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Quizzes > High School Quizzes > Mathematics

Algebra 1 EOC Practice Test

Boost Skills with EOC Review and Practice

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Algebra 1 EOC Edge practice quiz paper art for high school students to assess understanding.

Solve for x: 3x + 5 = 20.
5
8
15
20
Subtract 5 from both sides to obtain 3x = 15, then divide by 3 to get x = 5. This method clearly isolates the variable.
Simplify the expression: 2x + 3x.
5x
6x
x
2x
Combine like terms by adding the coefficients 2 and 3 to obtain 5, resulting in the simplified form 5x. This is a basic example of combining like terms.
What is the slope of a line with the equation 2x - 3y = 6?
2/3
-2/3
3/2
1/2
Rearrange the equation into the slope-intercept form: y = (2/3)x - 2, which shows that the slope is 2/3. This conversion is a key step in identifying the slope.
Identify the y-intercept of the line: y = -2x + 7.
7
-2
-7
2
In the slope-intercept form y = mx + b, the y-intercept is the value b. Here, b equals 7, indicating the point (0, 7) on the graph.
Solve for y in the equation: 5y = 45.
9
45
5
40
By dividing both sides of the equation by 5, you obtain y = 45/5, which simplifies to y = 9. This is a direct application of basic division to solve for the variable.
Solve for x in the equation: (1/2)x + 3 = 7.
8
10
7
4
Subtract 3 from both sides to get (1/2)x = 4, then multiply by 2 to obtain x = 8. This demonstrates proper handling of fractional coefficients.
Solve for x: 2(3x - 4) = 4x + 8.
8
4
6
2
Expanding the left side gives 6x - 8, and simplifying by subtracting 4x from both sides leads to 2x - 8 = 8, which results in x = 8. This question reinforces the distributive property and solving linear equations.
Simplify the expression: 3x² + 5x².
8x²
15x²
2x²
8x
By combining like terms, add the coefficients 3 and 5 to get 8, which results in 8x². This problem tests the basic skill of combining like terms in polynomial expressions.
Solve for y in the equation: 2y - 3 = 7y + 2.
-1
1
5
-5
Rearrange the terms by subtracting 7y from 2y to get -5y, and then add 3 to the other side, resulting in -5y = 5, so y = -1. This tests basic transposition of terms in an equation.
If f(x) = x² - 4x + 5, what is the value of f(3)?
2
3
5
0
Substitute x = 3 into the function: f(3) = 3² - 4(3) + 5, which simplifies to 9 - 12 + 5 = 2. This reinforces the process of function evaluation.
Determine the slope of the line through the points (2, 3) and (8, 15).
2
3
4
6
The slope is calculated by (15 - 3) / (8 - 2) = 12/6, which simplifies to 2. This question tests the understanding of the slope formula.
Solve the inequality: x - 5 > 3.
x > 8
x ≥ 8
x < 8
x ≤ 8
Add 5 to both sides to obtain x > 8. This straightforward manipulation of the inequality reinforces basic operations with inequalities.
Solve for x in the equation: (x - 3)/4 = 2.
11
5
8
7
Multiply both sides by 4 to get x - 3 = 8 and then add 3, resulting in x = 11. This question tests proper handling of linear equations with fractions.
Factor the quadratic expression: x² + 5x + 6.
(x + 2)(x + 3)
(x + 1)(x + 6)
(x - 2)(x - 3)
(x + 3)(x + 4)
The factors of 6 that add up to 5 are 2 and 3, which means x² + 5x + 6 factors as (x + 2)(x + 3). This is a standard factoring exercise.
Solve for x in the equation: 4(x - 2) = 2(2x + 1).
No solution
x = 5
All real numbers
x = -5
Expanding both sides gives 4x - 8 = 4x + 2, which simplifies to the false statement -8 = 2. This indicates the equation is inconsistent and has no solution.
Solve for x: 2/(x - 1) + 3/(x + 2) = 1.
x = 2 + √7 or x = 2 - √7
x = 2 + √7
x = 2 - √7
x = 2
Multiplying both sides by (x - 1)(x + 2) clears the denominators and leads to the quadratic equation x² - 4x - 3 = 0. Solving this quadratic using the quadratic formula yields x = 2 ± √7.
Solve the absolute value equation: |2x - 5| = 7.
x = 6 or x = -1
x = 6
x = -1
x = 1 or x = -6
The equation |2x - 5| = 7 splits into two linear equations: 2x - 5 = 7 and 2x - 5 = -7, which result in x = 6 and x = -1 respectively. Both solutions satisfy the original equation.
Determine the solution of the inequality: -2x + 5 ≥ 3.
x ≤ 1
x ≥ 1
x < 1
x > 1
Subtract 5 from both sides to obtain -2x ≥ -2, then divide by -2 and reverse the inequality sign to get x ≤ 1. This manipulation is key when working with inequalities and negative divisors.
Find the equation of the line passing through the point (3, -2) with a slope of 4.
y = 4x - 14
y = 4x + 14
y = -4x - 14
y = -4x + 14
Using the point-slope form y - y₝ = m(x - x₝) with point (3, -2) and slope 4, the equation becomes y + 2 = 4(x - 3), which simplifies to y = 4x - 14. This method directly applies the point-slope concept.
For a system of two linear equations to have no solution, what must be true about the lines?
They are parallel; they have the same slope and different y-intercepts.
They intersect at exactly one point.
They are identical.
They are perpendicular.
A system with no solution occurs when the lines are parallel and distinct, meaning they have the same slope but different y-intercepts. This condition prevents the lines from intersecting at any point.
0
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Study Outcomes

  1. Apply algebraic principles to solve linear equations and inequalities.
  2. Analyze algebraic expressions to simplify, factor, and expand them.
  3. Evaluate functions and graph equations to interpret their behavior.
  4. Identify errors in problem solving and correct misconceptions in algebraic reasoning.
  5. Assess performance to pinpoint areas for targeted improvement in algebra preparation.

Algebra 1 EOC Practice Test & Study Guide Cheat Sheet

  1. Master the order of operations (PEMDAS) - Keep your math in line by remembering Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction. This rule ensures you solve each part of an expression in the right sequence so your answers stay spot on. OpenStax Key Concepts
    2. openstax.org
  2. Solve linear equations - From one-step to multi-step problems, mastering the balance moves (addition, subtraction, multiplication, division) helps you isolate the variable and crack the solution. Practice plugging in numbers and checking your work to build confidence. Algebra-Class Tutorial
    3. algebra-class.com
  3. Graph lines in slope-intercept form - Use y = mx + b to plot points: 'm' for steepness, 'b' for where the line crosses the y-axis. A quick sketch of rise over run makes graphing feel like a breeze. CLRN Study Guide
    4. clrn.org
  4. Know exponent properties - Rules like a^m · a^n = a^(m+n) and (a^m)^n = a^(m·n) keep calculations tidy when numbers shoot sky-high. Memorize these shortcuts to simplify big expressions in a snap. OpenStax Exponent Rules
    5. openstax.org
  5. Factor polynomials - Pull out the greatest common factor first, then tackle trinomials by finding two numbers that multiply and add just right. Factoring turns monstrous expressions into friendly pieces. OpenStax Factoring Tips
    6. openstax.org
  6. Apply the quadratic formula - Plug coefficients into x = ( - b ± √(b² - 4ac))❄(2a) to find the roots of any quadratic. It's your trusty tool when factoring fails or equations get hairy. CLRN Quadratic Guide
    7. clrn.org
  7. Solve systems of equations - Use substitution or elimination to find where two lines intersect. Visualizing graphs or lining up terms makes these pair puzzles surprisingly straightforward. CLRN Systems Strategies
    8. clrn.org
  8. Understand functions - Get comfy with domain (input values) and range (output values), then practice plugging in x's to see what f(x) delivers. Functions are like vending machines: you put in a number, get out a result! CLRN Function Fundamentals
    9. clrn.org
  9. Work with inequalities - Flip the inequality sign when you multiply or divide by a negative, then practice shading solutions on number lines or coordinate planes. Graphing makes these comparisons crystal clear. Algebra-Class Inequality Tips
    10. algebra-class.com
  10. Memorize line formulas - Keep m = (y₂ - y₝)/(x₂ - x₝) and y - y₝ = m(x - x₝) in your pocket to craft equations from any two points. These are your go-to tools for straight-line success. Quizlet Formula Deck
    11. quizlet.com
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