Podcast
Questions and Answers
What are natural numbers?
What are natural numbers?
- Any number that can be written as a quotient of 2 integers
- All positive numbers including 0
- All positive and negative whole numbers
- All positive numbers not including 0 (correct)
Which of the following includes 0?
Which of the following includes 0?
- Natural numbers (N)
- Rational numbers (Q)
- Integers (Z)
- Whole numbers (W) (correct)
What are integers?
What are integers?
- All whole numbers including fractions
- All positive numbers
- All positive and negative whole numbers (correct)
- Any number that can be expressed as a decimal
Which number type can be written as a quotient of two integers?
Which number type can be written as a quotient of two integers?
What are irrational numbers?
What are irrational numbers?
What is an imaginary number?
What is an imaginary number?
What does 'element of' mean?
What does 'element of' mean?
Union sets together combine two sets.
Union sets together combine two sets.
Intersection includes numbers not found in either of the combined sets.
Intersection includes numbers not found in either of the combined sets.
What is a subset?
What is a subset?
What makes up the real number system?
What makes up the real number system?
What does a null set imply?
What does a null set imply?
What is the identity property for addition?
What is the identity property for addition?
What is the property of 0 in multiplication?
What is the property of 0 in multiplication?
What does substitution mean in mathematics?
What does substitution mean in mathematics?
What is the reflexive property?
What is the reflexive property?
What is the symmetric property?
What is the symmetric property?
What does transitive property mean?
What does transitive property mean?
What is an inverse in multiplication?
What is an inverse in multiplication?
What does the definition of subtraction suggest?
What does the definition of subtraction suggest?
What does the distributive property involve?
What does the distributive property involve?
The requirements for simplest form are that _____
The requirements for simplest form are that _____
Which of the following phrases also means add?
Which of the following phrases also means add?
What is the phrase associated with subtraction?
What is the phrase associated with subtraction?
What words are associated with multiplication?
What words are associated with multiplication?
What words are associated with division?
What words are associated with division?
Translate the verbal expression 'm increased by 5' into an algebraic expression.
Translate the verbal expression 'm increased by 5' into an algebraic expression.
Translate '7 less than a number' into an algebraic expression.
Translate '7 less than a number' into an algebraic expression.
Translate 'the product of 5 and a' into an algebraic expression.
Translate 'the product of 5 and a' into an algebraic expression.
Translate 'the quotient of x and y' into an algebraic expression.
Translate 'the quotient of x and y' into an algebraic expression.
Translate '6 times the sum of 10 and b' into an algebraic expression.
Translate '6 times the sum of 10 and b' into an algebraic expression.
Translate '(3 + b) divided by y' into an algebraic expression.
Translate '(3 + b) divided by y' into an algebraic expression.
Translate '9 times t' into an algebraic expression.
Translate '9 times t' into an algebraic expression.
Translate '5 times y plus 10 times x' into an algebraic expression.
Translate '5 times y plus 10 times x' into an algebraic expression.
Translate 'the quantity of 15 and n times 2' into an algebraic expression.
Translate 'the quantity of 15 and n times 2' into an algebraic expression.
Translate 's subtracted from 8 times r' into an algebraic expression.
Translate 's subtracted from 8 times r' into an algebraic expression.
Positive times a negative equals _____
Positive times a negative equals _____
Positive times a positive equals _____
Positive times a positive equals _____
Negative times a negative equals _____
Negative times a negative equals _____
What does the term 'domain' refer to?
What does the term 'domain' refer to?
What does the term 'range' refer to?
What does the term 'range' refer to?
What is a relation in mathematics?
What is a relation in mathematics?
What are four ways to represent relations?
What are four ways to represent relations?
A function assigns exactly one output value for each input value.
A function assigns exactly one output value for each input value.
What is an independent variable?
What is an independent variable?
What is a dependent variable?
What is a dependent variable?
What is a function rule?
What is a function rule?
What does the addition property state?
What does the addition property state?
What does the multiplication property state?
What does the multiplication property state?
What does the subtraction property state?
What does the subtraction property state?
What does the division property state?
What does the division property state?
Properties of equality are used _____ when isolating the variable.
Properties of equality are used _____ when isolating the variable.
When solving equations with variables on both sides, _____
When solving equations with variables on both sides, _____
What signifies infinitely many solutions in equations?
What signifies infinitely many solutions in equations?
What indicates no solution in equations?
What indicates no solution in equations?
What is a ratio?
What is a ratio?
Translate '2:3' into simplest form for the ratio '32:48'.
Translate '2:3' into simplest form for the ratio '32:48'.
Translate '1:3' into simplest form for the ratio '5:15'.
Translate '1:3' into simplest form for the ratio '5:15'.
What is a proportion?
What is a proportion?
What should you do when solving a proportion?
What should you do when solving a proportion?
How do you calculate the final price after a discount?
How do you calculate the final price after a discount?
How do you calculate the final price after tax?
How do you calculate the final price after tax?
What is the equation used to find percentage of change?
What is the equation used to find percentage of change?
What are variables for finding consecutive integers?
What are variables for finding consecutive integers?
What are variables for finding consecutive even or odd integers?
What are variables for finding consecutive even or odd integers?
What are the headings for mixture problems?
What are the headings for mixture problems?
What are the headings for mixture problems involving percentages?
What are the headings for mixture problems involving percentages?
What are the headings for mixture problems involving interest?
What are the headings for mixture problems involving interest?
What equation governs motion problems?
What equation governs motion problems?
What are three types of motion word problems?
What are three types of motion word problems?
What are the headers for work word problems?
What are the headers for work word problems?
Is fewer than means _____
Is fewer than means _____
Is more than means _____
Is more than means _____
What phrases mean less than or equal to?
What phrases mean less than or equal to?
What phrases mean greater than or equal to?
What phrases mean greater than or equal to?
What should you do when solving a proportion with an inequality symbol?
What should you do when solving a proportion with an inequality symbol?
What does {x|x>y} signify?
What does {x|x>y} signify?
What does a compound inequality involve?
What does a compound inequality involve?
What does disjunction represent?
What does disjunction represent?
What does conjunction represent?
What does conjunction represent?
When multiplying or dividing by a negative number, you must _____
When multiplying or dividing by a negative number, you must _____
The absolute value can be equal to a negative number.
The absolute value can be equal to a negative number.
What kind of compound inequality is associated with the less than symbol?
What kind of compound inequality is associated with the less than symbol?
What kind of compound inequality is associated with the greater than symbol?
What kind of compound inequality is associated with the greater than symbol?
What is an extraneous solution?
What is an extraneous solution?
What do you do when performing unit conversions?
What do you do when performing unit conversions?
What does f(x) represent?
What does f(x) represent?
What does the y value represent in functions?
What does the y value represent in functions?
What is a discrete function?
What is a discrete function?
What is a continuous function?
What is a continuous function?
What is the median?
What is the median?
What is the mean?
What is the mean?
What is the mode?
What is the mode?
How do you find the median?
How do you find the median?
Flashcards
Natural Numbers (N)
Natural Numbers (N)
All positive whole numbers, excluding zero. (e.g., 1, 2, 3, ...)
Whole Numbers (W)
Whole Numbers (W)
All positive whole numbers, including zero. (e.g., 0, 1, 2, 3, ...)
Integers (Z)
Integers (Z)
All positive and negative whole numbers, including zero. (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...)
Rational Numbers (Q)
Rational Numbers (Q)
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Irrational Numbers (I)
Irrational Numbers (I)
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Imaginary Numbers
Imaginary Numbers
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Element Of
Element Of
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Union
Union
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Intersection
Intersection
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Subset
Subset
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Null Set
Null Set
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Identity (+)
Identity (+)
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Identity (×)
Identity (×)
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Property of 0
Property of 0
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Substitution Property
Substitution Property
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Reflexive Property
Reflexive Property
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Symmetric Property
Symmetric Property
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Transitive Property
Transitive Property
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Inverse (+)
Inverse (+)
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Inverse (×)
Inverse (×)
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Definition of Subtraction
Definition of Subtraction
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Distributive Property
Distributive Property
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Commutative Property
Commutative Property
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Associative Property
Associative Property
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Consecutive Integers
Consecutive Integers
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Consecutive Odd/Even Integers
Consecutive Odd/Even Integers
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Inequality
Inequality
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Proportion
Proportion
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Cross Multiplication
Cross Multiplication
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Function
Function
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Independent Variable
Independent Variable
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Dependent Variable
Dependent Variable
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Mean
Mean
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Median
Median
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Mode
Mode
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Study Notes
Number Sets
- Natural Numbers (N): All positive numbers, excluding 0 (e.g., 1, 2, 3).
- Whole Numbers (W): All positive numbers, including 0 (e.g., 0, 1, 2).
- Integers (Z): All positive and negative whole numbers (e.g., -1, 0, 1).
- Rational Numbers (Q): Numbers that can be expressed as a quotient of two integers (e.g., 1/2, 2.4, 5).
- Irrational Numbers (I): Numbers that cannot be expressed as fractions, involving roots of non-perfect squares or π.
- Imaginary Numbers: Numbers resulting from the square root of a negative number.
Set Operations
- Element Of: Describes a member of a set.
- Union: Combines two sets, including all elements from both.
- Intersection: Includes only the elements common to both sets.
- Subset: Every element in the subset is also in another set.
- Null Set: A set with no elements.
Algebraic Properties
- Identity (+): Adding 0 to any number leaves it unchanged.
- Identity (×): Multiplying any number by 1 leaves it unchanged.
- Property of 0: Multiplying any number by 0 results in 0.
- Substitution: A number can be replaced by another in an equation.
- Reflexive Property: An equation is equal to itself.
- Symmetric Property: If a = b, then b = a.
- Transitive Property: If a = b and b = c, then a = c.
- Inverse (+): A number plus its additive inverse equals 0.
- Inverse (×): A number times its reciprocal equals 1.
Operations and Properties
- Definition of Subtraction: Subtraction can be viewed as adding a negative.
- Distributive Property: Distributing terms in parentheses to each other.
- Commutative Property: The order of numbers does not affect the sum or product.
- Associative Property: Grouping of numbers in addition or multiplication does not change the result.
Algebraic Expressions
- Understanding how to translate verbal expressions into algebraic forms and vice versa.
- Consecutive Integers: Identified using expressions like x, x+1, etc.
- Consecutive Odd/Even Integers: Expressed as x, x+2, x+4, etc.
Inequalities and Proportions
- Inequalities can be expressed in various ways, such as "is less than" or "is more than."
- Proportion: An equation that states that two ratios are equal.
- Cross Multiplication: A method used to solve proportions.
Function Basics
- Function: A relation assigning exactly one output for each input.
- Independent Variable: The variable that is changed or controlled in an experiment.
- Dependent Variable: The variable that is measured or affected.
- Function Notation: Typically written as f(x), indicating the output value when x is substituted.
Statistical Concepts
- Mean: The average of a set of numbers.
- Median: The middle value in a sorted list of numbers.
- Mode: The most frequently occurring number in a dataset.
Special Concepts
- Extraneous Solution: A solution derived from the equation that does not satisfy the original context.
- Continuous Function: A function where every value between two points is included.
- Discrete Function: A function where only specific points are defined and values in between do not apply.
Problem-Solving Techniques
- Employ properties of equality for solving equations with variables.
- The method of unit conversions requires careful attention to labels to maintain consistency in answers.
These notes combine definitions, properties, and explanations of fundamental concepts in algebra to aid in review and understanding.
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Description
Prepare for your Honors Algebra 1 final exam with this comprehensive review of key concepts from the first semester. This quiz covers essential definitions such as natural numbers, whole numbers, integers, and rational numbers, providing you with a solid foundation in number types. Test your knowledge and ensure you're ready for the exam!