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Function: A rule that associates (maps) elements from one set (domain) to elements of another set (range). In a function, each element of the domain is mapped to exactly one element of the range. For example, a function might associate a person with his/her height in centimeters. One individual cannot be two different heights at the same time (a person cannot be mapped to two different heights), but two people could be the same height.
Absolute Value: the distance from zero. |5| = 5 because 5 is five units from zero on the number line. Likewise, |-3| = 3 because -3 is three units from zero.
Constant: a value that does not change. For example, in the expression 2x + 4, the "4" is the constant term since its value does not depend on the value of x.
Logarithm: an exponent. Log's with a base of 10 are referred to as Common Logs. the expression log(1000) is presumed to have a base of 10. If 1000 is the input, the output is the 3 because 10^3 = 1000. The output of log(24) is approximately 1.380, because 10^1.380 is approximately 24.
Monomial: a constant, or the product of a constant and one or more variables. For example, 10x^3, but not 10x^(2/3).
Polynomial: the sum of several monomials. For example 5x^3 - 3x^2 + 12.
Quadratic: a polynomial that can be written in the form ax^2 + bx + c. The graph of a quadratic function is called a parabola.
Geometry
Congruent: having the same measure.
Similar Figures: having the same shape and proportional in size. If two figures are similar, all corresponding angles are congruent and all corresponding sides maintain the same proportion.
Bisect: to divide into two congruent (equal-sized) parts.
Complementary angles: angles whose measures add up to 90 degrees
Supplementary angles: angles whose measures add up to 180 degrees
Vertical angles: angles formed by two intersecting straight lines that only share a vertex (they are always congruent)
Adjacent angles: angles that share a vertex and one side, but no interior points
Linear Pair: two adjacent angles that together form a straight line
Perpendicular lines: two lines that meet at a right (90-degree) angle
Parallel lines: two lines in the same plane that never intersect
Transversal: a line that intersects two or more other lines in a plane
If two lines are cut by a transversal, the following pairs of angles are formed by the three lines:
Corresponding angles - angles that are on the same side of the transversal and are both above or both below the other lines lines (if the two lines are parallel, then they are congruent)
Alternate interior angles - angles that are between the other lines, but on opposite sides of the transversal (if the two lines are parallel, then they are congruent)
Same-side interior angles - angles that are between the two other lines and on the same side of the transversal (if the two lines are parallel, then they are supplementary)
Alternate exterior angles - angles that are outside the two lines, and are on opposite sides of the transversal (if the two lines are parallel, then they are congruent)
Same-side exterior angles - angles that are outside the two lines an on the same side of the transversal (if the two lines are parallel, then they are supplementary)
Quadrilateral: a closed figure in the plane with four straight sides
Trapezoid: a quadrilateral with one pair of parallel sides
Isosceles Trapezoid - a trapezoid with congruent legs (one pair of sides parallel, the other congruent)
Parallelogram: a quadrilateral with two pairs of parallel sides. Parallelograms have congruent opposite sides & congruent opposite angles; & the diagonals bisect each other.
Rectangle - a parallelogram with four right angles. The diagonals are congruent.
Rhombus - a parallelogram with four congruent sides. The diagonals are perpendicular.
Square - a parallelogram with four congruent angles and four congruent sides
Statistics
Bias: a factor that can influence the outcome of a survey. For example, asking people attending a soccer game if they are interested in soccer does not necessarily give a representative view of the entire population. Also, "Do you like this hideous dress?". The question guides the responder toward an answer by applying words reflecting a judgement, rather than asking objectively,"What do you think of this dress?".
Mean: commonly thought of as the "average". this measure of central tendency is computed by adding all the responses together and dividing the total by the number of responses.
Normal Distribution: data are symmetric about the mean with most data (68%) occurring within one standard deviation of the mean, and very few results (0.3%) occurring more than 3 standard deviations from the mean. The graph is also known as a "bell curve".
Parameter: a measurement of the entire population.
Population: the entire group being studied. For example every kindergarten teacher in the US (as opposed to a sample of kindergarten teachers from several states).
Random Sample: a sample of the population that is selected at random.
Representative Sample: a sample that is selected based on some strategy, for example, only women who attended a certain college, or specifically selecting groups from the freshman, sophomore, junior and senior classes.
Sample: a subset of the population of interest
Sampling methods: strategies for choosing the group from which data is to be collected
Cluster Sampling - all members of a certain subgroup(s) if a population are sampled (such as "every student taking biology received this survey")
Convenience Sampling - participants in a survey are chosen out of convenience to the pollster, for example, asking twenty people in the cafeteria
Simple Random Sampling - every potential subject has an equal chance of being chosen, for example, all members of a population have their names put into a hat, and a sample of names is selected at random.
Strategic Sampling - all members of the population are sorted (alphabetically, for instance) and every nth student is chosen.
Stratified Sampling - subgroups of the population are identified, and samples are taken from those subgroups in proportion to their representation in the population, for example, asking 5% of each of the 9th-, 10th-, 11th-, and 12-grade classes.
Voluntary Response Sampling - participants from the population self-select, for example, and announcement is made inviting students to visit a polling table in the cafeteria at lunch, and students choose to participate.
Standard Deviation: a measure of the spread or consistency of data around the mean. A data set with a small standard deviation will be clustered about the mean, while a set with a larger standard deviation will include readings that are more spread away.
Statistic: a measurement taken of a sample.
Transformations in the plane:
Preimage: a point (or set of points) that is to be transformed.
Image: a point (or set of points) that has been transformed.
Translation: also known as a "slide", the image is the same size, shape and orientation as the preimage. Symbolic Rule (x,y)®(x+h, y+k)
Reflection (across a line): also known as a "flip". The image of a point is the same distance from the line of symmetry as the preimage point on the opposite side of the line. We developed symbolic rules for reflections across the x-axis, the y-axis, the line y=x, and the line y=-x.
Rotation (about a point): The image of a point is the same distance from the center of rotation as the preimage, and has been rotated along some part of a circle in either the clockwise or counter-clockwise direction.
Dilation (from a point by a factor of m): The image of a point is m times as far from the center of dilation as its preimage.
Trigonometry - the study of the relationships between/among sides and angles in triangles.
cosine - in a right triangle, the cosine of an angle A is the ratio of the length of the adjacent leg (the leg that forms one side of the angle A) to the hypotenuse.
degree - a unit of measure for angles. One degree is the measure of an angle swept by travelling 1/360 of the circumference of the circle.
radian - a unit of measure for angles. One radian is the measure of an angle swept by travelling the length of one radius along the circle.
sine - in a right triangle, the sine of an angle A is the ratio of the length of the opposite leg (the leg that is across the triangle from angle A) to the hypotenuse.
tangent - in a right triangle, the tangent of an angle A is the ratio of the length of the opposite leg to the adjacent leg.
SOHCAHTOA - a mnemonic device used to remember the right-triangle trig relationships - Sine-Opposite-over-Hypotenuse--Cosine-Adjacent-over-Hypotenuse--Tangent-Opposite-over-Adjacent
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