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Quizzes > High School Quizzes > Mathematics

Envision Algebra 1 Practice Quiz

Master Algebra with expert answers and resources.

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Algebra Answers Unlocked, a high school algebra practice quiz.

What is the value of x in 2x + 3 = 11?
2
4
5
8
Subtract 3 from both sides to obtain 2x = 8, then divide by 2 to find x = 4. This direct manipulation of the equation confirms the correct answer.
Simplify the expression: 3(x + 4) - 2x.
x + 12
5x + 4
x + 4
x - 12
Distribute 3 over (x + 4) to get 3x + 12, then subtract 2x. Combining like terms results in x + 12.
Which property states that a + b = b + a for all numbers?
Commutative Property of Addition
Associative Property
Distributive Property
Identity Property
The commutative property of addition indicates that the order in which two numbers are added does not change their sum. This is a fundamental concept in algebra.
What is the slope of the line represented by the equation y = 3x + 5?
3
5
8
-3
The equation is in slope-intercept form, y = mx + b, where m is the slope. Here, m equals 3, which is the coefficient of x.
Evaluate the expression 4x - 7 when x = 2.
3
1
2
-1
Substitute x with 2 in the expression 4x - 7 to obtain 4(2) - 7, which simplifies to 8 - 7. The resulting value is 1.
Solve for x: 5x - 2 = 3x + 6.
2
4
8
1
Subtract 3x from both sides to obtain 2x - 2 = 6, then add 2 to both sides to get 2x = 8. Dividing by 2 results in x = 4.
Solve for y: 2(y - 3) = 14.
8
10
11
7
First expand the left side to get 2y - 6 = 14. Then, add 6 to both sides to find 2y = 20, and divide by 2 yielding y = 10.
Factor the quadratic expression: x² + 5x + 6.
(x + 2)(x + 3)
(x + 1)(x + 6)
(x + 3)(x + 4)
(x + 2)(x + 4)
Identify two numbers that multiply to 6 and add up to 5; these are 2 and 3. Therefore, the expression factors into (x + 2)(x + 3).
Solve for x: x² - 9 = 0.
x = 3 or x = -3
x = 9
x = -9
x = 0
Recognize that the equation represents a difference of squares and can be factored as (x - 3)(x + 3) = 0. Setting each factor equal to zero gives the solutions x = 3 and x = -3.
What is the value of 2² * 3³?
108
72
36
54
First calculate 2 squared (which is 4) and 3 cubed (which is 27). Multiplying 4 by 27 yields 108, making it the correct answer.
If f(x) = 2x + 1, what is f(5)?
10
11
12
9
Substitute 5 for x in the function f(x) to get f(5) = 2(5) + 1. This computes as 10 + 1, which equals 11.
Solve the inequality: 3x + 4 < 16.
x < 4
x > 4
x ≤ 4
x ≥ 4
Begin by subtracting 4 from both sides to obtain 3x < 12, then divide both sides by 3 to get x < 4. This isolates x and provides the solution.
Simplify the expression: (3x² * 2x) / (6x³).
1
x
3
6x
Multiply 3x² by 2x to obtain 6x³ in the numerator. Since the denominator is also 6x³, the expression simplifies neatly to 1.
Solve for x: (1/2)x - (1/3)x = 3.
6
18
9
12
Combine the terms by finding a common denominator: (3x - 2x)/6 = x/6, so the equation becomes x/6 = 3. Multiplying both sides by 6 gives x = 18.
Express the square root of 81 as an integer.
9
8
-9
3
The square root operation asks for the number that, when multiplied by itself, equals 81. Since 9 × 9 = 81, the integer square root is 9.
Solve for x: 2(x + 3) = x - 2.
8
-8
-2
-6
Distribute to get 2x + 6 = x - 2. Subtract x from both sides to obtain x + 6 = -2, then subtract 6 to find x = -8.
Find the x-intercept of the line 4x - 2y = 8.
2
4
8
-2
The x-intercept is found by setting y = 0 in the equation. With y = 0, 4x becomes 8, resulting in x = 2.
Solve the system of equations: x + y = 7 and x - y = 3.
x = 5, y = 2
x = 2, y = 5
x = 4, y = 3
x = 3, y = 4
Adding the two equations eliminates y, giving 2x = 10, so x = 5. Substituting back into one of the equations reveals that y = 2.
If 3^x = 81, what is the value of x?
4
3
5
2
Realize that 81 can be expressed as 3^4. Therefore, equating the exponents gives x = 4.
Solve for x: (x/3) + 2 = 5.
6
9
21
8
Subtract 2 from both sides to obtain x/3 = 3. Multiplying both sides by 3 gives x = 9, which is the correct solution.
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Study Outcomes

  1. Analyze linear equations to determine variables and constants.
  2. Apply algebraic techniques to simplify expressions.
  3. Interpret word problems using algebraic models.
  4. Solve multi-step equations with one or more variables.
  5. Evaluate functions and their corresponding graphs.
  6. Identify common factoring methods to simplify expressions.

Envision Algebra 1 Quiz & Answers Cheat Sheet

  1. Master the Order of Operations - Picture PEMDAS as your algebraic treasure map: start with Parentheses, then Exponents, tackle Multiplication and Division (left to right), and finish with Addition and Subtraction. For example, in 3 + 6 × (5 + 4) ÷ 3 - 7 you'd conquer the parentheses 5 + 4 = 9 before moving on. Using this golden rule keeps your calculations accurate and drama-free. OpenStax Key Concepts
  2. Understand Properties of Real Numbers - Become best buds with commutative, associative, and distributive properties to shuffle and simplify terms like a puzzle master. Remember, a(b + c) = ab + ac unpacks grouped expressions into bite-sized pieces. These cornerstones of algebra give you the power to tackle complex problems with confidence. OpenStax Key Concepts
  3. Work with Exponents and Scientific Notation - Treat exponents as your multiplication shortcuts: a^m × a^n = a^(m+n) and keep zero and negative exponents in check to avoid slip-ups. When numbers get unwieldy, convert them into scientific notation - like turning 0.00045 into 4.5 × 10^-4 - to keep digits in line. This combo of exponent rules and neat notation keeps your math sleek and manageable. OpenStax Key Concepts
  4. Perform Operations with Polynomials - Brush up on adding, subtracting, multiplying, and even dividing polynomials until you can do it in your sleep. Remember that (x + y)^2 expands to x^2 + 2xy + y^2, so you can predict the results before you multiply. Practicing these operations helps you see patterns and speeds up problem-solving. OpenStax Key Concepts
  5. Factor Polynomials Effectively - Sniff out the greatest common factor (GCF) and use tricks like factoring by grouping to break polynomials into simpler pieces. For instance, x^2 + 5x + 6 transforms into (x + 2)(x + 3) once you spot the numbers that multiply to 6 and add to 5. Factoring is like reverse engineering algebraic expressions - find the pieces, and the puzzle is solved. OpenStax Key Concepts
  6. Simplify Rational Expressions - Treat rational expressions like fractions: factor the numerator and denominator, cancel common factors, and find a simplified form. For example, (x^2 - 9)/(x + 3) becomes x - 3 once you factor the top into (x + 3)(x - 3). Mastering this process clears the way for adding, subtracting, multiplying, and dividing more complex fractions. OpenStax Key Concepts
  7. Understand the Real Number System - Explore the universe of numbers: natural, whole, integers, rationals, and irrationals each have their own club. Recognize that π is irrational because it can't be written as a precise fraction, while 3/4 is happily rational. Knowing these categories helps you classify and manipulate numbers with confidence. OpenStax Key Concepts
  8. Apply the Quadratic Formula - When factoring falters, let x = (-b ± √(b^2 - 4ac)) / (2a) swoop in to rescue your quadratic equation ax^2 + bx + c = 0. Calculate the discriminant first to see if your solutions are real or complex - it's like checking the weather before you head out. This formula is your all-purpose tool for nailing down precise roots every time. Sierra College Algebra Resources
  9. Work with Radicals and Rational Exponents - Flip between radicals (√x) and rational exponents (x^(1/2)) like a language translator to simplify or solve equations. Remember that √(a^2) = |a| to avoid sign surprises, and nth roots follow the same pattern: x^(1/3) is the cube root of x. Mastering these conversions unleashes new strategies for tackling roots and powers. OpenStax Key Concepts
  10. Practice Solving Linear Equations and Inequalities - Hone your skills by tackling equations and inequalities, including ones with absolute values. Always balance both sides, and don't forget: multiply or divide by a negative flips the inequality sign - your math ninja reflex must stay sharp. Consistent practice turns these foundational skills into second nature. OpenStax Key Concepts
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