GRADES EIGHT THROUGH TWELVE MATHEMATICS
absolute value. A number’s distance from zero
on the number line . The absolute value of -4 is
4; the absolute value of 4 is 4.
algorithm. An organized procedure for performing
a given type of calculation or solving a
given type of problem. An example is long
arithmetic sequence . A sequence of elements,
. , such that the difference of
successive terms is a constant
for example, the sequence
where the common difference is 3.
asymptotes. Straight lines that have the property
of becoming and staying arbitrarily close to the
curve as the distance from the origin increases
to infinity. For example, the x-axis is the only
asymptote to the graph of sin(x)/x.
axiom. A basic assumption about a mathematical
system from which theorems can be deduced.
For example, the system could be the points
and lines in the plane. Then an axiom would be
that given any two distinct points in the plane,
there is a unique line through them.
binomial. In algebra, an expression consisting of
the sum or difference of two monomials (see
the definition of monomial), such as 4a-8b.
binomial distribution . In probability, a binomial
distribution gives the probabilities of k outcomes
A (or n-k outcomes B) in n independent
trials for a two-outcome experiment in which
the possible outcomes are denoted A and B.
dilation. In geometry, a transformation D of the
parallel. Given distinct lines in the plane
binomial theorem. In mathematics, a theorem
that specifies the complete expansion of a
binomial raised to any positive integer power.
box-and-whisker plot. A graphical method for
showing the median, quartiles, and extremes of
data. A box plot shows where the data are
spread out and where they are concentrated.
complex numbers . Numbers that have the form
a + bi where a and b are real numbers and i
satisfies the equation i2 = -1. Multiplication is
denoted by (a+bi)(c+di) = (ac-bd) + (ad+bc)i,
and addition is denoted by (a+bi) + (c + di) =
(a+c) + (b+d)i.
congruent. Two shapes in the plane or in space
are congruent if there is a rigid motion that
identifies one with the other (see the definition
of rigid motion).
conjecture. An educated guess.
coordinate system. A rule of correspondence by
which two or more quantities locate points
unambiguously and which satisfies the further
property that points unambiguously determine
the quantities; for example, the usual Cartesian
coordinates x, y in the plane.
cosine. Cos(θ) is the x-coordinate of the point on
the unit circle so that the ray connecting the
point with the origin makes an angle of θ with
the positive x-axis. When θ is an angle of a
right triangle, then cos(θ) is the ratio of the
adjacent side with the hypotenuse.
histogram. A vertical block graph with no spaces
reflection. The reflection through a line
sine. Sin(θ) is the y-coordinate of the
point on the
unit circle so that the ray connecting the point
with the origin makes an angle of θ with the
positive x-axis. When θ is an angle of a right
triangle, then sin(θ) is the ratio of the opposite
side with the hypotenuse.
square root. The square roots of n are all the
numbers m so that m2 = n. The square roots
of 16 are 4 and -4. The square roots of -16 are
4 i and -4 i.
standard deviation. A statistic that measures the
dispersion of a sample.
symmetry. A symmetry of a shape S in the plane
or space is a rigid motion T that takes S onto
itself (T(S) = S). For example, reflection
through a diagonal and a rotation through a
right angle about the center are both symmetries
of the square.
system of linear equations. Set of equations of
the first degree (e.g., x + y = 7 and x - y = 1).
A solution of a set of linear equations is a set of
numbers . so that when the variables
are replaced by the numbers all the equations
are satisfied. For example, in the equations
above, x = 4 and y = 3 is a solution.
translation. A rigid motion of the plane or space
of the form X goes to X + V for a fixed vector V.
transversal. In geometry, given two or more lines
in the plane a transversal is a line distinct from
the original lines and intersects each of the
given lines in a single point.
unit fraction. A fraction whose numerator is 1
(e.g., 1⁄π, 1⁄3, 1⁄x). Every nonzero number may be
written as a unit fraction since, for n not equal
to 0, n = 1/(1/n).
variable. A placeholder in algebraic expressions;
for example, in 3x + y = 23, x and y are variables.
vector. Quantity that has magnitude (length) and
direction. It may be represented as a directed
zeros of a function. The points at which the value of a function is zero.