Grade 8 Mathematics - Inequality and Variables
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Questions and Answers

What defines the overlap in a system of linear inequalities?

  • The area with no inequality solutions
  • The overlapping shaded region representing all solutions (correct)
  • The region outside all inequalities
  • The union of all shaded regions

    • Which of the following statements is true about ordered pairs in linear inequalities?

  • An ordered pair is a solution if it satisfies the inequality. (correct)
  • An ordered pair can only be a solution if the statement is an equation.
  • An ordered pair cannot be a solution if both values are positive.
  • An ordered pair must contain integers to be a solution.

    • What should you do first to solve a problem involving linear inequalities?

  • Assume values for x and y.
  • Graph the inequalities directly without calculations.
  • Translate the problem into a mathematical inequality. (correct)
  • Eliminate one of the variables algebraically.

    • How can relations be classified based on their mappings?

    <p>By the relationship between x-values and y-values.</p> Signup and view all the answers

    What is the domain in a relation?

    <p>The set of all x-values.</p> Signup and view all the answers

    What is described as the value that is determined by one or more other variables?

    <p>Dependent variable</p> Signup and view all the answers

    Which term describes a relationship where one element in the domain corresponds to multiple elements in the range?

    <p>One-to-many</p> Signup and view all the answers

    In a function, what is the set of all possible input values called?

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

    What describes the variable that influences the dependent variable in an equation?

    <p>Independent variable</p> Signup and view all the answers

    Which relationship is characterized by multiple elements in the domain corresponding to multiple elements in the range?

    <p>Many-to-many</p> Signup and view all the answers

    What is the term for when one student can take many subjects?

    <p>One-to-many</p> Signup and view all the answers

    In a functional relationship, the outcome is based on what kind of variable?

    <p>Dependent variable</p> Signup and view all the answers

    What type of relationship has multiple elements in the domain corresponding to a single element in the range?

    <p>Many-to-one</p> Signup and view all the answers

    Which symbol is NOT used in mathematical inequalities?

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

    What type of line is used to graph the inequality $y < 2x + 3$?

    <p>Dashed line</p> Signup and view all the answers

    In the process of graphing a linear inequality, which step follows graphing the boundary line?

    <p>Test points to determine which half-plane to shade</p> Signup and view all the answers

    Which of the following correctly represents a linear inequality?

    <p>3y - 2 &lt; 5</p> Signup and view all the answers

    What is the purpose of using a solid line when graphing inequalities?

    <p>It shows the range of solutions includes the boundary</p> Signup and view all the answers

    What must be done first when solving a linear inequality?

    <p>State the problem</p> Signup and view all the answers

    Which characteristic is different between linear equations and linear inequalities?

    <p>Use of equality and inequality symbols</p> Signup and view all the answers

    When graphing the linear inequality $y ≥ 3x - 2$, what should be done with the boundary line?

    <p>It should be a solid line</p> Signup and view all the answers

    What is a linear function represented by?

    <p>f(x) = mx + b</p> Signup and view all the answers

    What does the 'm' in the linear equation f(x) = mx + b represent?

    <p>The slope</p> Signup and view all the answers

    Which of the following methods can represent a relation?

    <p>Mapping diagram</p> Signup and view all the answers

    What is the first step in applying linear functions to word problems?

    <p>Identify given information</p> Signup and view all the answers

    What does the vertical line test determine about a graph?

    <p>If it's a linear function</p> Signup and view all the answers

    Which of the following accurately describes the y-intercept in a linear function?

    <p>The value of y when x=0</p> Signup and view all the answers

    What is the purpose of creating a table of values in a linear function?

    <p>To list pairs of x and y values</p> Signup and view all the answers

    Which of the following is NOT a method for representing a relation?

    <p>Schematic diagram</p> Signup and view all the answers

    What is a conditional statement typically structured as?

    <p>An 'if-then' statement</p> Signup and view all the answers

    How can two premises A and B lead to a conclusion C?

    <p>If A=B and B=C, then A=C</p> Signup and view all the answers

    What does the inverse of a conditional statement involve?

    <p>Negating both the hypothesis and conclusion</p> Signup and view all the answers

    Which statement is accepted as true without proof?

    <p>An axiom</p> Signup and view all the answers

    What is a theorem?

    <p>A statement proven deductively</p> Signup and view all the answers

    What part of a conditional statement is represented by the hypothesis?

    <p>The 'if' part</p> Signup and view all the answers

    Which of the following best describes a proof?

    <p>A logical argument supported by given information</p> Signup and view all the answers

    What is the formal structure of the inverse of 'if p, then q'?

    <p>not p implies not q</p> Signup and view all the answers

    What is the contrapositive of the statement 'if p, then q'?

    <p>if not q, then not p</p> Signup and view all the answers

    Which of the following best describes inductive reasoning?

    <p>Drawing conclusions from specific instances</p> Signup and view all the answers

    Which proof format involves writing statements and justifications in two separate columns?

    <p>Two-column proof</p> Signup and view all the answers

    What is the definition of a direct proof?

    <p>A proof consisting of statements justified by previous information</p> Signup and view all the answers

    What is the converse of the statement 'if p, then q'?

    <p>if q, then p</p> Signup and view all the answers

    What does deductive reasoning primarily rely on?

    <p>Established facts and laws</p> Signup and view all the answers

    In indirect proof, what is the general approach taken?

    <p>Assuming the negation of the conclusion and proving it leads to a contradiction</p> Signup and view all the answers

    Which reasoning method uses specific examples to reach a general conclusion?

    <p>Inductive reasoning</p> Signup and view all the answers

    Study Notes

    Grade 8 Mathematics - Inequality

    • Inequality is a statement where one expression is not equal to another
    • Inequality symbols include ≤, ≥, ≠
    • Equation uses the = symbol
    • Linear inequalities can be written as Ax + By < C, Ax + By > C, Ax + By ≤ C, Ax + By ≥ C, where A, B, and C are real numbers and A and B are not both zero.
    • In graphing a linear inequality: replace the inequality symbol with an equals sign to find the boundary line, graph the boundary line (solid line for ≤ or ≥, dashed line for < or >), and test points in each half-plane to determine which satisfies the inequality. Shade the half-plane containing the points that satisfy the inequality.
    • A system of linear inequalities is a group of linear inequalities solved simultaneously.

    Grade 8 Mathematics - Variables

    • Variables can be independent or dependent
    • A dependent variable's value is determined by other variables.
    • An independent variable's value is not affected by other variables.
    • A function's domain is the set of possible input values (x-values), and its range is the set of possible output values (y-values).
    • Linear functions are of the form f(x) = mx + b, where m is the slope and b is the y-intercept.

    Grade 8 Mathematics - Representation

    • Relations can be represented using tables, mapping diagrams, and graphs.
    • A table of values lists pairs of x and y values satisfying an equation.
    • Mapping diagrams visually represent relations connecting paired elements.
    • A graph visually represents the relationship between x and y values using points and lines.

    Grade 8 Mathematics - Conditional Statements

    • Conditional statements can be expressed as "if-then" statements.
    • The subject of the sentence is the hypothesis (the "if" part), and the predicate is the conclusion (the "then" part).
    • The inverse of a conditional statement negates both the hypothesis and conclusion.
    • The contrapositive switches and negates both the hypothesis and conclusion.
    • The converse switches the hypothesis and conclusion.

    Grade 8 Mathematics - Reasoning

    • Inductive reasoning uses specific examples to reach a general rule.
    • Deductive reasoning uses facts, properties, and laws to reach a conclusion.
    • A syllogism is a form of deductive reasoning where two premises lead to a conclusion.
    • Proofs are logical arguments supporting a statement. Direct proofs are a series of statements justified by previous statements. Indirect proofs work by assuming the opposite to arrive at a contradiction.

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    Grade 8 Mathematics Inequality PDF

    Description

    This quiz covers key concepts in Grade 8 Mathematics related to inequalities and variables. It includes definitions, symbols, and graphing techniques for linear inequalities, as well as the distinctions between independent and dependent variables. Test your understanding of these important mathematical principles.

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