Question Types for Algebra Quiz and Algebra Four

In Algebra Quiz and Algebra Four, questions are designed to help the user practice solving linear and quadratic algebraic equations, and to prepare them for questions of various levels of difficulty. Questions are categorized by a combination of level (which determines the difficulty) and by types of problems listed. These different categories are defined in two different organizational structures. The first organization looks at problem types, then considers how problems vary by level within that type. The second organization considers the difficulty level first, then looks at different problem types within that level. All number ranges are inclusive. Both are provided below.

Descriptions by Problem Type:

Variables on Both Sides:

• Whole Numbers Only: Solve for x by combining like terms from both sides of the equation. Answers and coefficients will be integers between 1 and 5, and constants will be integers between 1 and 50, with most between 1 and 25.
• Level 1: Solve for x by combining like terms from both sides of the equation. Answers and coefficients will be integers between -5 and 5, and constants will be between -50 and 50, with most between -25 and 25.
• Level 2: Solve for x by combining like terms from both sides of the equation. Coefficients and constants in the equation will be integers, but answers may be fractions.
• Level 3: Solve for x by combining like terms, which include fractional coefficients and constant terms.

Distributive:

• Whole Numbers Only: Distribute a value between 1 and 5 across parentheses while the initial coefficient of x is 1. Resulting answer will be a positive integer.
• Level 1: Distribute a value between -5 and 5 across parentheses while the initial coefficient of x is 1. Resulting answer may be fractional or negative.
• Level 2: Distribute a value between -5 and 5 across parentheses on both sides of the equation to solve for x, which may be fractional.
• Level 3: Solve for x by distributing a fractional constant across parentheses on one or both sides of the equation.

Quadratic:

• Whole Numbers Only: Find one or two solutions to quadratic equations, both of which are positive integers.
• Level 1: Find one or two integer solutions to quadratic equations.
• Level 2: Find solutions to quadratic equations with integer coefficients and constants. There may be one fractional solution or two solutions: an integer and a fraction.
• Level 3: Find two fractional solutions to quadratic equations with integer coefficients and constants.

Two-Step Problems:

• Whole Numbers Only: Combine like terms and then divide by a coefficient with values between 1 and 5 to solve for x, which will be a positive integer.
• Level 1: Combine like terms and then divide by a coefficient with values between -5 and 5 to solve for x, which may be fractional or negative.
• Level 2: Combine like terms (must be an integer) and then divide by a fractional coefficient to solve for x, which may be a fraction.
• Level 3: Combine fractional like terms and then divide by a fractional coefficient to solve for x, which may be a fraction.

One-Step Problems:

• Whole Numbers Only: Solve for a positive integer solution of x by combining constants or dividing out a coefficient of x, all of which are positive integers.
• Level 1: Solve for an integer solution of x by combining constants or dividing out a coefficient of x.
• Level 2: Add constants (an integer and a proper fraction) to solve for x, which should be entered as an improper fraction.
• Level 3: Add or divide fractions to solve for x, which is typically a fraction.

Descriptions by Difficulty Level:

Whole Numbers Only:

• Variables on Both Sides: Solve for x by combining like terms from both sides of the equation. Answers and coefficients will be integers between 1 and 5, and constants will be integers between 1 and 50, with most between 1 and 25.
• Distributive Property: Distribute a value between 1 and 5 across parentheses while the initial coefficient of x is 1. Resulting answer will be a positive integer.
• Quadratics: Find one or two solutions to quadratic equations, both of which are positive integers.
• Two-Step Problems: Combine like terms and then divide by a coefficient with values between 1 and 5 to solve for x, which will be a positive integer.
• One-Step Problems: Solve for a positive integer solution of x by combining constants or dividing out a coefficient of x, all of which are positive integers.

Level 1:

• Variables on Both Sides: Solve for x by combining like terms from both sides of the equation. Answers and coefficients will be integers between -5 and 5, and constants will be between -50 and 50, with most between -25 and 25.
• Distributive Property: Distribute a value between -5 and 5 across parentheses while the initial coefficient of x is 1. Resulting answer may be fractional or negative.
• Quadratics: Find one or two integer solutions to quadratic equations.
• Two-Step Problems: Combine like terms and then divide by a coefficient with values between -5 and 5 to solve for x, which may be fractional or negative.
• One-Step Problems: Solve for an integer solution of x by combining constants or dividing out a coefficient of x.

Level 2:

• Variables on Both Sides: Solve for x by combining like terms from both sides of the equation. Coefficients and constants in the equation will be integers, but answers may be fractions.
• Distributive Property: Distribute a value between -5 and 5 across parentheses on both sides of the equation to solve for x, which may be fractional.
• Quadratics: Find solutions to quadratic equations with integer coefficients and constants. There may be one fractional solution or two solutions: an integer and a fraction.
• Two-Step Problems: Combine like terms (must be an integer) and then divide by a fractional coefficient to solve for x, which may be a fraction.
• One-Step Problems: Add constants (an integer and a proper fraction) to solve for x, which should be entered as an improper fraction.

Level 3:

• Variables on Both Sides: Solve for x by combining like terms, which include fractional coefficients and constant terms.
• Distributive Property: Solve for x by distributing a fractional constant across parentheses on one or both sides of the equation.
• Quadratics: Find two fractional solutions to quadratic equations with integer coefficients and constants.
• Two-Step Problems: Combine fractional like terms and then divide by a fractional coefficient to solve for x, which may be a fraction.
• One-Step Problems: Add or divide fractions to solve for x, which is typically a fraction.