Algebra I

Number and Quantity

Real Number System: Rational exponents; Rational and Irrational Numbers

Algebra
Algebra encompasses linear, exponential, and quadratic expressions. It involves interpreting parts of an expression, such as terms, factors, and coefficients, and simplifying complex expressions by viewing one or more parts as a single entity. For quadratic expressions, factorization is used to reveal the zeros of the function they define, and completing the square is used to find the maximum or minimum value of the function. Exponential functions require understanding the properties of exponents to transform expressions. Arithmetic operations on linear and quadratic polynomials are also fundamental. Creating equations and inequalities in one variable, including those with absolute values, helps solve various problems. Additionally, creating equations in two or more variables represents relationships between quantities. Graphing equations on coordinate axes is essential, as is representing constraints with equations or inequalities and interpreting their solutions. Solving equations and inequalities in one variable includes handling linear inequalities, literal equations, and quadratic equations with real solutions, both algebraically and graphically.

 

Functions

Understand the concept of a function and use function notation, Sets, Subsets, Domain, Range. Sequences; linear, quadratic, and exponential functions; Interpret key features of graphs of the functions that include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Calculate and interpret the average rate of change of a function from graphs.Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions; Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior; Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Building a function that models a relationship between two quantities; Building new functions from existing functions.
 

 

Statistics and Probability

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 deviation) of two or more different data sets; Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points; Summarize, represent, and interpret data on two categorical and quantitative variables; Interpret the slope (rate of change) and the intercept (constant term) of a linear model; 

Understand independence and conditional probability and use them to interpret data; Use the rules of probability to compute probabilities of compound events in a uniform probability model.