Subjects
Shows
Understand that two events A and B are independent if the probability of A and B occurring together is the [...]
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as [...]
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the [...]
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the [...]
Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and [...]
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in [...]
(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the [...]
(+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and [...]
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a [...]
(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of [...]
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given [...]
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation [...]
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and [...]
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a [...]
(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid [...]
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso [...]
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic [...]
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; [...]
Represent data with plots on the real number line (dot plots, histograms, and box plots).*
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard [...]
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme [...]
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate [...]
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including [...]
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.*
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. [...]
Informally assess the fit of a function by plotting and analyzing residuals.*
Verify experimentally the properties of dilations given by a center and a scale factor:
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a [...]
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain [...]
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, [...]
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions [...]
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and [...]
(+) Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from [...]
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed [...]
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a [...]
Construct a tangent line from a point outside a given circle to the circle.
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, [...]
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find [...]
Derive the equation of a parabola given a focus and directrix.
(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use [...]
Subjects
Shows
Understand that two events A and B are independent if the probability of A and B occurring together is the [...]
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as [...]
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the [...]
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the [...]
Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and [...]
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in [...]
(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and interpret the [...]
(+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and [...]
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a [...]
(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of [...]
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given [...]
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation [...]
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of polygons and areas of triangles and [...]
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a [...]
(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid [...]
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso [...]
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic [...]
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; [...]
Represent data with plots on the real number line (dot plots, histograms, and box plots).*
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard [...]
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme [...]
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate [...]
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including [...]
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.*
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. [...]
Informally assess the fit of a function by plotting and analyzing residuals.*
Verify experimentally the properties of dilations given by a center and a scale factor:
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a [...]
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain [...]
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, [...]
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions [...]
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and [...]
(+) Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from [...]
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed [...]
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a [...]
Construct a tangent line from a point outside a given circle to the circle.
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, [...]
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find [...]
Derive the equation of a parabola given a focus and directrix.
(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use [...]
