Honors Algebra 2
RELATED GLOSSARY TERM DEFINITIONS (90)
Absolute value: / A number's distance form zero on a number line. Distance is expressed as a positive value.Approximate: / A number or measurement that is close to or near its exact value.
Area: / The number of square units needed to cover a surface.
Asymptote: / A straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line.
Axes: / The horizontal and vertical number lines used in a coordinate plane system.
Coefficient: / The number that multiplies the variable(s) in an algebraic expression (e.g., 4xy). If no number is specified, the coefficient is 1.
Complex number: / A number that can be written in the form a + bi, where a and b are real numbers and i is the square root of -1.
Composition of functions: / Combining two functions by taking the output of one and using it as the input of another. If the output of g is used as the input of f, then the composition is referred to as "f of g of x" and is denoted f(g(x)) or f?g(x).
Conjugate root theorem: / If P is a polynomial in one variable with real coefficients, and a + bi is a zero of P with a and b real numbers, then its complex conjugate a - bi is also a zero of P.
Constant: / Any value that does not change.
Coordinate plane: / A two-dimensional network of horizontal and vertical lines that are parallel and evenly-spaced; especially designed for locating points, displaying data, or drawing maps.
Difference: / A number that is the result of subtraction
Dimension: / The number of coordinates used to express a position.
Discriminant: / An algebraic expression related to the coefficients of a quadratic equation that can be used to determine the number and type of solutions to the equation. If ax^2+bx+c=0, the discriminant is D=b^2-4ac.
Domain: / The set of values of the independent variable(s) for which a function or relation is defined.
e: / e=2.7182818284...., is an irrational number and the base of the natural logarithm. e is sometimes known as Napier’s constant although the symbol e honors Euler.
End behavior: / A function’s value for extreme values of its independent variable.
Equal: / Having the same value (=).
Equation: / A mathematical sentence stating that the two expressions have the same value. Also read the definition of equality.
Expression: / A mathematical phrase that contains variables, functions, numbers, and/or operations. An expression does not contain equal or inequality signs.
Factor: / A number or expression that is multiplied by one or more other numbers or expressions to yield a product.
Formula: / A rule that shows the relationship between two or more quantities; involving numbers and/or variables.
Height: / A line segment extending from the vertex or apex of a figure to its base and forming a right angle with the base or plane that contains the base.
Imaginary part: / The coefficient of i in a complex number.
Independent variable: / The factor that is changed in an experiment in order to study changes in the dependent variable.
Infinite: / Has no end or goes on forever, not finite. A set is infinite if it can be placed in one-to-one correspondence with a proper subset of itself.
Integers: / The numbers in the set {…-4, -3, -2, -1, 0, 1, 2, 3, 4…}.
Intercept: / The points where a curve or line drawn on a rectangular-coordinate-system graph intersect the vertical and horizontal axes.
Joint variation: / A quantity varies directly with two or more quantities. For example, z varies jointly with x and y means that z=kxy, where k is a constant.
Length: / A one-dimensional measure that is the measurable property of line segments.
Line: / A collection of an infinite number of points in a straight pathway with unlimited length and having no width.
Linear equation: / An algebraic equation in which the variable quantity or quantities are raised to the zero or first power.
Net: / A two-dimensional diagram that can be folded or made into a three-dimensional figure.
Oblique: / Tilted at an angle; neither vertical nor horizontal.
Operation: / Any mathematical process, such as addition, subtraction, multiplication, division, raising to a power, or finding the square root.
Plane: / An infinite two-dimensional geometric surface defined by three non-linear points or two distance parallel or intersecting lines.
Point: / A specific location in space that has no discernable length or width.
Product: / The result of multiplying numbers together.
Proportional: / Having the same or a constant ratio. Two quantities that have the same ratio are considered directly proportional. Two quantities whose products are always the same are considered inversely proportional.
Radius: / A line segment extending from the center of a circle or sphere to a point on the circle or sphere. Plural radii.
Real number: / The set of all rational and irrational numbers.
Real-world problem: / A problem that is an application of a mathematical concept in a real-life situation.
Rectangle: / A parallelogram with four right angles.
Remainder: / In a whole-number division problem, the final undivided part that is less than the divisor and “left over” after dividing.
Remainder Theorem: / If a polynomial P(x) is divided by (x-r), then the remainder is a constant given by P(r).
Root: / A root of a polynomial is a number x such that P(x)=0. A polynomial of degree n has n complex roots.
Rule: / A general statement written in numbers, symbols, or words that describes how to determine any term in a pattern or relationship. Rules or generalizations may include both recursive and explicit notation. In the recursive form of pattern generalization, the rule focuses on the rate of change from one element to the next. Example: Next = Now + 2; Next = Now x 4. In the explicit form of pattern generalization, the formula or rule is related to the order of the terms in the sequence and focuses on the relationship between the independent variable and the dependent variable. For example: y=5t - 3 Words may also be used to write a rule in recursive or explicit notation. Example: to find the total fee, multiply the total time with 3; take the previous number and add two to get the next number.
Sequence: / A list of numbers set apart by commas, such as -1, 1, -1, 1, -1, …
Series: / An indicated sum of successive terms of a sequence.
Set: / A set is a finite or infinite collection of distinct objects in which order has no significance.
Side: / The edge of a polygon (e.g., a triangle has three sides), the face of a polyhedron, or one of the rays that make up an angle.
Similarity: / A term describing figures that are the same shape but are not necessarily the same size or in the same position.
Simplify: / The process of converting a fraction or mixed number, to an equivalent fraction, or mixed number, in which the greatest common factor of the numerator and the denominator of the fraction is one. Simplify also refers to using the rules of arithmetic and algebra to rewrite an expression as simply as possible.
Square: / A rectangle with four congruent sides; also, a rhombus with four right angles.
Sum: / The result of adding numbers or expressions together.
Symmetry: / An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformations (such as rotation, reflection, or translation).
Synthetic division: / A shortcut method for dividing a polynomial by another polynomial of the first degree. It can be used in place of the standard long division algorithm. This method reduces the polynomials factor into a set of numeric values. After these values are processed, the resulting set of numeric outputs is used to construct the polynomial quotient and the polynomial remainder.
System of equations: / A group of two or more equations that are related to the same situation and share variables. The solution to a system of equations is an ordered number set that makes all of the equations true.
Theorem: / A statement or conjecture that can be proven to be true based on postulates, definitions, or other proven theorems. The process of showing a theorem to be correct is called a proof.
Transformation: / An operation on a figure by which another image is created. Common transformations include reflections (flips), translations (slides), rotations (turns) and dilations.
Triangle: / A polygon with three sides.
Unit: / A determinate quantity (as of length, time, heat, or value) adopted as a standard of measurement.
Variable: / Any symbol, usually a letter, which could represent a number. A variable might vary as in f(x)=2x+1, or a variable might be fixed as in 2x+1=5.
Binomial Theorem: / A theorem that specifies the expansion of a binomial of the form (x + y)n as the sum of n + 1 terms of which the general term is of the form where k takes on values from 0 to n.
Change of Base Formula: / A formula that allows you to rewrite a logarithm in terms of logs written with another base. Assume that x, a, and b are all positive. Also assume that a ≠1, b ≠1. Change of base formula:
Circle: / A closed plane figure with all points of the figure the same distance from the center. The equation for a circle with center (h, k) and radius r is: (x - h)2 + (y - k)2 = r2
Conic section: / The family of curves including circles, ellipses, parabolas, and hyperbolas. All of these geometric figures may be obtained by the intersection of a double cone with a plane. All conic sections have equations of the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.
Degree: / The unit of measure for angles (°), equal to 1/360 of a complete revolution. There are 360 degrees in a circle.
Eccentricity: / A number that indicates how drawn out or attenuated a conic section is . Eccentricity is represented by the letter e (no relation to e = 2.718...). The eccentricity can be interpreted as the fraction of the distance along the half of the major axis at which the focus lies: . Here, c = the distance from the center to a focus, a = the distance of the half of the major axis.
Exponent (exponential form): / The number of times the base occurs as a factor, for example 23 is the exponential form of 2 x 2 x 2. The number two (2) is called the base, and the number three (3) is called the exponent.
Exponential Function: / A function of the form y = abcx+b + e, where a,b,c,d,e,x are real numbers, a, b, c are nonzero, b≠1, and b>0.
Function: / A relation in which each value of x is paired with a unique value of y. More formally, a function from A to B is a relation f such that every a A is uniquely associated with an object F(a) B.
Fundamental Theorem of Algebra: / Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers. Corollary: Every polynomial P(x) of degree n (n > 0) can be written as the product of a constant k (k ≠ 0) and n linear factors P(x) = k (x – r1) (x – r2 ) (x – r3 )…(x – rn) Thus a polynomial equation of degree n has exactly n complex roots, namely r1, r2, r3,…, rn.
Geometric Sequence: / A sequence in which consecutive terms have a common ratio. A geometric sequences can be written as an=a1rn-1 (n=1, 2, 3, …) where an is the nth term of the sequence, a1 is the first term, r is the common ratio.
Geometric Series: / The sum of the terms of a geometric sequence. The sum of the first n terms of a geometric sequence is given by
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Inequality: / A sentence that states one expression is greater than (>), greater than or equal to (≥), less than (<), less than or equal to (≤), another expression.
Limit: / A number to which the terms of a sequence get closer so that beyond a certain term all terms are as close as desired to that number. A function f(z) is said to have a limit if, for all e>0, there exists a d>0 such that whenever .
Logarithm: / “The logarithm of x to the base b” is the power to which b must be raised to be equal to x. f(x) = logbx is the inverse function of h(x) = bx.
Monomial: / A polynomial with one term such as 5, -2xyz, or xy4
Parabola: / A locus of points whose perpendicular distances to a line, called the directrix, and to a fixed point, called the focus, are equal. The graph of any quadratic function is a parabola and a parabola always has a quadratic equation. The equation for a vertical parabola is y = a(x - h)2 + k, where (h,k) is the vertex of the parabola.