercept. Here, b is 1, so the y-intercept is 1.
Determine the inverse of the function f(x) = 3x - 7.
f❻¹(x) = (x + 7)/3
f❻¹(x) = (x - 7)/3
f❻¹(x) = 3x + 7
f❻¹(x) = 3x - 7
To find the inverse, swap x and y to get x = 3y - 7 and solve for y, resulting in y = (x + 7)/3. Thus, the inverse function is f❻¹(x) = (x + 7)/3.
Solve the system of equations: x + y = 7 and x - y = 3.
(5, 2)
(2, 5)
(4, 3)
(3, 4)
Adding the two equations yields 2x = 10, so x = 5, and substituting back gives y = 2. The solution to the system is (5, 2).
Simplify the rational expression (x² - 9)/(x + 3) for x ≠ -3.
x - 3
x + 3
x² - 3
x - 9
Factor x² - 9 as (x + 3)(x - 3) and cancel the common factor (x + 3) with the denominator, leaving x - 3. This is the simplified form.
Find the solutions of the absolute value equation |x - 4| = 3.
x = 1 or x = 7
x = 3 or x = 5
x = -1 or x = 7
x = 1 or x = 3
The equation |x - 4| = 3 splits into x - 4 = 3 and x - 4 = -3, yielding x = 7 and x = 1, respectively. Thus, the correct solutions are x = 1 or x = 7.
Simplify the expression a³ * a❻❵ using exponent rules.
a❻²
a❸
a²
1/a❸
When multiplying with the same base, add the exponents: 3 + (-5) = -2, which gives a❻². This follows the rules of exponents.
Simplify the radical expression √50.
5√2
√25 + √2
10√2
√100
Express 50 as 25 × 2, so √50 = √25 × √2 = 5√2. This is the simplest radical form.
Expand the product (2x + 3)(x - 4).
2x² - 5x - 12
2x² + 5x - 12
2x² - 7x - 12
2x² + 7x - 12
Expanding the product gives 2x² - 8x + 3x - 12, which simplifies to 2x² - 5x - 12. This is the correct expansion.
Solve the quadratic equation 2x² - 4x - 6 = 0 using the quadratic formula.
x = 3 or x = -1
x = 1 or x = -3
x = 3 or x = 1
x = -1 or x = -3
Dividing the equation by 2 gives x² - 2x - 3 = 0. Applying the quadratic formula yields x = (2 ± √16)/2, which simplifies to x = 3 or x = -1.
Find the vertex of the quadratic function f(x) = -x² + 4x + 1.
(2, 5)
(-2, 5)
(2, -5)
(-2, -5)
The vertex of a quadratic function is found using x = -b/(2a). Here, x = -4/(-2) = 2, and substituting back yields f(2) = 5. Thus, the vertex is (2, 5).
Determine the composition (g ∘ f)(x) if f(x) = 2x + 3 and g(x) = x².
(2x + 3)²
2x² + 3
4x² + 9
2x² + 6x + 9
The composition g(f(x)) is obtained by substituting f(x) into g(x), which gives (2x + 3)². This is the correctly composed function.
Solve the inequality x² - 4 > 0.
x < -2 or x > 2
-2 < x < 2
x ≤ -2 or x ≥ 2
x > -2 and x < 2
Factor the expression into (x - 2)(x + 2) > 0, which means the product is positive when x is less than -2 or greater than 2. This is the correct interval solution.
Factor the cubic polynomial x³ - 6x² + 11x - 6.
(x - 1)(x - 2)(x - 3)
(x + 1)(x + 2)(x + 3)
(x - 1)(x + 2)(x - 3)
(x - 1)(x - 2)(x + 3)
Testing for possible roots shows that x = 1, 2, and 3 satisfy the equation, and the polynomial factors completely as (x - 1)(x - 2)(x - 3). This is the correct factorization.
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Study Outcomes

  1. Analyze and simplify complex algebraic expressions.
  2. Solve linear and quadratic equations using appropriate methods.
  3. Apply factoring techniques to decompose polynomial expressions.
  4. Interpret function behavior through graphing and evaluation.
  5. Verify solutions and troubleshoot common algebraic errors.

AP Physics & Stats Progress Check MCQs Cheat Sheet

  1. General form of a quadratic function - Your classic quadratic looks like f(x) = ax2 + bx + c and paints a cheerful parabola that might grin upwards or frown downwards depending on the sign of a. Hunting down the vertex and axis of symmetry helps you find its highest peak or lowest dip - think of it as the bullseye of your graph. Keep an eye on how changing b and c shifts everything around like sliders on a video game. OpenStax: Key Concepts
  2. Standard form for vertex spotting - When you rewrite a quadratic as f(x) = a(x - h)2 + k, the pair (h, k) jumps out as the vertex so you know exactly where your parabola lives. This form is like switching on "map view" for graph shifts - it tells you if you're sliding left/right or up/down. Play around with a to stretch or squish your curve and become the master of transformations. OpenStax: Key Concepts
  3. Factoring quadratics to find roots - Break down expressions like x2 - 5x + 6 = 0 into neat little factors (x - 2)(x - 3) = 0 to spot solutions in a flash: x = 2 or 3. It's like turning a big puzzle into smaller Lego blocks you can snap together - and solve! Mastering this process gives you a superpower for tackling equations and graph intercepts. OpenStax: Key Concepts
  4. Polynomial functions basics - Polynomials are sums of terms like 5x4 or - 2x that play nicely together under addition, subtraction, and multiplication. The highest exponent tells you the degree, which predicts how many turns and wiggles your graph can have. Think of each term as a musical instrument - together they create the full symphony of your function's behavior. OpenStax: Key Concepts
  5. Polynomial long division - Just like dividing big numbers, polynomial long division helps you break down a complex polynomial into a quotient and remainder using step‑by‑step subtraction. It's a fantastic tool for simplifying nasty expressions and preparing for rational function analysis. Keep your work neat - lining up like terms is the secret sauce for avoiding sign errors. OpenStax: Key Concepts
  6. Remainder Theorem magic - The Remainder Theorem says if you divide f(x) by (x - c), the result's remainder is just f(c). It's like having a magic wand to instantly evaluate the leftover without full division. Use it to test values, check factors, or speed‑run polynomial evaluations. OpenStax: Key Concepts
  7. Factor Theorem detective work - If plugging c into f(x) gives zero, then (x - c) is a factor - case closed! This theorem turns root-finding into a crime scene investigation: test suspects, spot the culprit, and factor your way to solutions. It's a must‑know for cracking polynomial mysteries. OpenStax: Key Concepts
  8. Rational functions and their quirks - A rational function is simply one polynomial divided by another, like (x2 - 1)/(x - 3). Tracking domains, vertical/horizontal asymptotes, and intercepts reveals their dramatic behavior - think of vertical asymptotes as walls you can't cross! Graph these carefully and you'll never get lost in the land of fractions. OpenStax: Key Concepts
  9. Direct and inverse variation relationships - In direct variation y = kx, y zooms up or down in lockstep with x, while in inverse variation y = k/x, y tips in the opposite direction as x moves. These simple formulas model real‑world phenomena like speed vs. time or Boyle's gas law. Spotting variation helps you build equations that reflect real relationships! OpenStax: Key Concepts
  10. Understanding inverses of functions - An inverse function f - 1(x) swaps inputs and outputs, essentially rewinding the action of f(x). Only one‑to‑one functions can do this without confusion - think of a perfect slide that you can climb back up exactly the way you went down. Mastering inverses helps you solve equations and decode outputs like a secret agent. OpenStax: Key Concepts
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