Mathematics Concepts and Formulas Quiz
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Questions and Answers

What is the absolute value?

The distance a number is from zero on a number line.

What is the absolute value function in regression?

f(x)=|x|

What shape does the graph of an absolute value function take?

V shape

What is the formula for the area of a square?

<p>A=s²</p> Signup and view all the answers

What is the formula for the area of a rectangle?

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

What is the formula for the area of a triangle?

<p>A=1/2 bh</p> Signup and view all the answers

What is an arithmetic sequence?

<p>A sequence in which the difference between any two consecutive terms is the same.</p> Signup and view all the answers

What is the axis of symmetry?

<p>A line that divides a plane figure or a graph into two congruent reflected halves.</p> Signup and view all the answers

What is a binomial?

<p>A polynomial with two terms.</p> Signup and view all the answers

What does a box plot represent?

<p>Data is shown using the median and range of a data set.</p> Signup and view all the answers

What is causation?

<p>A cause and effect relationship in which one variable controls the changes in another variable.</p> Signup and view all the answers

What is a coefficient?

<p>A number multiplied by a variable in an algebraic expression.</p> Signup and view all the answers

What does completing the square mean?

<p>A process used to make a quadratic expression into a perfect square trinomial.</p> Signup and view all the answers

What is compound interest?

<p>Interest paid on interest previously earned.</p> Signup and view all the answers

What are consecutive integers?

<p>Integers in counting order, such as 4, 5, 6.</p> Signup and view all the answers

What are consecutive even integers?

<p>Even numbers that follow each other on a number line.</p> Signup and view all the answers

What are consecutive odd integers?

<p>Odd numbers that follow each other on a number line.</p> Signup and view all the answers

What is a constant?

<p>A term without a variable.</p> Signup and view all the answers

What is correlation?

<p>A measure of the relationship between two variables.</p> Signup and view all the answers

What is the correlation coefficient?

<p>Statistical measures of the degree of association between two variables.</p> Signup and view all the answers

What is the cubic function?

<p>f(x)=x^3</p> Signup and view all the answers

What is the cube root function?

<p>f(x)=3√x</p> Signup and view all the answers

What is the degree of a polynomial?

<p>The greatest degree of any term in the polynomial.</p> Signup and view all the answers

What is a dependent variable?

<p>A variable whose value depends on that of another.</p> Signup and view all the answers

What is direct variation?

<p>The relationship between two variable quantities that have a constant ratio.</p> Signup and view all the answers

What is the discriminant?

<p>A function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial.</p> Signup and view all the answers

What is the domain of a function?

<p>All the possible x-values of a function.</p> Signup and view all the answers

What is a dot plot?

<p>A graphical display of data using dots.</p> Signup and view all the answers

What is an equation?

<p>A mathematical sentence that contains an equals sign.</p> Signup and view all the answers

What does 'equivalent to' mean?

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

What is an explicit formula?

<p>Describes the nth term of a sequence using the number n.</p> Signup and view all the answers

What is an exponential function?

<p>A function of the form f(x) = ab^x, where a and b are real numbers with a ≠ 0, b&gt;0, and b ≠ 1.</p> Signup and view all the answers

What is the exponential graph formula?

<p>y=a(b)^x</p> Signup and view all the answers

What is the exponential growth function formula?

<p>y = a(1 + r)^t, where a &gt;0.</p> Signup and view all the answers

What is the exponential decay function formula?

<p>y = a(1- r)^t, where a &gt;0.</p> Signup and view all the answers

What is an expression in mathematical terms?

<p>A mathematical phrase that contains operations, numbers, and/or variables.</p> Signup and view all the answers

What is factoring?

<p>To express a polynomial as the product of monomials and polynomials.</p> Signup and view all the answers

What is a geometric sequence?

<p>There is a pattern in which you multiply or divide by a common number.</p> Signup and view all the answers

What is the greatest common factor (GCF)?

<p>The largest factor that two or more numbers have in common.</p> Signup and view all the answers

What is a histogram?

<p>Used when data is continuous; the bars touch each other.</p> Signup and view all the answers

What is an independent variable?

<p>A variable whose variation does not depend on that of another.</p> Signup and view all the answers

What are inequalities?

<p>Algebraic statements that have ≠, &lt;, ≤, or ≥ as their symbols of comparison.</p> Signup and view all the answers

What is a system of inequalities?

<p>Similar to systems of equations, but have shaded regions for their solutions.</p> Signup and view all the answers

Flashcards

Absolute Value

The distance of a number from zero on the number line. It's always positive regardless of the number's sign.

Expression

A mathematical expression that combines numbers, variables, and operations, but does not include an equals sign.

Equation

A mathematical statement that equates two expressions using an equals sign.

Inequality

A statement that compares two expressions using symbols like <, >, ≤, or ≥.

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Binomial

A polynomial with two terms.

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Degree of a Polynomial

The highest exponent in a polynomial, indicating the polynomial's complexity.

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Factoring

The process of rewriting a polynomial as a product of simpler polynomials.

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Dependent Variable

A function where the output (y) changes as a direct result of the input (x).

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Independent Variable

A function that stands alone and is not affected by other variables. Its value is independent of the dependent variable.

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Causation

A relationship where one variable directly causes a change in another variable.

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Correlation

A measure of how closely two variables move together. It is quantified by the correlation coefficient.

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Arithmetic Sequence

A sequence where the difference between consecutive terms is constant. Each term is found by adding a fixed value to the previous term.

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Geometric Sequence

A sequence where each term is obtained by multiplying or dividing the previous term by a constant factor.

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Axis of Symmetry

The line that divides a figure into two identical halves. It's a line of symmetry.

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Dot Plot

A visual representation of data using dots placed above a number line. The number of dots above each point indicates the frequency of that value.

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Box Plot

A graph that summarizes data using quartiles, highlighting the median and range. It shows the spread and distribution of data.

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Compound Interest

Interest calculated on the principal amount and also on the accumulated interest from previous periods.

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Exponential Growth Function

A mathematical function that represents exponential growth, where the rate of growth is proportional to the current value.

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Exponential Decay Function

A mathematical function that represents exponential decay, where the rate of decrease is proportional to the current value.

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Cubic Function

A function that involves a cubed term, represented by f(x) = x³.

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Cube Root Function

A function that involves a cube root, represented by f(x) = ³√x.

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Exponential Function

A function that involves an exponential term, represented by f(x) = ab^x where a is non-zero and b is a positive number not equal to one.

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Completing the Square

A method of transforming a quadratic expression into a perfect square trinomial.

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Constant

A value that remains constant and does not have a variable component.

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Discriminant

A measure that indicates the nature of a polynomial's roots, based on its coefficients.

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System of Inequalities

A representation of solutions to systems of inequalities on a graph.

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Consecutive Integers

Counting numbers that follow a sequence, like 1, 2, 3, 4, etc.

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Consecutive Even/Odd Integers

Even numbers or odd numbers that follow each other in sequence.

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Completing the Square

Transforms a quadratic expression into a perfect square trinomial.

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Study Notes

Absolute Value

  • Represents the distance from zero on a number line.
  • Mathematical representation: f(x) = |x|.
  • Graphically depicted as a V shape.

Area Formulas

  • Square: ( A = s^2 ), where s is the length of a side.
  • Rectangle: ( A = lw ), where l is length and w is width.
  • Triangle: ( A = \frac{1}{2} bh ), where b is base and h is height.

Sequences and Series

  • An Arithmetic Sequence has a constant difference between consecutive terms.
  • A Geometric Sequence involves multiplying or dividing by a common factor.

Graphical Concepts

  • Axis of Symmetry divides a figure into two equal halves.
  • Box Plot (or box and whisker plot) summarizes data using quartiles, highlighting median and range.
  • Dot Plot visually represents data points using dots.

Relations and Functions

  • Causation indicates a direct cause-and-effect relationship between variables.
  • Correlation measures the degree of relationship between two variables, quantified by the correlation coefficient.
  • Dependent Variable (y) changes in response to another variable.
  • Independent Variable (x) stands alone and isn't affected by other variables.

Polynomials and Expressions

  • A Binomial consists of two terms.
  • The highest term's exponent defines the Degree of a Polynomial.
  • Factoring involves rewriting a polynomial as a product of simpler polynomials.

Interest and Growth

  • Compound Interest refers to earning interest on previously earned interest.
  • Exponential Growth Function is represented by ( y = a(1 + r)^t ) with a positive initial value.
  • Exponential Decay Function uses ( y = a(1 - r)^t ) for a declining value.

Special Functions

  • Cubic Function is expressed as ( f(x) = x^3 ).
  • Cube Root Function is represented by ( f(x) = \sqrt[3]{x} ).
  • The Exponential Function has the form ( f(x) = ab^x ) where a is non-zero and b is a positive number not equal to one.

Key Definitions

  • A mathematical Expression comprises numbers, variables, and operations but lacks an equals sign.
  • An Equation equates two expressions using an equals sign.
  • Inequalities provide comparison using symbols like <, >, ≤, or ≥.

Other Concepts

  • Completing the Square transforms a quadratic expression into a perfect square trinomial.
  • Correlation Coefficient quantifies how closely two variables move in relation to each other.
  • The Discriminant provides insights into the nature of a polynomial's roots based on its coefficients.

Additional Notions

  • Consecutive Integers are counting numbers in sequence, while Consecutive Even/Odd Integers follow their respective sequences.
  • A Constant is a term that has no variable component.
  • Understanding Systems of Inequalities is essential for visualizing solutions, which are represented by shaded regions in graphs.

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Description

Test your knowledge on essential mathematics concepts including absolute value, area formulas, sequences, and graphical representations. This quiz covers a variety of topics that are fundamental to understanding mathematics and its applications.

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