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Quizzes > High School Quizzes > Mathematics

AP Algebra 1 Practice Quiz

Enhance your skills with engaging algebra challenges

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Colorful paper art promoting AP Algebra Ace quiz for high school students.

Solve for x: 2x + 3 = 11.
3
8
4
5
Subtract 3 from both sides to obtain 2x = 8, then divide by 2 to find x = 4. This is the correct and unique solution to the equation.
Simplify the expression: 3x + 4x.
7x
0
x
12x
Combine like terms by adding the coefficients: 3 + 4 equals 7, so 3x + 4x simplifies to 7x. This straightforward combination of like terms yields the correct answer.
Given the equation y - 3 = 2(x - 1), find y when x = 4.
6
8
7
9
First substitute x = 4 into the equation: y - 3 = 2(4 - 1) becomes y - 3 = 6. Adding 3 to both sides gives y = 9, which is the correct answer.
Which property allows you to write a(b + c) as ab + ac?
Commutative Property
Associative Property
Distributive Property
Identity Property
The distributive property of multiplication over addition states that a(b + c) can be rewritten as ab + ac. This property is fundamental to algebraic manipulation.
Simplify the expression: -3(x - 4).
-3x + 12
3x + 12
3x - 12
-3x - 12
Distribute -3 to both x and -4 to obtain -3x + 12. This correctly applies the distributive property, yielding the simplified expression.
Solve for x: (x - 2)/3 = 4.
12
14
10
15
Multiply both sides of the equation by 3 to eliminate the denominator, resulting in x - 2 = 12. Adding 2 gives x = 14, which is the correct answer.
Solve the equation: 5(x + 2) = 3x + 14.
2
8
4
-2
Expanding the left side gives 5x + 10, so the equation becomes 5x + 10 = 3x + 14. Subtracting 3x and then 10 from both sides leads to 2x = 4, and dividing by 2 gives x = 2.
Factor the quadratic: x^2 + 5x + 6.
(x - 2)(x - 3)
(x + 2)(x + 3)
(x + 2)(x - 3)
(x + 1)(x + 6)
The factors of 6 that add up to 5 are 2 and 3, so the quadratic can be factored as (x + 2)(x + 3). This is the correct factorization of the given quadratic.
Solve for x: 2(x - 3) + 4 = 10.
7
8
6
5
Subtract 4 from both sides to obtain 2(x - 3) = 6, then divide by 2 to get x - 3 = 3. Adding 3 to both sides results in x = 6.
Given f(x) = 3x - 7, what is f(4)?
5
1
4
7
Substitute x = 4 into the function to calculate f(4) = 3(4) - 7 = 12 - 7 = 5. This is the correct evaluation of the function at x = 4.
Simplify the expression: 2x - 3x + 4y - 2y.
-x + 2y
-x - 2y
x - 2y
x + 2y
Combine like terms by subtracting the coefficients separately: 2x - 3x equals -x, and 4y - 2y equals 2y. This results in the simplified expression -x + 2y.
Solve the inequality: 3x - 5 > 1.
x > 2
x < 2
x ≥ 2
x ≤ 2
Adding 5 to both sides gives 3x > 6, and dividing by 3 yields x > 2. This inequality describes all numbers greater than 2.
If a = 3 and b = -2, evaluate the expression: 4a + 3b.
-6
12
6
10
Substitute a = 3 and b = -2 into the expression to get 4(3) + 3(-2) = 12 - 6 = 6. This calculation confirms that the correct answer is 6.
Solve the system: x + y = 7 and x - y = 3.
x=4, y=3
x=3, y=4
x=5, y=2
x=2, y=5
Adding the two equations eliminates y, resulting in 2x = 10, so x = 5. Substituting back into one of the original equations gives y = 2. Thus, the solution is x=5 and y=2.
Solve for x: (1/2)x + 3 = 7.
4
8
10
6
Subtract 3 from both sides to obtain (1/2)x = 4, then multiply by 2 to find x = 8. This method correctly isolates the variable, yielding the answer.
Solve the quadratic equation: 2x^2 - 5x - 3 = 0.
x = -1/2 only
x = 3 only
x = -1/2 or x = 3
x = -3 or x = 1/2
Factoring the quadratic gives (2x + 1)(x - 3) = 0. Setting each factor equal to zero leads to the solutions x = -1/2 and x = 3, both of which satisfy the original equation.
Determine the vertex of the parabola given by y = x^2 - 4x + 1.
(4, 1)
(-2, 3)
(-4, -1)
(2, -3)
The vertex of a parabola in the form y = ax^2 + bx + c can be found with the formula (-b/(2a), f(-b/(2a))). Here, a = 1 and b = -4 so the vertex is (2, -3).
Solve for x: √(x + 5) = x - 1.
-1
5
4
2
Squaring both sides yields x + 5 = (x - 1)^2, which simplifies to a quadratic equation. After solving and checking for extraneous solutions, x = 4 is the only valid solution.
If f(x) = 2x + 3 and g(x) = x^2, find f(g(2)).
8
11
7
10
First, evaluate g(2) which is 2^2 = 4. Then substitute into f to get f(4) = 2(4) + 3 = 11, making this the correct outcome.
Solve the system of equations: 2x + 3y = 13 and 4x - y = 5.
x=2, y=3
x=4, y=1
x=3, y=2
x=1, y=4
First, solve the second equation for y: y = 4x - 5. Substitute this into the first equation to obtain 2x + 3(4x - 5) = 13, which simplifies to 14x = 28 and gives x = 2. Substituting back finds y = 3, the correct solution.
0
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Study Outcomes

  1. Analyze algebraic expressions and equations to determine their key characteristics.
  2. Apply problem-solving techniques to solve multi-step algebra problems efficiently.
  3. Evaluate functions and graphs to interpret real-world relationships.
  4. Understand and manipulate algebraic formulas to isolate and solve for variables.
  5. Synthesize review strategies to boost readiness for AP-level algebra exams.

AP Algebra 1 Practice Cheat Sheet

  1. Master the Order of Operations - Nail the correct sequence of steps (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to crack any expression like a code. Use the catchy PEMDAS acronym as your trusty sidekick and watch mistakes vanish. Practice on random combos and you'll breeze through homework! OpenStax Intermediate Algebra Key Concepts
    2. OpenStax Intermediate Algebra Key Concepts
  2. Understand the Properties of Real Numbers - Dive into the Commutative, Associative, Distributive, Identity, and Inverse properties that make algebra feel like magic tricks. These rules let you shuffle and simplify expressions without breaking a sweat. Spot them in action and you'll simplify equations faster than ever! OpenStax Intermediate Algebra 2e Key Concepts
    3. OpenStax Intermediate Algebra 2e Key Concepts
  3. Practice Solving Linear Equations - Tackle equations by isolating the variable with inverse operations and keep the balance scale even. Remember, adding, subtracting, multiplying, or dividing both sides by the same number is your mantra. Soon you'll solve for x like a detective cracking cases! OpenStax Intermediate Algebra Key Concepts
    4. OpenStax Intermediate Algebra Key Concepts
  4. Get Comfortable with Factoring Polynomials - Always hunt for the greatest common factor (GCF) before anything else and don't forget those special products like a2−b2=(a+b)(a−b). Factoring turns scary expressions into friendly binomials in minutes. Mastering this feels like unlocking cheat codes for tougher algebra puzzles! OpenStax Algebra and Trigonometry Key Concepts
    5. OpenStax Algebra and Trigonometry Key Concepts
  5. Learn the Quadratic Formula - Memorize x = (−b ± √(b²−4ac))/(2a) and you'll have a universal problem-solver for any quadratic equation. It might look intense, but plugging in a, b, and c is as simple as following a recipe. Use it when factoring feels like a dead end and watch the roots appear! Sierra College Algebra Resources
    6. Sierra College Algebra Resources
  6. Understand Exponents and Scientific Notation - Rule the exponent laws, like am×an=am+n and (am)n=amn, to conquer power games. Scientific notation lets you express huge or tiny numbers in a snap, like 6.02×1023 instead of a giant string of digits. This hack is essential for science and tech calculations! OpenStax Algebra and Trigonometry Key Concepts
    7. OpenStax Algebra and Trigonometry Key Concepts
  7. Work on Graphing Linear Equations - Plot y=mx+b by identifying slope (m) and y-intercept (b) to turn algebraic lines into visual art. Sketching graphs helps you see how changes in m and b tilt and shift your line. Soon, you'll predict intersections and trends like a pro data analyst! OpenStax Intermediate Algebra Key Concepts
    8. OpenStax Intermediate Algebra Key Concepts
  8. Practice Operations with Fractions - Add/subtract by finding that all-important common denominator, multiply straight across, and divide by flipping the second fraction (reciprocal!). Fractions don't have to be fearsome - just follow the steps. With practice, you'll simplify, convert, and compare fractions in your sleep! Sierra College Algebra Resources
    9. Sierra College Algebra Resources
  9. Learn about Radicals and Rational Exponents - Convert between √[n] and a1/n effortlessly and simplify radicals by pulling out perfect powers. Rational exponents let you rewrite roots as fractions (like a3/2=√(a3)), which streamlines expression handling. Master these to break down compound expressions like a champ! OpenStax Algebra and Trigonometry Key Concepts
    10. OpenStax Algebra and Trigonometry Key Concepts
  10. Explore Special Products - Recognize patterns like (a+b)2=a2+2ab+b2 and (a−b)2=a2−2ab+b2, plus difference of squares a2−b2=(a+b)(a−b) to speed up expansions and factorizations. These shortcuts save time and prevent errors on tests. Spotting them is like finding shortcuts in your favorite video game! Sierra College Algebra Resources
    11. Sierra College Algebra Resources
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