I will provide you with a PDF and Word Document (editable) of the test.

No answer key at the moment, I encourage teachers to take the test before giving the test to students

My students take this test within the 1-hour class

Here is the breakdown of the topics:

Section 1: Expression Analysis

• Expression Terms: Analyzing an algebraic expression.
  • Identifying the number of terms.
  • Finding the coefficient of a specific term.
  • Identifying constants.

Section 2: Solving Equations

• Linear and Fractional Equations: Solving various types of equations involving:
  • Linear equations with fractions.
  • Multi-variable and multi-step equations.
  • Distributive property.
  • Absolute value equations.

Section 3: Word Problems

• Setting Up Equations for Word Problems: Writing equations to represent real-life scenarios but not solving them.
  • Car rental problem (linear equation setup).
  • Savings comparison problem between two people.
  • Comparing two pricing options for a gym membership.
  • Determining the weight of a mother dog given the weight of a puppy.
  • Setting up an equation for the perimeter of a rectangle.

Section 4: Formula Rearrangement

• Rearranging Equations: Solving for a specific variable in:
  • A distance-time-speed formula.
  • A temperature conversion formula.

Section 5: Special Cases for Linear Equations

• Special Cases in Linear Equations:
  • Explaining when a linear equation has no solution or infinitely many solutions.
  • Creating an equation that results in infinitely many solutions.

Extra Credit:

• Quadratic Equation: Solve a quadratic equation.
• Word Problem with System of Equations: Valet work with different hourly pay rates.
• Solving for a Variable in a Formula: Rearranging a surface area formula involving three variables.

Common Core Standards:

• CCSS.MATH.CONTENT.HSA.SSE.A.1:
  • Interpret expressions that represent a quantity in terms of its context.
  • Students must break down algebraic expressions into terms, coefficients, and constants, aligning with the first section of the test.

2. Solving Equations and Inequalities

• CCSS.MATH.CONTENT.HSA.REI.A.1:
  
  • Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step.
  • The test asks students to show their work and justify their steps when solving linear and fractional equations.

• CCSS.MATH.CONTENT.HSA.REI.B.3:
  
  • Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • Most of the second section of the test focuses on solving linear equations and inequalities, with variables and constants.

• CCSS.MATH.CONTENT.HSA.REI.D.10-12:
  
  • Solve systems of linear equations (exact solutions or approximate solutions), focusing on graphing, substitution, and elimination.
  • Although not explicitly stated, some problems like the word problems involving two people (savings account, valet jobs) can be solved using systems of equations.

3. Understanding the Structure of Expressions

• CCSS.MATH.CONTENT.HSA.SSE.A.2:
  • Use the structure of an expression to identify ways to rewrite it.
  • Students work with more complex expressions and manipulate them, especially in the solving of equations section.

4. Modeling Real-World Situations

• CCSS.MATH.CONTENT.HSA.CED.A.1:
  
  • Create equations and inequalities in one variable and use them to solve problems.
  • This standard relates to the word problems section, where students create algebraic models from real-world situations, such as renting cars, gym memberships, and comparing bank savings.

• CCSS.MATH.CONTENT.HSA.CED.A.2:
  
  • Create equations in two or more variables to represent relationships between quantities.
  • The test includes scenarios where students need to set up equations involving multiple variables (like the word problems about savings accounts and valet jobs).

5. Reasoning with Equations

• CCSS.MATH.CONTENT.HSA.REI.C.5-6:
  • Solve systems of equations exactly or approximately, focusing on solving linear systems algebraically.
  • This ties to the problems involving balancing savings and salary jobs, where students could potentially solve using systems of equations.

6. Special Cases and Solutions

• CCSS.MATH.CONTENT.HSA.REI.B.2:
  • Solve equations of the form x² = p and ax + b = c, including cases where there are no solutions, infinitely many solutions, or exactly one solution.
  • The section about determining when a linear equation has special cases (no solution, infinitely many solutions) directly aligns with this standard.

7. Rearranging Formulas

• CCSS.MATH.CONTENT.HSA.CED.A.4:
  • Rearrange formulas to highlight a quantity of interest.
  • Problems where students are asked to solve for specific variables in formulas, such as in the temperature conversion and distance formulas, target this standard.

8. Solving Absolute Value Equations

• CCSS.MATH.CONTENT.HSA.REI.A.2: