
BELOW YOU WILL FIND VOCABULARYFOR EACH MODULEModule 1Focus Area Topic A: Introduction to Functions Studied This Year— Graphing StoriesWords to KnowPiecewise Linear Function: Given nonoverlapping intervals on the real number line, a (real) piecewise linear function is a function from the union of the intervals on the real number line that is defined by (possibly different) linear functions on each interval.Focus Area Topic B: The Structure of ExpressionsWords to KnowNumerical Symbol: A numerical symbol is a symbol that represents a specific number.Variable Symbol: A variable symbol is a symbol that is a placeholder for a number. It is possible that a question may restrict the type of number that a placeholder might permit, maybe integers only or a positive real number, for instance.Numerical Expression: A numerical expression is an algebraic expression that contains only numerical symbols (no variable symbols) and that evaluates to a single number.Algebraic Expression: An algebraic expression is either (1) a numerical symbol or a variable symbol or (2) the result of placing previously generated algebraic expressions into the two blanks of one of the four operators ((__)+(__), (__)–(__), (__)×(__), (__)÷(__)) or into the base blank of an exponentiation with an exponent that is a rational number.Equivalent Numerical Expressions: Two numerical expressions are equivalent if they evaluate to the same number.Equivalent Algebraic Expressions: Two algebraic expressions are equivalent if we can convert one expression into the other by repeatedly applying the Commutative, Associative, and Distributive Properties and the properties of rational exponents to components of the first expression.Polynomial Expression: A polynomial expression is either (1) a numerical expression or a variable symbol or (2) the result of placing two previously generated polynomial expressions into the blanks of the addition operator (__+__) or the multiplication operator (__×__). Monomial: A monomial is a polynomial expression generated using only the multiplication operator (__×__). Monomials are products whose factors are numerical expressions or variable symbols.Degree of a Monomial: The degree of a nonzero monomial is the sum of the exponents of the variable symbols that appear in the monomial.Standard Form of a Polynomial Expression in One Variable: A polynomial expression with one variable symbol ݔ is in standard form if it is expressed as ܽ݊ݔ݊ + ܽ݊−1ݔ݊−1 + ⋯+ ܽ1ݔ + ܽ0, where ݊ is a nonnegative integer, and ܽ0, ܽ1, ܽ2,…, ܽ݊ are constant coefficients with ܽ݊ ≠ 0. A polynomial expression in ݔ that is in standard form is often called a polynomial in ݔ.Degree of a Polynomial in Standard Form: The degree of a polynomial in standard form is the highest degree of the terms in the polynomial, namely ݊.Leading Term and Leading Coefficient of a Polynomial in Standard Form: The term ܽ݊ݔ݊ is called the leading term, and ܽ݊ is called the leading coefficient.Constant Term of a Polynomial in Standard Form: The constant term is the value of the numerical expression found by substituting 0 into all the variable symbols of the polynomial, namely ܽ0.The Distributive Property: If , , and are real numbers, then a (b + c) = ab + ac.The Commutative Property of Addition: If and are real . + = + numbers, thenThe Associative Property of Addition: If , , and are real ( + ) + = + ( + ) numbers, thenThe Commutative Property of Multiplication: If and are . × = × real numbers, thenThe Associative Property of Multiplication: If , , and are real numbers, then () = ().Standard form of the polynomial: A polynomial expression with one variable symbol ݔ is in standard form if it is expressed as, ܽ݊ݔ݊+ܽ݊−1ݔ݊−1+⋯+ܽ1ݔ+ܽ0, where ݊ is a nonnegative integer, and ܽ0,ܽ1,ܽ2…,ܽ݊ are constant coefficients with ܽ݊≠0. A polynomial expression in ݔ that is in standard form is often called a polynomial in ݔ.Focus Area Topic C: Solving Equations and InequalitiesWords to KnowNumber Sentence: A number sentence is a statement of equality between two numerical expressions. A number sentence is said to be true if both numerical expressions are equivalent (that is, both evaluate to the same number). It is said to be false otherwise. True and false are called truth values.Algebraic equation: An algebraic equation is a statement of equality between two expressions. Algebraic equations can be number sentences (when both expressions are numerical), but often they contain symbols whose values have not been determined.Domain: Stating what type of number the variable symbol represents is called stating its domain.Solution set: The solution set of an equation written with only one variable is the set of all values one can assign to that variable to make the equation a true statement. Any one of those values is said to be a solution to the equation.Identity: An identity is an equation that is always true.Addition Property of Inequality: If A>B, then A+c>B+c for any real number c.Multiplication Property of Inequality: If A>B, then kA>kB for any positive real number k.Compound sentence: a sentence that contains at least two clauses Declarative sentence: a sentence in the form of a statementZeroproduct property: The zeroproduct property says that If ab=0, then either a=0 or b=0 or a=b=0.Focus Area Topic D: Creating Equations to Solve ProblemsWords to KnowGraph of an Equation in Two Variables: The set of all points in the coordinate plane that are solutions to an equation in two variables. Sequence: An ordered list of elementsTerms of a Sequence: Elements of the list (sequence)Recursive Sequence: A sequence that is defined by (1) specifying the values of one or more initial term, and (2) having the property that the remaining terms satisfy a recurrence relation that describes the value of a term based upon an algebraic expression in numbers, previous terms, or the index of the term.Module 2Focus Area Topic A: Shapes and Center of DistributionsWords to KnowDot plot: a plot of each data value on a scale or a number line.Box plot: a graph that provides a picture of the data ordered and divided into four intervals with each interval containing 25% of the data. Histogram: a graph of data that groups the data based on intervals and represents the data in each interval by a bar.Focus Area Topic B: Describing Variability and Comparing DistributionsWords to KnowSkewed data distributions: a data distribution is said to be skewed if the distribution is not symmetric with respect to its mean. Leftskewed or skewed to the left is indicated by the data spreading out longer (like a tail) on the left side. Rightskewed or skewed to the right is indicated by the data spreading out longer (like a tail) on the right side.Outliers: an outlier of a finite numerical data set is a value that is greater than Q3 by a distance of 1.5 x IQR or a value that is less than Q1 by a distance of 1.5 x IQR. Outliers are usually identified by a * or a ● in a box plot.Sample variance: The sample variance for a numerical sample data set of n values is the sum of the squared distance the values are from the mean divided by (n1).Sample standard deviation: the sample standard deviation is the principle (positive) square root of the sample variance.Interquartile range: the interquartile range (or IQR) is the distance between the first quartile and the second quartile: IQR = Q3 – Q1. The IQR describes variability by identifying the length of the interval that contains the middle 50% of the data values.Focus Area Topic C: Categorical Data on Two VariblesWords to KnowAssociation: a statistical association is any relationship between measures of two types of quantities so that one is statistically dependent on the other.Conditional relative frequency: a conditional relative frequency compares a frequency count to the marginal total that represents the condition of interest.Focus Area Topic D: Numerical Data on Two VariablesWords to KnowCorrelation coefficient: The correlation coefficient, often denoted by r, is a number between 1 and +1 inclusively that measures the strength and direction of a linear relationship between the two types of quantities. If r = 1, the the graph of data points of the bivariate data set lie on a line of positive slope. If r = 1, then the graph of data points of the bivariate data set lie on a line of negative slope.Module 3Focus Area Topic A: Linear and Exponential SequencesWords to KnowExplicit Formula: A formula used to represent a sequence that specifies the nth term of a sequence as an expression in n and uses the first term number (an integer).Recursive Formula: A formula used to represent a sequence that specifies the nth term of a sequence as an expression in the previous term (or previous couple of terms).Arithmetic Sequence: A sequence in which the same number is being added to a term to get the next term.Geometric Sequence: A sequence in which the same number is being multiplied by a term to get the next term.Simple Interest: Interest that is calculated once per year on the original amount borrowed or invested; it does not become part of the amount borrowed or owed (the principal).Compound Interest: Interest that is calculated once per period on the current amount borrowed or invested; each period, the interest becomes part of the principal.Exponential Growth: A formula with a growth factor, b, such that b > 1; output will grow over time.Exponential Decay: A formula with a growth factor, b, such that b < 1; output will diminish (decay) over time.Focus Area Topic B: Functions and Their GraphsWords to KnowFunction: A correspondence between two sets, X and Y, in which each element of X is matched to one and only one element of Y. Domain: The set X of a function; input values.Range: The set Y of a function; output values.Linear Function: A polynomial function of degree 1.Average Rate of Change: Given a function f whose domain includes the closed interval of real numbers [a, b] and whose range is a subset of the real numbers, the average rate of change on the interval [a, b] is 𝑓(𝑏)−𝑓(𝑎) 𝑏−𝑎 .SetBuilder Notation: An abbreviation of the elements that satisfy a function. {type of element │condition on each element}Focus Area Topic D Using Functions and Graphs to Solve ProblemsWords to KnowLinear Function: Has a General Form of 𝑓(𝑥) = 𝑎𝑥 + 𝑏.Exponential Function: Has a General Form of 𝑓(𝑥) = 𝑎(𝑏𝑥).
Module 4
Words to KnowAxis of symmetry of the graph of a quadratic function (Given a quadratic function in standard form, , the vertical line given by the graph of the equation, , is called the axis of symmetry of the graph of the quadratic function.)
Cube root function (The parent function .)
Cubic function (A polynomial function of degree .)
Degree of a monomial term (The degree of a monomial term is the sum of the exponents of the variables that appear in a term of a polynomial.)
Degree of a polynomial (The degree of a polynomial in one variable in standard form is the highest degree of the terms in the polynomial.)
Discriminant (The discriminant of a quadratic function in the form is . The nature of the roots of a quadratic equation can be identified by determining if the discriminant is positive, negative, or equal to zero.)
End behavior of a quadratic function (Given a quadratic function in the form (or ), the quadratic function is said to open up if and open down if .)
Factored form for a quadratic function (A quadratic function written in the form.)
Leading coefficient (The leading coefficient of a polynomial is the coefficient of the term of highest degree.)
Parent function (A parent function is the simplest function in a “family” of functions that can each be formed by one or more transformations of another.)
Quadratic formula (The quadratic formula is the formula that emerges from solving the general form of a quadratic equation by completing the square, . It can be used to solve any quadratic equation.)
Quadratic function (A polynomial function of degree .)
Roots of a polynomial function (The domain values for a polynomial function that make the value of the polynomial function equal zero when substituted for the variable.)
where is a nonnegative integer, and , , , are constant coefficients with .)
Square root function (The parent function .)
Standard form for a quadratic function (A quadratic function written in the form.)
Standard form of a polynomial in one variable (A polynomial expression with one variable symbol is in standard form if it is expressed as,
Vertex form (Completedsquare form for a quadratic function; in other words, written in the form .)
Vertex of the graph of a quadratic function (The point where the graph of a quadratic function and its axis of symmetry intersect is called the vertex. The vertex is either a maximum or a minimum of the quadratic function, depending on whether the leading coefficient of the function in standard form is negative or positive, respectfully.)
Module 5Words to knowAnalytic Model (A model that seeks to explain data based on deeper theoretical ideas. For example, by using an algebraic equation. This is sometimes referred to as a symbolic model.)Descriptive Model (A model that seeks to describe phenomena or summarize them in a compact form. For example, by using a graph.)