Algebra Concepts and Functions
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Questions and Answers

What is the slope-intercept equation?

  • y = mx + b (correct)
  • y = x + b
  • y = mx - b
  • y = m + b

    • What is a perfect square?

    The answer when you multiply a number by itself.

    What does the inequality symbol represent?

    A greater than or less than symbol.

    What is a constant?

    <p>A value that does not change.</p> Signup and view all the answers

    What does it mean to intersect in a system of equations?

    <p>The solutions represent where the lines intersect.</p> Signup and view all the answers

    What is a square root?

    <p>The number that, when multiplied by itself, gives you the original product.</p> Signup and view all the answers

    What does a vertical line test determine?

    <p>If a relation is a function.</p> Signup and view all the answers

    What does the term 'inverse' refer to?

    <p>Operations that undo each other.</p> Signup and view all the answers

    How many equations are in a system of equations?

    <p>Two or more.</p> Signup and view all the answers

    What does a negative exponent indicate?

    <p>To take the reciprocal.</p> Signup and view all the answers

    What does a closed circle on a number line indicate?

    <p>It is equal to.</p> Signup and view all the answers

    What does the 'F' in the FOIL method stand for?

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

    What is a variable?

    <p>A letter that represents an unknown number.</p> Signup and view all the answers

    What does the numerator represent in a fractional exponent?

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

    What is an identity in an equation?

    <p>An equation that is true for every possible value of the variable.</p> Signup and view all the answers

    What does an equation contain?

    <p>An equals sign.</p> Signup and view all the answers

    What are the solutions of the first equation compared to the second in a system of equations?

    <p>The same.</p> Signup and view all the answers

    What do you do with exponents when you have one outside the parentheses and another inside?

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

    What does 'no solution' mean in an equation?

    <p>When you eliminate the variable and what remains is not true.</p> Signup and view all the answers

    What is the inverse of addition?

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

    What indicates the steepness of a line?

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

    What is the hypotenuse?

    <p>The side across from the right angle in a right triangle.</p> Signup and view all the answers

    What shows the solution in a system of inequalities?

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

    What is a solution in an equation?

    <p>Makes an equation true.</p> Signup and view all the answers

    What is the y-intercept?

    <p>The point where the line crosses the y-axis.</p> Signup and view all the answers

    What is scientific notation?

    <p>The product of two numbers, one greater than or equal to one but less than ten, the other a power of ten.</p> Signup and view all the answers

    What defines a function?

    <p>For every x value, there is only one y value.</p> Signup and view all the answers

    What is a monomial?

    <p>One term.</p> Signup and view all the answers

    What is an expression?

    <p>A mathematical phrase that does not contain an equals sign.</p> Signup and view all the answers

    What type of slope does a line going uphill have?

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

    What is a reciprocal?

    <p>A fraction inverted (flipped upside down).</p> Signup and view all the answers

    What type of line is used when graphing a linear inequality that is not equal to?

    <p>Dotted line.</p> Signup and view all the answers

    How many solutions does an identity have?

    <p>Infinitely many.</p> Signup and view all the answers

    What is elimination in systems of equations?

    <p>Creating opposites.</p> Signup and view all the answers

    What is substitution in systems of equations?

    <p>The other method of solving a system of equations.</p> Signup and view all the answers

    What is a factor?

    <p>A number involved in multiplications.</p> Signup and view all the answers

    What is any number with an exponent of zero equal to?

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

    What does the 'O' in the FOIL method stand for?

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

    What is a polynomial?

    <p>One or more terms connected by + or -.</p> Signup and view all the answers

    What does 'M' represent in the equation y = mx + b?

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

    What does an open circle on a number line indicate?

    <p>If it is not equal to.</p> Signup and view all the answers

    What is the slope of a horizontal line?

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

    What is the slope of a vertical line?

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

    What is a right triangle?

    <p>A triangle with one 90 degree angle.</p> Signup and view all the answers

    What does the denominator represent in a fractional exponent?

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

    What does the distributive property state?

    <p>Multiply the term outside the parentheses by each term inside the parentheses.</p> Signup and view all the answers

    What is the greatest common factor?

    <p>The largest number that will divide evenly into a group of numbers.</p> Signup and view all the answers

    What does '<' represent?

    <p>Less than or equal to.</p> Signup and view all the answers

    What does '>' represent?

    <p>Greater than or equal to.</p> Signup and view all the answers

    What does parallel lines mean?

    <p>Lines that never intersect.</p> Signup and view all the answers

    What is the formula for rise/run used for?

    <p>To calculate slope.</p> Signup and view all the answers

    What do you do with exponents when multiplying the same base?

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

    What does an exponent tell you?

    <p>How many factors of the base.</p> Signup and view all the answers

    What is a coefficient?

    <p>A number attached to a variable by multiplication.</p> Signup and view all the answers

    What does the 'L' in the FOIL method stand for?

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

    What does a solid line indicate when graphing a linear inequality?

    <p>If it is equal to.</p> Signup and view all the answers

    What does '>' represent as a symbol?

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

    What does '<' represent as a symbol?

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

    What is the point-slope equation?

    <p>y - y1 = m(x - x1).</p> Signup and view all the answers

    What is the Pythagorean theorem?

    <p>c^2 = a^2 + b^2.</p> Signup and view all the answers

    What do you do with exponents when dividing the same base?

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

    What is division in relation to multiplication?

    <p>The inverse of multiplication.</p> Signup and view all the answers

    What is the least common multiple?

    <p>The smallest number that is a multiple of two or more numbers.</p> Signup and view all the answers

    What is a trinomial?

    <p>Three terms connected by + or -.</p> Signup and view all the answers

    What is a binomial?

    <p>Two terms connected by + or -.</p> Signup and view all the answers

    What does 'Inside' refer to in the FOIL method?

    <p>It stands for multiplying the inside terms of two binomials.</p> Signup and view all the answers

    Study Notes

    Algebra Concepts

    • Slope Intercept Equation: Defined by the formula (y = mx + b), where (m) is the slope and (b) is the y-intercept.
    • Perfect Square: Result from multiplying a number by itself.
    • Inequality Symbol: Indicates greater than (>) or less than (<).
    • Constant: A value that remains unchanged.
    • Intersect: Point where lines meet in the context of a system of equations.

    Mathematical Functions and Terms

    • Square Root: The number that, when multiplied by itself, yields a given product.
    • Vertical Line Test: A method to determine if a relation qualifies as a function by checking if any vertical line intersects the graph at more than one point.
    • Inverse Operations: Operations that cancel each other out (e.g., addition and subtraction).
    • System of Equations: Composed of two or more equations to solve simultaneously.
    • Negative Exponent: Indicates the reciprocal of the base raised to the corresponding positive exponent.

    Graphing Inequalities

    • Closed Circle: Used in graphing when an inequality includes equality (≥ or ≤).
    • Dotted Line: Represents inequalities that exclude equality ( (> ) or (<)).
    • Solid Line: Indicates that the inequality includes equality in graphing.

    Problem Solving Techniques

    • FOIL Method: Acronym for First, Outside, Inside, Last; a technique for multiplying two binomials.
    • Solutions: Values that satisfy an equation.
    • Elimination and Substitution: Two primary methods for solving systems of equations.

    Types of Numbers and Operations

    • Monomial: A single term expression.
    • Polynomial: Composed of one or more terms, connected by addition or subtraction.
    • Coefficient: A number that multiplies a variable.
    • Reciprocal: An inverted form of a fraction.
    • Exponent: Indicates the number of times a base is multiplied by itself.

    Lines and Angles

    • Slope: Measures the steepness of a line; calculated as rise over run.
    • Y-intercept: The point where a line crosses the y-axis.
    • Hypotenuse: The longest side of a right triangle, opposite the right angle.
    • Zero and Undefined Slopes: Zero slope refers to horizontal lines; undefined slope refers to vertical lines.

    Algebraic Identities and Properties

    • Identity: Equations that hold true for every possible variable value.
    • Greatest Common Factor (GCF): The largest number that divides a set of numbers evenly.
    • Least Common Multiple (LCM): The smallest number that is a multiple of given numbers.

    Additional Concepts

    • Rise/Run: Provides a way to calculate slope based on vertical and horizontal movement between two points.
    • Trinomial and Binomial: A trinomial has three terms, while a binomial has two, both connected by addition or subtraction.
    • Pythagorean Theorem: Relates the sides of a right triangle through the formula (c^2 = a^2 + b^2).

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    Description

    Test your knowledge on various algebra concepts including slope-intercept equations, perfect squares, and functions. This quiz will cover key terms and operations that are essential for mastering algebra. Challenge yourself with problems related to systems of equations and inverse operations.

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