Honors Algebra 1 Final Review
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Questions and Answers

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?

  • Natural numbers (N)
  • Rational numbers (Q)
  • Integers (Z)
  • Whole numbers (W) (correct)

    • 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?

    <p>Rational numbers (Q)</p> Signup and view all the answers

    What are irrational numbers?

    <p>Any number with pi or the square root of a non-perfect number.</p> Signup and view all the answers

    What is an imaginary number?

    <p>Any equation where the negative is inside the square root sign.</p> Signup and view all the answers

    What does 'element of' mean?

    <p>Member of a set.</p> Signup and view all the answers

    Union sets together combine two sets.

    <p>True</p> Signup and view all the answers

    Intersection includes numbers not found in either of the combined sets.

    <p>False</p> Signup and view all the answers

    What is a subset?

    <p>Every number in this set is also a number in another set.</p> Signup and view all the answers

    What makes up the real number system?

    <p>Rational numbers, natural numbers, whole numbers, integers, and irrational numbers.</p> Signup and view all the answers

    What does a null set imply?

    <p>No numbers in this set.</p> Signup and view all the answers

    What is the identity property for addition?

    <p>Any number plus 0 equals that number</p> Signup and view all the answers

    What is the property of 0 in multiplication?

    <p>Any number times 0 equals 0</p> Signup and view all the answers

    What does substitution mean in mathematics?

    <p>Any number can be replaced by another number.</p> Signup and view all the answers

    What is the reflexive property?

    <p>Both sides of the equation mirror each other.</p> Signup and view all the answers

    What is the symmetric property?

    <p>If a = b, then b = a</p> Signup and view all the answers

    What does transitive property mean?

    <p>If a = b, and b = c, then a = c.</p> Signup and view all the answers

    What is an inverse in multiplication?

    <p>Any number times its reciprocal equals 1.</p> Signup and view all the answers

    What does the definition of subtraction suggest?

    <p>Subtraction can be changed to adding a negative</p> Signup and view all the answers

    What does the distributive property involve?

    <p>Distributing everything outside parentheses to terms inside</p> Signup and view all the answers

    The requirements for simplest form are that _____

    <p>all like terms are combined and all parentheses have been removed.</p> Signup and view all the answers

    Which of the following phrases also means add?

    <p>Plus, sum</p> Signup and view all the answers

    What is the phrase associated with subtraction?

    <p>Minus, difference</p> Signup and view all the answers

    What words are associated with multiplication?

    <p>Times, product</p> Signup and view all the answers

    What words are associated with division?

    <p>Quotient, half</p> Signup and view all the answers

    Translate the verbal expression 'm increased by 5' into an algebraic expression.

    <p>m + 5</p> Signup and view all the answers

    Translate '7 less than a number' into an algebraic expression.

    <p>x - 7</p> Signup and view all the answers

    Translate 'the product of 5 and a' into an algebraic expression.

    <p>5a</p> Signup and view all the answers

    Translate 'the quotient of x and y' into an algebraic expression.

    <p>x/y</p> Signup and view all the answers

    Translate '6 times the sum of 10 and b' into an algebraic expression.

    <p>6(10 + b)</p> Signup and view all the answers

    Translate '(3 + b) divided by y' into an algebraic expression.

    <p>(3 + b)/y</p> Signup and view all the answers

    Translate '9 times t' into an algebraic expression.

    <p>9t</p> Signup and view all the answers

    Translate '5 times y plus 10 times x' into an algebraic expression.

    <p>5y + 10x</p> Signup and view all the answers

    Translate 'the quantity of 15 and n times 2' into an algebraic expression.

    <p>2(15 + n)</p> Signup and view all the answers

    Translate 's subtracted from 8 times r' into an algebraic expression.

    <p>8r - s</p> Signup and view all the answers

    Positive times a negative equals _____

    <p>a negative.</p> Signup and view all the answers

    Positive times a positive equals _____

    <p>a positive.</p> Signup and view all the answers

    Negative times a negative equals _____

    <p>a positive.</p> Signup and view all the answers

    What does the term 'domain' refer to?

    <p>Another word for x values.</p> Signup and view all the answers

    What does the term 'range' refer to?

    <p>Another word for y values.</p> Signup and view all the answers

    What is a relation in mathematics?

    <p>A set of ordered pairs.</p> Signup and view all the answers

    What are four ways to represent relations?

    <p>Order pairs, table, mapping, graphs</p> Signup and view all the answers

    A function assigns exactly one output value for each input value.

    <p>True</p> Signup and view all the answers

    What is an independent variable?

    <p>The thing being changed.</p> Signup and view all the answers

    What is a dependent variable?

    <p>The thing being measured.</p> Signup and view all the answers

    What is a function rule?

    <p>Equation that describes the function relationship.</p> Signup and view all the answers

    What does the addition property state?

    <p>If a = b, then a + c = b + c</p> Signup and view all the answers

    What does the multiplication property state?

    <p>If a = b, then a c = b c</p> Signup and view all the answers

    What does the subtraction property state?

    <p>If a = b, then a - c = b - c</p> Signup and view all the answers

    What does the division property state?

    <p>If a = b, then a / c = b / c, c cannot equal 0</p> Signup and view all the answers

    Properties of equality are used _____ when isolating the variable.

    <p>to maintain balance in an equation.</p> Signup and view all the answers

    When solving equations with variables on both sides, _____

    <p>move the variable first.</p> Signup and view all the answers

    What signifies infinitely many solutions in equations?

    <p>Variables fall out and leave you with a true statement (like x = x).</p> Signup and view all the answers

    What indicates no solution in equations?

    <p>Variables fall out and leave you with a false statement (like x = y).</p> Signup and view all the answers

    What is a ratio?

    <p>A comparison of two numbers by division.</p> Signup and view all the answers

    Translate '2:3' into simplest form for the ratio '32:48'.

    <p>1:1.5</p> Signup and view all the answers

    Translate '1:3' into simplest form for the ratio '5:15'.

    <p>1:3</p> Signup and view all the answers

    What is a proportion?

    <p>An equation where two ratios are equal.</p> Signup and view all the answers

    What should you do when solving a proportion?

    <p>Cross multiply.</p> Signup and view all the answers

    How do you calculate the final price after a discount?

    <p>Multiply the percentage decimal by the original price and subtract that from the original price.</p> Signup and view all the answers

    How do you calculate the final price after tax?

    <p>Multiply the percentage decimal by the original price and add that to the original price.</p> Signup and view all the answers

    What is the equation used to find percentage of change?

    <p>percent of change/100 = new - original/original.</p> Signup and view all the answers

    What are variables for finding consecutive integers?

    <p>x, x + 1, x + 2, etc.</p> Signup and view all the answers

    What are variables for finding consecutive even or odd integers?

    <p>x, x + 2, x + 4, etc.</p> Signup and view all the answers

    What are the headings for mixture problems?

    <p>What, cost per item, quantity, total value</p> Signup and view all the answers

    What are the headings for mixture problems involving percentages?

    <p>What, percentage, quantity, total value</p> Signup and view all the answers

    What are the headings for mixture problems involving interest?

    <p>What, amount invested, rate, interest</p> Signup and view all the answers

    What equation governs motion problems?

    <p>Rate × Time = Distance.</p> Signup and view all the answers

    What are three types of motion word problems?

    <p>Opposite direction, round trip, leaving later</p> Signup and view all the answers

    What are the headers for work word problems?

    <p>Who, rate, time, work</p> Signup and view all the answers

    Is fewer than means _____

    <p>less than.</p> Signup and view all the answers

    Is more than means _____

    <p>greater than.</p> Signup and view all the answers

    What phrases mean less than or equal to?

    <p>At most, no more than</p> Signup and view all the answers

    What phrases mean greater than or equal to?

    <p>At least, no greater than</p> Signup and view all the answers

    What should you do when solving a proportion with an inequality symbol?

    <p>You don't cross multiply; you clear the fractions.</p> Signup and view all the answers

    What does {x|x>y} signify?

    <p>Example of set notation.</p> Signup and view all the answers

    What does a compound inequality involve?

    <p>Two inequalities connected by and/or.</p> Signup and view all the answers

    What does disjunction represent?

    <p>All of them together</p> Signup and view all the answers

    What does conjunction represent?

    <p>Intersection with 'and'</p> Signup and view all the answers

    When multiplying or dividing by a negative number, you must _____

    <p>flip the inequality symbol.</p> Signup and view all the answers

    The absolute value can be equal to a negative number.

    <p>False</p> Signup and view all the answers

    What kind of compound inequality is associated with the less than symbol?

    <p>Conjunction</p> Signup and view all the answers

    What kind of compound inequality is associated with the greater than symbol?

    <p>Disjunction</p> Signup and view all the answers

    What is an extraneous solution?

    <p>Solution to the equation that does not satisfy the original equation.</p> Signup and view all the answers

    What do you do when performing unit conversions?

    <p>Eliminate all labels other than the ones you are using in your final answer through cross simplification.</p> Signup and view all the answers

    What does f(x) represent?

    <p>Example of function notation.</p> Signup and view all the answers

    What does the y value represent in functions?

    <p>What does f(x) really mean?</p> Signup and view all the answers

    What is a discrete function?

    <p>Function where numbers in between points don't work</p> Signup and view all the answers

    What is a continuous function?

    <p>Function where everything in between the two points works</p> Signup and view all the answers

    What is the median?

    <p>Middle number.</p> Signup and view all the answers

    What is the mean?

    <p>Average.</p> Signup and view all the answers

    What is the mode?

    <p>Most common number.</p> Signup and view all the answers

    How do you find the median?

    <p>Line your numbers up in numerical order and find the middle number.</p> Signup and view all the answers

    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!

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