In Order of Operations Quiz and Order of Operations Four, questions are designed to help the user to practice order of operations with addition/subtraction, multiplication/division, exponents, and parentheses, 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:
Addition, Subtraction, Multiplication, and Division only:
- Whole Numbers Only: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers equal to or greater than 0.
- Level 1: An arithmetic problem including 3 integers between 1 and 9 and 2 binary operators, resulting in integer answers.
- Level 2: An arithmetic problem including 4 integers between -9 and 9, excluding 0, and 3 binary operators, resulting in integer answers.
- Level 3: An arithmetic problem including 5 integers between -9 and 9, excluding 0, and 4 binary operators, resulting in integer answers.
With Parentheses and no Exponents:
- Whole Numbers Only: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers equal to or greater than 0. There will also be 1 set of parentheses.
- Level 1: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers. There will also be 1 set of parentheses.
- Level 2: An arithmetic problem including 4 integers between -9 and 9, excluding 0, and 3 binary operators, resulting in integer answers. There will also be 1 or 2 sets of parentheses.
- Level 3: An arithmetic problem including 5 integers between -9 and 9, excluding 0, and 4 binary operators, resulting in integer answers. There will also be 1, 2, or 3 sets of parentheses.
With Exponents and no Parentheses:
- Whole Numbers Only: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers equal to or greater than 0. Additionally, 1 integer will be raised to an exponent between 1 and 4.
- Level 1: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers. Additionally, 1 integer will be raised to an exponent between 1 and 4.
- Level 2: An arithmetic problem including 4 integers between -9 and 9, excluding 0, and 3 binary operators, resulting in integer answers. Additionally, 1 integer will be raised to an exponent between 0 and 4.
- Level 3: An arithmetic problem including 5 integers between -9 and 9, excluding 0, and 4 binary operators, resulting in integer answers. Additionally, 1 integer or expression will be raised to an exponent between 0 and 4.
With Parentheses and Exponents:
- Whole Numbers Only: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers equal to or greater than 0. There will also be 1 set of parentheses. Additionally, 1 integer will be raised to an exponent between 1 and 4.
- Level 1: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers. There will also be 1 set of parentheses. Additionally, 1 integer will be raised to an exponent between 1 and 4.
- Level 2: An arithmetic problem including 4 integers between -9 and 9, excluding 0, and 3 binary operators, resulting in integer answers. There will also be 1 or 2 sets of parentheses. Additionally, 1 integer will be raised to an exponent between 0 and 4.
- Level 3: An arithmetic problem including 5 integers between -9 and 9, excluding 0, and 4 binary operators, resulting in integer answers. There will also be 1, 2, or 3 sets of parentheses. Additionally, 1 integer or expression will be raised to an exponent between 0 and 4.
Descriptions by Difficulty Level:
Whole Numbers Only:
- Addition, Subtraction, Multiplication, and Division only: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers equal to or greater than 0.
- With Parentheses and no Exponents: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers equal to or greater than 0. There will also be 1 set of parentheses.
- With Exponents and no Parentheses: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers equal to or greater than 0. Additionally, 1 integer will be raised to an exponent between 1 and 4.
- With Exponents and Parentheses: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers equal to or greater than 0. There will also be 1 set of parentheses. Additionally, 1 integer will be raised to an exponent between 1 and 4.
Level 1:
- Addition, Subtraction, Multiplication, and Division only: An arithmetic problem including 3 integers between 1 and 9 and 2 binary operators, resulting in integer answers.
- With Parentheses and no Exponents: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers. There will also be 1 set of parentheses.
- With Exponents and no Parentheses: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers. Additionally, 1 integer will be raised to an exponent between 1 and 4.
- With Exponents and Parentheses: An arithmetic problem including 3 integers between 1 and 9 and 2 operators, resulting in integer answers. There will also be 1 set of parentheses. Additionally, 1 integer will be raised to an exponent between 1 and 4.
Level 2:
- Addition, Subtraction, Multiplication, and Division only:: An arithmetic problem including 4 integers between -9 and 9, excluding 0, and 3 binary operators, resulting in integer answers.
- With Parentheses and no Exponents: An arithmetic problem including 4 integers between -9 and 9, excluding 0, and 3 binary operators, resulting in integer answers. There will also be 1 or 2 sets of parentheses.
- With Exponents and no Parentheses: An arithmetic problem including 4 integers between -9 and 9, excluding 0, and 3 binary operators, resulting in integer answers. Additionally, 1 integer will be raised to an exponent between 0 and 4.
- With Exponents and Parentheses: An arithmetic problem including 4 integers between -9 and 9, excluding 0, and 3 binary operators, resulting in integer answers. There will also be 1 or 2 sets of parentheses. Additionally, 1 integer will be raised to an exponent between 0 and 4.
Level 3:
- Addition, Subtraction, Multiplication, and Division only:: An arithmetic problem including 5 integers between -9 and 9, excluding 0, and 4 binary operators, resulting in integer answers.
- With Parentheses and no Exponents: An arithmetic problem including 5 integers between -9 and 9, excluding 0, and 4 binary operators, resulting in integer answers. There will also be 1, 2, or 3 sets of parentheses.
- With Exponents and no Parentheses: An arithmetic problem including 5 integers between -9 and 9, excluding 0, and 4 binary operators, resulting in integer answers. Additionally, 1 integer or expression will be raised to an exponent between 0 and 4.
- With Exponents and Parentheses: An arithmetic problem including 5 integers between -9 and 9, excluding 0, and 4 binary operators, resulting in integer answers. There will also be 1, 2, or 3 sets of parentheses. Additionally, 1 integer or expression will be raised to an exponent between 0 and 4.