Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided. Example: 3^12 × 3^⎯15 = 3^⎯3 = 1/(3^3 )
Apply concepts of rational and irrational numbers.
Use rational approximations of irrational numbers to compare and order irrational numbers.
Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).
Represent and use expressions and equations to solve problems involving radicals and integer exponents.
Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Write and identify linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear.
Identify and apply properties of rotations, reflections, and translations. Example: Angle measures are preserved in rotations, reflections, and translations.
Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.
Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.
Apply the Pythagorean theorem to find the distance between two points in a coordinate system.
Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided.
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative correlation, linear association, and nonlinear association.
For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of the data points to the line.
Understand that patterns of association can be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
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