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MTTC - Mathematics (Secondary) (022)
Test
Real Numbers - Answer -the set of all rational and irrational numbers Absolute Value - Answer -the distance away from zero a number is on the number line; |x| Operation - Answer -a mathematical process that takes some value(s) as input(s) and produces an output Parentheses - Answer -used to designate which operations should be done first when there are multiple operations Exponent - Answer -a superscript number placed next to another number at the top right; it indicates how many times the base number is to be multiplied by itself Perfect Square - Answer -a number that has an integer for its square root Order of Operations - Answer -a set of rules that dictates the order in which we must perform each operation in an expression so that we will evaluate it accurately (PEMDAS) Prime Number - Answer -any whole number greater than 1 that has only two factors, itself and 1; that is, a number that can be divided evenly only by 1 and itself
Common Factor - Answer -a number that divides exactly into two or more other numbers Greatest Common Factor (GCF) - Answer -the largest number that is a factor of two or more numbers Numerator - Answer -the top number of a fraction; it represents the number of parts under consideration Denominator - Answer -the bottom number of a fraction; it represents the total number of equal parts; cannot be zero or else it is undefined Common Denominator - Answer -when two fractions are manipulated so that they have the same denominator; the number chosen should be the least common multiple of the two original denominators Proper Fraction - Answer -a fraction whose denominator is greater than its numerator; has a value less than one Improper Fraction - Answer -a fraction whose numerator is greater than its denominator; has a value greater than one Mixed Number - Answer -a number that contains both an integer and a fraction Multiplying Decimals - Answer -multiplicand and multiplier Dividing Decimals - Answer -divisor and dividend; the dividend is the number that is being divided Percentages - Answer -fractions that are based on a whole of 100 Rational Number - Answer -the number can be expressed as a ratio or fraction; a number, r, is rational iff it can be represented by a fraction a/b where a and b are integers and b does not equal 0; includes integers and decimals
Binary System (base 2) - Answer -a number system that uses something other than ten digits; used by computers, which uses only the numbers 0 and 1 Premise - Answer -a statement that precedes a conclusion, in an argument. It is the proposition, or assumption, of an argument. An argument will always have two or more Statement - Answer -in propositional logic, any sentence or expression that has a truth value - that is, that may in principle be considered true or false Compound Statement - Answer -a statement that contains one or more other statements, combined or modified in some way Simple Statement (Proposition) - Answer -a statement that cannot be broken down further into smaller statements Conjunctions - Answer -an operation that combines two or more statements into a compound statement that is true iff all of the component statements are true; marked by the word "and" Disjunction - Answer -an operation that combines two or more statements into a compound statement that is true iff at least one of the component statements is true; marked by the word "or" Conditional Statement (implication) - Answer -a compound statement of the form "if P, then Q." It can also be written "P implies Q" or "P only if Q." This statement is true when both P and Q are true, and even when P is false, regardless of Q. In other words, this statement is false only when P is true and Q is false. Written as P --> Q Side Note: P = premise and Q = conclusion Biconditional Statement - Answer -a combination of two conditional statements: both "if P, then Q" and "if Q, then P." More concisely, "P iff Q." This statement is true when P and Q are either both true or both false. Written as P <--> Q
Quantifier - Answer -a logical construct used in a compound statement to give information on the number of subjects for which a statement is true Existential Quantifier - Answer -specifies that the statement is true for at least one subject; usually introduced as "there exists." Denoted as ∃ specifies that there exists a unique such subject; denoted as ∃! Universal Quanitifer - Answer -specifies that the statement is true for every subject; usually said as "all" or "for all." Denoted as ∀ Truth Table - Answer -shows the truth value of one or more compound statements for each possible combination of truth values of the propositions within it; since each proposition has two possible truth values, the number of possible combinations of N propositions is 2^N, so the truth table with have 2^N rows; useful for comparing two compound statements to see if they are equivalent; they are also useful for analyzing whether complicated compound statements are true or false The Rule of Detachment - Answer -given the premises, P --> Q and P, the valid conclusion is Q The Chain Rule - Answer -given the premises, P --> Q and Q --> R, the valid conclusion is P --> R Negation - Answer -refers to the inversion of the truth value of a statement; it is true if the original statement is false, and false if the original statement is true; signified by the word "not"; denoted as ¬; two of these cancel each other out De Morgan's Laws - Answer -a set of useful relations connecting negation, conjunction, and disjunction. "the negation of a conjunction is the disjunction of the negations" AND "the negation of a disjunction is the conjunction of the negations" Converse - Answer -a conditional statement with the premise and conclusion interchanged; P --> Q is Q --> P
Proofs by Contraposition - Answer -proofs that show that the negation of the conclusion will yield the negation of the hypothesis; the negation of the conclusion is assumed to be true, and it must be shown that the negation of the hypothesis is also true Proofs by Induction - Answer -utilizes inductive reasoning in its assumption that if P(k) is true, then P(k+1) is also true. The induction hypothesis is P(k). This step utilizes inductive reasoning because an observation is used to make the conjecture that P(k+1) is also true. Proportion - Answer -a relationship between two quantities that dictates how one changes when the other changes Direct Proportion - Answer -describes a relationship in which a quantity increases by a set amount for every increase in the other quantity, or decreases by that same amount for every decrease in the other quantity Inverse Proportion - Answer -a relationship in which an increase in one quantity is accompanied by a decrease in the other, or vice versa Ratio - Answer -a comparison of two quantities in a particular order Constant of Proportionality - Answer -when two quantities have a proportional relationship; the product of this constant and one of the quantities is equal to the other quantity; this is the unit price Unit Price - Answer -the price for one item Unit Rate - Answer -expresses a quantity of one thing in terms of one unit of another Slope - Answer -m = (y2-y1)/(x2-x1) for two points (x1,y1) and (x2,y2); positive: the line has an upward direction from left or right; negative: the line has a downward direction from left to right Mathematical Expression - Answer -consists of a combination of one or more values arranged in terms that are added together
Variable Term - Answer -the product of a real number (coefficient) and one or more variables, each of which may be raised to an exponent Coefficient - Answer -a number multiplied by a variable in an mathematical expression Constants - Answer -numbers without a variable in a mathematical expression Single Variable Linear Expression - Answer -the sum of a single variable term, where the variable has no exponent, and a constant, which may be zero Linear Expression - Answer -the sum of any number of variable terms so long as none of the variables have an exponent One Variable Linear Equations - Answer -equations that can be written as ax + b = 0, where a does not equal 0 Root - Answer -a solution to an equation Solution Set - Answer -the set of all solutions of an equation Empty Set - Answer -when an equation has not true solutions Equivalent Equations - Answer -equations with identical solution sets Identity - Answer -a term whose value or determinant is equal to 1 Like Terms - Answer -terms in an equation that have the same variable, regardless of whether or not they also have the same coefficient
System of Equations - Answer -A set of simultaneous equations that all use the same variables. A solution must be true for each equation Consistent Systems - Answer -Systems with at least one solution Inconsistent Systems - Answer -Systems that have no solution Monomial - Answer -a single variable or product of constants and variables, such as x, 2x, or 2/x; there will never be addition or subtraction symbols Polynomials - Answer -algebraic expressions that use addition and subtraction to combine two or more monomials Binomial - Answer -A polynomial with two terms Trinomial - Answer -A polynomial with three terms Degree of a Monomial - Answer -the sum of the exponents of the variables in the monomial Degree of a Polynomial - Answer -The highest degree of any term of the polynomial Rational Expressions - Answer -fractions with polynomials in both numerator and denominator; the value of the polynomial in the denominator cannot be equal to zero Roots - Answer -the solutions of a quadratic equation that satisfy the equation when y=0; where the graph touches the x-axis Quadratic Formula - Answer -used to solve quadratic equations when other methods are more difficult Zero Product Property - Answer -when the product of two or more factors is zero, one of these factors must equal zero
Relation - Answer -a set of data in which there is not a unique y-value for each x-value in the dataset; there can be two of the same x-values assigned to different y-values; a relationship between the x and y- values in each coordinate but does not apply to the relationship between the values of x and y in the data set Function - Answer -a relation where one quantity depends on the other; each x-value in the data set has one unique y-value because the y-value depends on the x-value Data Table - Answer -contains the values for x and y, which you can also list as coordinates Direct Variation - Answer -the value of y increases as the value of x increases and the value of y decreases as the value of x decreases Inverse Variation - Answer -The value of y increases as the value of x decreases and the value of y decreases as the value of x increases
