OCG - Algebra 1 Honors

Key Concepts

Standards

Arithmetic with Polynomials and Rational Expressions

The student will:

A1.AAPR.1*

Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations. (Limit to linear; quadratic.)

Creating Equations

The student will:

A1.ACE.1*

Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable.  (Limit to linear; quadratic; exponential with integer exponents.)

A1.ACE.2*

Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales.  (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.)

A1.ACE.4*

Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

Reasoning with Equations and Inequalities

The student will:

A1.AREI.1*

Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original. 

A1.AREI.3*

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

A1.AREI.4*

Solve mathematical and real-world problems involving quadratic equations in one variable.  (Note: A1.AREI.4a and 4b are not Graduation Standards.)

1. Use the method of completing the square to transform any quadratic equation in  into an equation of the form  that has the same solutions.  Derive the quadratic formula from this form.
2. Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.  Recognize when the quadratic formula gives complex solutions and write them as  for real numbers  and .  (Limit to non-complex roots.)

A1.AREI.5

Justify that the solution to a system of linear equations is not changed when one of the equations is replaced by a linear combination of the other equation.

A1.AREI.6*

Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in two variables. 

(Note: A1.AREI.6a and 6b are not Graduation Standards.)

1. Solve systems of linear equations using the substitution method.
2. Solve systems of linear equations using linear combination.

A1.AREI.10*

Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

A1.AREI.11*

Solve an equation of the form  graphically by identifying the -coordinate(s) of the point(s) of intersection of the graphs of  and .  (Limit to linear; quadratic; exponential.)

A1.AREI.12*

Graph the solutions to a linear inequality in two variables.

Structure and Expressions

The student will:

A1.ASE.1*

Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts.  Interpret complicated expressions as being composed of simpler expressions.  (Limit to linear; quadratic; exponential.)

A1.ASE.2*

Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions.

A1.ASE.3*

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. 

a.       Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain the connection between the zeros of the function, its linear factors, the x-intercepts of its graph, and the solutions to the corresponding quadratic equation.

Building Functions

The student will:

A1.FBF.3*

Describe the effect of the transformations , , , and combinations of such transformations on the graph of  for any real number .  Find the value of  given the graphs and write the equation of a transformed parent function given its graph.  (Limit to linear; quadratic; exponential with integer exponents; vertical shift and vertical stretch.)

Interpreting Functions

The student will:

A1.FIF.1*

Extend previous knowledge of a function to apply to general behavior and features of a function.

1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.
2. Represent a function using function notation and explain that  denotes the output of function  that corresponds to the input . 
3. Understand that the graph of a function labeled as  is the set of all ordered pairs  that satisfy the equation . 

A1.FIF.2*

Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation. 

A1.FIF.4*

Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form.  Sketch the graph of a function from a verbal description showing key features.  Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.  (Limit to linear; quadratic; exponential.)

A1.FIF.5*

Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.  (Limit to linear; quadratic; exponential.)

A1.FIF.6*

Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval.  Interpret the meaning of the average rate of change in a given context.  (Limit to linear; quadratic; exponential.)

A1.FIF.7*

Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.  Graph simple cases by hand and use technology for complicated cases.  (Limit to linear; quadratic; exponential only in the form .) 

A1.FIF.8*

Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function.  (Limit to linear; quadratic; exponential.)   (Note: A1.FIF.8a is not a Graduation Standard.)

1. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

A1.FIF.9*

Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal.  (Limit to linear; quadratic; exponential.)

Linear, Quadratic, and Exponential

The student will:

A1.FLQE.1*

Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by a constant percent rate per unit interval. 

(Note: A1.FLQE.1a is not a Graduation Standard.)

1. Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

A1.FLQE.2*

Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables.  (Limit to linear; exponential.)

A1.FLQE.3*

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or more generally as a polynomial function.

A1.FLQE.5*

Interpret the parameters in a linear or exponential function in terms of the context.  (Limit to linear.)

Quantities

The student will:

A1.NQ.1*

Use units of measurement to guide the solution of multi-step tasks. Choose and interpret appropriate labels, units, and scales when constructing graphs and other data displays.

A1.NQ.2*

Label and define appropriate quantities in descriptive modeling contexts.

A1.NQ.3*

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities in context.

Real Number System

The student will:

A1.NRNS.1*

Rewrite expressions involving simple radicals and rational exponents in different forms.

A1.NRNS.2*

Use the definition of the meaning of rational exponents to translate between rational exponent and radical forms.

A1.NRNS.3

Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Interpreting Data

The student will:

A1.SPID.6*

Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data.

A1.SPID.7*

Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem.

A1.SPID.8*

Using technology, compute and interpret the correlation coefficient of a linear fit.