Sampling techniques are used to gather data from real-world situations. If the data are representative of the larger population, inferences can be made about that population.
Biased sampling techniques yield data unlikely to be representative of the larger population.
Sets of numerical data are described using measures of central tendency and dispersion.
Data Representation
The most appropriate data representations depend on the type of data—quantitative or qualitative, and univariate or bivariate.
Line plots, box plots, and histograms are different ways to show distribution of data over a possible range of values.
Probability
Probability expresses the likelihood that a particular event will occur.
Data can be used to calculate an experimental probability, and mathematical properties can be used to determine a theoretical probability.
Either experimental or theoretical probability can be used to make predictions or decisions about future events.
Various counting methods can be used to develop theoretical probabilities.
Geometry
Visualization
Visualization can help you see the relationships between two figures and help you connect properties of real objects with two-dimensional drawings of these objects.
Transformations
Transformations are mathematical functions that model relationships with figures.
Transformations may be described geometrically or by coordinates.
Symmetries of figures may be defined and classified by transformations.
Measurement
Some attributes of geometric figures, such as length, area, volume, and angle measure, are measurable. Units are used to describe these attributes.
Reasoning & Proof
Definitions establish meanings and remove possible misunderstanding.
Other truths are more complex and difficult to see. It is often possible to verify complex truths by reasoning from simpler ones using deductive reasoning.
Similarity
Two geometric figures are similar when corresponding lengths are proportional and corresponding angles are congruent.
Areas of similar figures are proportional to the squares of their corresponding lengths.
Volumes of similar figures are proportional to the cubes of their corresponding lengths.
Coordinate Geometry
A coordinate system on a line is a number line on which points are labeled, corresponding to the real numbers.
A coordinate system in a plane is formed by two perpendicular number lines, called the x - and y-axes, and the quadrants they form. The coordinate plane can be used to graph many functions.
It is possible to verify some complex truths using deductive reasoning in combination with the distance, midpoint, and slope formulas.