Algebra 1

Select a Standard:

APRArithmetic with Polynomials and Rational Expressions
APRArithmetic with Polynomials and Rational Expressions
The symbol for a binomial squared. A plus B in parentheses squared.
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
A-APR.1.1
The symbol for a binomial squared. A plus B in parentheses squared.
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
A-APR.2.3
CEDCreating Equations
CEDCreating Equations
The symbol for a binomial squared. A plus B in parentheses squared.
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. ★
A-CED.1.1
The symbol for a binomial squared. A plus B in parentheses squared.
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. ★
A-CED.1.4
The symbol for a binomial squared. A plus B in parentheses squared.
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. ★
A-CED.1.2
The symbol for a binomial squared. A plus B in parentheses squared.
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. ★
A-CED.1.3
REIReasoning With Equations and Inequalities
REIReasoning With Equations and Inequalities
The symbol for a binomial squared. A plus B in parentheses squared.
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A-REI.1.1
The symbol for a binomial squared. A plus B in parentheses squared.
Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for x² = 49), 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 a ± bi for real numbers a and b.
A-REI.2.4.b
The symbol for a binomial squared. A plus B in parentheses squared.
Understand that 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).
A-REI.4.10
The symbol for a binomial squared. A plus B in parentheses squared.
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
A-REI.2.3
The symbol for a binomial squared. A plus B in parentheses squared.
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.
A-REI.3.5
The symbol for a binomial squared. A plus B in parentheses squared.
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. ★
A-REI.4.11
The symbol for a binomial squared. A plus B in parentheses squared.
Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.
A-REI.2.4.a
The symbol for a binomial squared. A plus B in parentheses squared.
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A-REI.3.6
The symbol for a binomial squared. A plus B in parentheses squared.
Graph the 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.
A-REI.4.12
SSESeeing Structure in Expressions
SSESeeing Structure in Expressions
The symbol for a binomial squared. A plus B in parentheses squared.
Interpret expressions that represent a quantity in terms of its context. ★ a. Interpret parts of an expression, such as terms, factors, and coefficients.
A-SSE.1.1.a
The symbol for a binomial squared. A plus B in parentheses squared.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ★ a. Factor a quadratic expression to reveal the zeros of the function it defines.
A-SSE.2.3.a
The symbol for a binomial squared. A plus B in parentheses squared.
Interpret expressions that represent a quantity in terms of its context. ★ b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.
A-SSE.1.1.b
The symbol for a binomial squared. A plus B in parentheses squared.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ★ b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
A-SSE.2.3.b
The symbol for a binomial squared. A plus B in parentheses squared.
Use the structure of an expression to identify ways to rewrite it. For example, see x^4- y^4 as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).
A-SSE.1.2
The symbol for a binomial squared. A plus B in parentheses squared.
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ★ c. Use the properties of exponents to transform expressions for exponential functions. For example the expression can be rewritten as ≈ to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
A-SSE.2.3.c
BFBuilding Functions
BFBuilding Functions
Functions Logo. f(x)
Write a function that describes a relationship between two quantities. ★ a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-BF.1.1.a
Functions Logo. f(x)
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
F-BF.2.3
Functions Logo. f(x)
Write a function that describes a relationship between two quantities. ★ b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
F-BF.1.1.b
Functions Logo. f(x)
Write a function that describes a relationship between two quantities. ★ c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
F-BF.1.1.c
IFInterpreting Functions
IFInterpreting Functions
Functions Logo. f(x)
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. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F-IF.1.1
Functions Logo. f(x)
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ★
F-IF.2.4
Functions Logo. f(x)
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.
F-IF.3.7.a
Functions Logo. f(x)
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★ e. Graph exponential showing intercepts and end behavior.
F-IF.3.7.e
Functions Logo. f(x)
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
F-IF.3.9
Functions Logo. f(x)
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F-IF.1.2
Functions Logo. f(x)
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble engines in a factory, then the positive integers would be an appropriate domain for the function. ★
F-IF.2.5
Functions Logo. f(x)
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★ b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
F-IF.3.7.b
Functions Logo. f(x)
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. 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.
F-IF.3.8.a
Functions Logo. f(x)
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n is greater than or equal to 1.
F-IF.1.3
Functions Logo. f(x)
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. ★
F-IF.2.6
Functions Logo. f(x)
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★ c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
F-IF.3.7.c
Functions Logo. f(x)
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = 1.02^t, y = 0.97^t, y = 1.01^12t, y = 1.2^(t/10), and classify them as representing exponential growth or decay.
F-IF.3.8.b
LELinear, Quadratic, and Exponential Models
LELinear, Quadratic, and Exponential Models
Functions Logo. f(x)
Distinguish between situations that can be modeled with linear functions and with exponential functions. ★ a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
F-LE.1.1.a
Functions Logo. f(x)
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). ★
F-LE.1.2
Functions Logo. f(x)
Distinguish between situations that can be modeled with linear functions and with exponential functions. ★ b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F-LE.1.1.b
Functions Logo. f(x)
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. ★
F-LE.1.3
Functions Logo. f(x)
Distinguish between situations that can be modeled with linear functions and with exponential functions. ★ c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F-LE.1.1.c
Functions Logo. f(x)
Interpret the parameters in a linear or exponential function in terms of a context. ★
F-LE.2.5
QQuantities
QQuantities
Number and Quantity Logo
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. ★
N-Q.1.1
Number and Quantity Logo
Define appropriate quantities for the purpose of descriptive modeling. ★
N-Q.1.2
Number and Quantity Logo
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. ★
N-Q.1.3
RNThe Real Number System
RNThe Real Number System
Number and Quantity Logo
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^3 = 5^((1/3)*3) to hold, so (5^(1/3))^3 must equal 5.
N-RN.1.1
Number and Quantity Logo
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
N-RN.1.2
Number and Quantity Logo
Explain why the sum or product of two 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.
N-RN.2.3
IDInterpreting Categorical and Quantitative Data
IDInterpreting Categorical and Quantitative Data
Statistics and Probability Logo. Includes four types of graphs.
Represent data with plots on the real number line (dot plots, histograms, and box plots). ★
S-ID.1.1
Statistics and Probability Logo. Includes four types of graphs.
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. ★
S-ID.2.5
Statistics and Probability Logo. Includes four types of graphs.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. ★ c. Fit a linear function for a scatter plot that suggests a linear association.
S-ID.2.6.c
Statistics and Probability Logo. Includes four types of graphs.
Distinguish between correlation and causation. ★
S-ID.3.9
Statistics and Probability Logo. Includes four types of graphs.
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. ★
S-ID.1.2
Statistics and Probability Logo. Includes four types of graphs.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. ★ a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, and exponential models.
S-ID.2.6.a
Statistics and Probability Logo. Includes four types of graphs.
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. ★
S-ID.3.7
Statistics and Probability Logo. Includes four types of graphs.
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). ★
S-ID.1.3
Statistics and Probability Logo. Includes four types of graphs.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. ★ b. Informally assess the fit of a function by plotting and analyzing residuals.
S-ID.2.6.b
Statistics and Probability Logo. Includes four types of graphs.
Compute (using technology) and interpret the correlation coefficient of a linear fit. ★
S-ID.3.8
Additional Course Resources
Additional Course Resources
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Algebra 1 EOC Practice
Algebra 1 EOC Practice
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Click on this text to download the Answer KEY for the PARCC Summative for Algebra I.
PARCC Spring 2016 Answer KEY Paper Based Practice
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Three additional Algebra 1 EOC test prep resources with answer keys.
More Algebra 1 EOC Practice
Document symbol in gray on a green background.
Click on this text to download the PARCC Summative Practice Test for Algebra I.
PARCC Spring 2016 Paper Based Practice