Understand and apply elementary set theory and logic as used in simple internet searches.

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Solve systems of equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Understand the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Graph solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. A) Graph linear and quadratic functions and show intercepts, maxima, and minima. B) Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. C) Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. D) (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. E) Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Evaluate reports based on data.

Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subjects among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.