Page 62 - Math 9-10 (2009)

GLOSSARY 61
cosine ratio. For either of the two acute angles in a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse.
counter-example. An example that proves that a hypothesis or conjecture is false.
curve of best fit. The curve that best describes the distribution of points in a scatter plot.
deductive reasoning. The process of reach- ing a conclusion by applying arguments that have already been proved and using evidence that is known to be true.
diagonal. In a polygon, a line segment join- ing two vertices that are not next to each other (i.e., not joined by one side).
difference of squares. An expression of the form a2 – b2, which involves the subtraction of two squares.
direct variation. A relationship between two variables in which one variable is a constant multiple of the other.
dynamic geometry software. Computer software that allows the user to plot points and create graphs on a coordinate system, measure line segments and angles, construct two- dimensional shapes, create two-dimensional representations of three-dimensional objects, and transform constructed figures by moving parts of them.
evaluate. To determine a value for.
exponent. A special use of a superscript in mathematics. For example, in 32, the exponent is 2. An exponent is used to denote repeated multiplication. For example, 54 means
5 x 5 x 5 x 5.
extrapolate. To estimate values lying outside the range of given data. For example, to extrapolate from a graph means to estimate coordinates of points beyond those that are plotted.
factor. To express a number as the product of two or more numbers, or an algebraic expression as the product of two or more other algebraic expressions. Also, the individ- ual numbers or algebraic expressions in such a product.
finite differences. Given a table of values in which the x-coordinates are evenly spaced, the first differences are calculated by subtracting consecutive y-coordinates. The second differ- ences are calculated by subtracting consecutive first differences, and so on. In a linear relation, the first differences are constant; in a quadratic relationoftheformy=ax2 +bx+c(a≠0), the second differences are constant. For example:
x
y
First Difference
Second Difference
1 2 3 4 5
1 4 9 16 25
4–1=3
9–4=5 16–9=7 25–16=9
5–3=2 7–5=2 9–7=2
first-degree equation. An equation in which the variable has the exponent 1; for example, 5(3x – 1) + 6 = –20 + 7x + 5.
first-degree polynomial. A polynomial in which the variable has the exponent 1; for example, 4x + 20.
first differences. See finite differences.
generalize. To determine a general rule or make a conclusion from examples. Specifically, to determine a general rule to represent a pat- tern or relationship between variables.
graphing calculator. A hand-held device capable of a wide range of mathematical oper- ations, including graphing from an equation, constructing a scatter plot, determining the equation of a curve of best fit for a scatter plot, making statistical calculations, performing symbolic manipulation. Many graphing calcu- lators will attach to scientific probes that can be used to gather data involving physical mea- surements (e.g., position, temperature, force).