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LSU College Readiness Program
COURSE PROFILE with CCSS
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COURSE/UNIT CREDIT:
GRADE(S):
PREREQUISITE(S):
High School Algebra I
Algebra 1 in MyMathLab
Elayn Martin-Gay, with contributions from Robert Blitzer
1 Carnegie Unit
7, 8, or 9
Completion of 8th grade math or placement by high school
CHAPTERS
1 - Review of Real Numbers
2 - Solving Equations and Problem Solving
3 - Graphs and Functions
4 - Solving Inequalities and Absolute Value
Equations and Inequalities
5 - Solving Systems of Linear Equations and
Inequalities
6 - Exponents and Polynomials
7 - Factoring Polynomials
8 - Rational Expressions
9 – Roots and Radicals
10 - Quadratic Equations
SECTION NAMES (NUMBER OF EXERCISES), LEARNING OBJECTIVES, AND
CCSS CORRELATIONS
CHAPTER 1: Review of Real Numbers
8.NS.A.1
1.2 Symbols and Sets of Numbers (47)
Use a number line to order numbers
6.NS.C.5
Translate sentences into mathematical statements
6.NS.C.7
Use integers to express values in statements
6.EE.A.2
Use a graph to answer questions
Identify types of numbers
Determine if a statement is true or false
Order numbers involving absolute value
6.NS.A.1
1.3 Fractions (51)
5.NF.A.1
Write numbers as products of primes
5.NF.A.2
Write fractions in simplest form
5.NF.B.6
Multiply and divide fractions
Add and subtract fractions
Write equivalent fractions
7.EE.B.4
1.4 Variable Expressions and Equations (52)
Evaluate expressions with exponents
6.EE.A.1
Simplify expressions using the order of operations
6.EE.A.2
Evaluate algebraic expressions, given replacement values for variables
6.EE.A.3
Determine whether a number is a solution of a given equation
6.EE.B.5
Translate phrases to algebraic expressions
Translate sentences to equations or inequalities
1
1.5 Adding Real Numbers (47)
Add real numbers with the same sign
Add real numbers with unlike signs
Solve problems that involve addition of real numbers
Find the opposite of a number
Determine if a given number is a solution to a given equation
1.6 Subtracting Real Numbers (48)
Subtract real numbers
Add and subtract real numbers
Evaluate algebraic expressions using real numbers
Solve problems that involve subtraction of real numbers
Determine if a given number is a solution to a given equation
1.7 Adding and Subtracting Matrices (13)
Use matrix notation
Find the value of the variables that will make the matrices equal
Add and subtract matrices
Solve problems involving addition and subtraction of matrices
1.8 Multiplying and Dividing Real Numbers (73)
Multiply real numbers
Simplify using the order of operations
Identify the reciprocal of a real number
Divide real numbers
Simplify using the order of operations
Evaluate algebraic expressions using real numbers
Determine if a given number is a solution to a given equation
1.9 Properties of Real Numbers (51)
Vocabulary and Readiness Check
Use the commutative and associative properties
Use the distributive property
Name the properties illustrated by the statements
1.4,5,6,8 Real Life Linear Relationships (23)
Evaluate algebraic expressions, given replacement values for variables
Solve problems that involve addition of real numbers
Solve problems that involve subtraction of real numbers
Multiply real numbers
1.10 Data: Probability and Odds (29)
Compute theoretical probability
Understand and use odds
Determine effects of linear transformations of data
Determine effects of outliers
2
7.NS.A.1
7.NS.A.2
6.EE.B.5
7.NS.A.1
7.NS.A.2
6.EE.A.2
6.EE.B.5
N-VM.C.6(+)
N-VM.C.7(+)
7.NS.A.1
7.NS.A.2
6.EE.A.2
6.EE.B.5
N-VM.C.7(+)
A-SSE.A.2
7.EE.A.1
7.NS.A.1
7.NS.A.3
S-ID.C.8
7.SP.C.5
7.SP.C.7
CHAPTER 2: Solving Equations and Problem Solving
2.1 Simplifying Algebraic Expressions (57)
Combine like terms
Use the distributive property to remove parentheses
Write word phrases as algebraic expressions
Name the properties illustrated by the statements
Review and Preview
2.2 Addition Property of Equality (54)
Use the addition property of equality to solve linear equations
Simplify an equation and then use the addition property of equality
Write word phrases as algebraic expressions
2.3 Multiplication Property of Equality (53)
Use the multiplication property of equality to solve linear equations
Use addition and multiplication properties of equality to solve linear equations
Write word phrases as algebraic expressions
2.4 Solving Multi-step Equations (40)
Apply a general strategy for solving a linear equation
Solve equations containing fractions
Write word phrases as algebraic expressions
2.5 Introduction to Problem Solving (33)
Solve problems involving direct translations
Solve problems involving relationships among unknown quantities
Solve problems involving consecutive integers
2.6 Formulas and Problem Solving (45)
Substitute values into a formula and solve for the unknown variable
Solve a formula for one of its variables
Use formulas to solve problems
2.7 Percent and Problem Solving (36)
Solve percent equations
Solve discount and mark-up problems
Solve percent increase and percent decrease problems
2.8 Mixture and Distance Problem Solving (21)
Solve mixture problems
Solve uniform motion problems
CHAPTER 3: Graphs and Functions
3.1 Reading Graphs and Rectangular Coordinate System (54)
Read bar and line graphs
Define the rectangular coordinate system and plot ordered pairs of numbers
Graph paired data to create a scatter diagram and determine correlation
Determine whether an ordered pair is a solution of an equation in two
variables
Find missing coordinate of an ordered pair solution given one coordinate of
the pair
Interpret information given in a scatter plot
3
A-APR.A.1
A-SSE.A.1a
6.EE.A.2
6.EE.A.3
7.EE.A.1
A-REI.A.1
A-REI.B.3
6.EE.B.6
A-REI.A.1
A-REI.B.3
6.EE.B.6
A.REI.A.1
A-REI.B.3
8.EE.C.7a
6.EE.B.6
A-REI.B.3
A-CED.A.1
N-Q.A.1
A-CED.A.4
A-REI.B.3
7.RP.A.3
N-Q.A.1
A-CED.A.1
A-CED.A.3
A-REI.B.3
S-ID.C.9
8.SP.A.1
6.EE.B.5
3.2 Graphing Linear Equations (38)
Identify linear equations
Graph an equation by finding and plotting ordered pair solutions
Solve application problems
3.3 Intercepts (35)
Identify intercepts of a graph
Graph a linear equation by finding and plotting intercepts
Identify and graph vertical and horizontal lines
3.4a Slope and Rate of Change (37)
Find the slope of a line given points on the line
Find the slopes of horizontal and vertical lines
Find the slope of a line given its equation
Compare the slopes of parallel and perpendicular lines
Slope as a rate of change
3.4b Slope and Rate of Change - Review and Preview (20)
Slope as a rate of change
3.5a Equations of a Line (25)
Use the slope-intercept form to write an equation of a line
Use the slope-intercept form to graph a linear equation
Use the point-slope form to find equation of line given slope and a point on
the line
Use the point-slope form to find an equation of a line given two points of the
line
Find equations of vertical and horizontal lines
3.5b Equations of a Line - Review and Preview (23)
Use the point-slope form to solve problems
3.6a Functions (28)
Identify relations, domains, and ranges
Identify functions
Use the vertical line test
Use function notation
3.6b Function Review and Graphing Functions (30)
Identify relations, domains, and ranges
Graph linear functions
Graph linear functions by finding intercepts
Graph vertical and horizontal lines
Decide whether a situation describes a linear function
4
A-REI.D.10
F-IF.C.7a
A-REI.D.10
F-IF.C.7a
F-IF.B.6
F-LE.B.5
S-ID.C.7
A-REI.D.10
G-GPE.B.5
8.EE.B.6
F-IF.B.6
F-LE.B.5
S-ID.C.7
G-GPE.B.5
A-REI.D.10
A-CED.A.2
G-GPE.B.5
A-CED.A.2
G-GPE.B.5
F-LE.A.1b
F-LE.A.2
F-LE.B.5
F-IF.A.1
F-IF.A.2
F-IF.A.1
F-IF.A.2
F-IF.B.5
F-IF.C.7a
F-BF.A.1a
F-BF.B.3
F-IF.A.2
3.7 Graphing Functions (25)
Graph piecewise-defined functions
F-IF.C.7ab
Use vertical and horizontal shifts to graph a function
F-BF.B.3
Use function notation
A-REI.D.10
Graph nonlinear equations
Vertical and horizontal shifts
CHAPTER 4: Solving Inequalities and Absolute Value Equations and Inequalities
A-CED.A.1
4.1 Linear Inequalities and Problem Solving (40)
Graph inequalities on number lines
A-REI.B.3
Solve inequalities
Solve inequality applications
A-REI.B.3
4.2 Compound Inequalities (49)
Find the union of two sets
Find the intersection of two sets
Solve compound inequalities involving or
Solve compound inequalities involving and
A-REI.B.3
4.3 Absolute Value Equations (42)
Solve absolute value equations
A-REI.B.3
4.4a Absolute Value Inequalities (29)
Solve absolute value inequalities of the form |x|
Solve absolute value inequalities of the form |x|>a
A-REI.B.3
4.4b Absolute Value Inequalities (26)
Solve absolute value inequalities of the form |x|
Solve absolute value inequalities of the form |x|>a
Mixed Practice
A-REI.D.12
4.5a Graphing Linear Inequalities (25)
Determine ordered pairs that are solutions to linear inequalities in two
variables
Graph linear inequalities in two variables
A-REI.D.12
4.5b Graphing Linear Inequalities (12)
Review and Preview
CHAPTER 5: Solving Systems of Linear Equations and Inequalities
5.1 Systems of Linear Equations by Graphing (36)
Determine if an ordered pair is a solution of a system of equations in two
variables
Solve a system of linear equations by graphing
Without graphing, determine the number of solutions of a system
5.2 Systems of Linear Equations by Substitution (29)
Use the substitution method to solve a system of linear equations
5.3a Systems of Linear Equations by Addition (20)
Use the addition method to solve a system of linear equations
5.3b Systems of Linear Equations by Addition (19)
Use the substitution method to solve a system of linear equations
5
A-REI.C.6
A-REI.C.6
A-REI.C.6
A-REI.C.6
5.4a Systems of Linear Equations and Problem Solving (15)
Choose a solution that satisfies the given conditions
Write a system of equations to describe a situation
Use a system of equations to solve problems
5.4b Systems of Linear Equations and Problem Solving (16)
Choose a solution that satisfies the given conditions
Write a system of equations to describe a situation
Use a system of equations to solve problems
5.5 Systems of Linear Inequalities (23)
Solve systems of linear inequalities
Use mathematical models involving linear inequalities
5.6a Frequency Distributions (6)
Organize and present data using frequency distributions
5.6b Statistical Graphs (15)
Answer questions involving concepts and/or definitions
Make data displays to convey information about data
Construct a frequency distribution and/or statistical graphs
Use a given statistical graph to answer questions
Organize and present data using histograms and frequency polygons
5.7a Mean, Median, Mode and Trends in Statistics (23)
Calculate mean, median, and mode
Determine effects of linear transformations of data
Work with box plots
Use box plots to discuss and compare data sets
Determine the median, first and third quartiles, and interquartile range of a
data set
Work with measures of central tendency
5.7b Review Mean, Median, Mode, and Range (15)
Review mean, median, and mode
Determine the range for a data set
Calculate mean, median, and mode
5.7c Standard Deviation for a Data Set (11)
Determine the standard deviation for a data set
CHAPTER 6: Exponents and Polynomials
6.1a Exponents (12)
Evaluate exponential expressions
6.1b Properties of Exponents (35)
Use the product rule for exponents
Use the power rules for products and quotients
Use the quotient rule for exponents, and define a number raised to the 0
power
Decide which rule(s) to use to simplify an expression
6.1c Negative Exponents (34)
Simplify expressions containing negative exponents
Use all the rules and definitions for exponents to simplify exponential
expressions
6
A-REI.C.6
A-CED.A.3
A-REI.C.6
A-CED.A.3
A-REI.C.6
A-CED.A.3
S-ID.A.1
S-ID.A.1
S-ID.A.2
S-ID.A.3
6.SP.B.5c
S-ID.A.2
8.EE.A.1
8.EE.A.1
8.EE.A.1
6.1d The Meaning of a^(1/n) Rational Exponents (11)
Understand the meaning of a^(1/n)
Understand the meaning of a^(m/n)
Simplify expressions containing negative exponents
6.1e Rational Exponents (12)
Understand the meaning of a^(m/n)
Understand the meaning of a^(1/n)
Solve equations of the form b^x = b^y
6.2a Adding and Subtracting Polynomials (35)
Vocabulary and Readiness Check
Define polynomial, monomial, binomial, trinomial, and degree
Find the value of a polynomial given replacement values for the variables
Simplify a polynomial by combining like terms
Add and subtract polynomials
6.2b Adding and Subtracting Polynomials (29)
Define polynomial, monomial, binomial, trinomial, and degree
Find the value of a polynomial given replacement values for the variables
Simplify a polynomial by combining like terms
Add and subtract polynomials
6.3a Multiplying Polynomials (26)
Use the distributive property to multiply polynomials
Multiply polynomials vertically
6.3b Multiplying Polynomials (27)
Use the distributive property to multiply polynomials
Multiply polynomials vertically
6.4a Special Products (24)
Multiply two binomials using the FOIL method
Square a binomial
6.4b Special Products (14)
Multiply the sum and difference of two terms
6.4c Special Products (11)
Square a binomial
6.4d Special Products – Distributive Property (14)
Multiply the sum and difference of two terms
6.4e Special Products - Review and Extension (22)
Multiply the sum and difference of two terms
Square a binomial
Use the distributive property to find the product of two polynomials
6.5a Scientific Notation and Review of Negative Exponents (44)
Simplify expressions containing negative exponents
Use all the rules and definitions for exponents to simplify exponential
expressions
6.5b Computing Scientific Notation (10)
Perform operations on numbers written in scientific notation
Compute, using scientific notation
7
N-RN.A.1
N-RN.A.2
N-RN.A.1
N-RN.A.2
A-SSE.A.1a
A-APR.A.1
A-SSE.A.1a
A-APR.A.1
A-APR.A.1
A-APR.A.1
A-APR.A.1
A-SSE.A.2
A-APR.A.1
A-SSE.A.2
A-APR.A.1
A-SSE.A.2
A.APR.A.1
A-SSE.A.2
A-APR.A.1
A-SSE.A.2
8.EE.A.1
8.EE.A.4
8.EE.A.4
F-BF.B.3
F-LE.A.2
F-IF-C.7e
6.6a Graphing Exponential Functions (23)
Graph exponential functions
Graph transformations of exponential functions
6.6b Compound Interest Formula - Review and Preview (38)
Graph exponential functions
Graph transformations of exponential functions
Use the compound interest formula
6.7 Exponential Growth and Decay Functions (14)
Model exponential growth
Model exponential decay
Model exponential decay with half-life
6.8a Dividing Polynomials (25)
Divide a polynomial by a monomial
Use long division to divide a polynomial by another polynomial
Use synthetic division to divide a polynomial by a binomial
Use the remainder theorem to evaluate polynomials
6.8b Dividing Polynomials - Review and Extension (18)
Use synthetic division to divide a polynomial by a binomial
Use the remainder theorem to evaluate polynomials
Divide a polynomial by a monomial
Use long division to divide a polynomial by another polynomial
CHAPTER 7: Factoring Polynomials
7.1a Greatest Common Factor and Factoring (27)
Find the greatest common factor of a list of integers
Factor out the greatest common factor from a polynomial
7.1b Factoring Four-term Polynomials by Grouping (16)
Factor a polynomial by grouping
Factor out the greatest common factor from a polynomial
7.1c Factoring - Review and Preview (16)
Find the greatest common factor of a list of integers
Factor out the greatest common factor from a polynomial
Factor a polynomial by grouping
Factor out the greatest common factor from a polynomial
7.2a Factoring Trinomials of the Form x^2+bx+c (27)
Factor trinomials of the form x^2+bx+c
Factor out greatest common factor and factor a trinomial of the form
x^2+bx+c
7.2b Factoring Trinomials of the Form x^2+bx+c (21)
Factor out greatest common factor and factor a trinomial of the form
x^2+bx+c
7.5a Factoring Binomials (22)
Factor the difference of two squares
Factor the sum or difference of two cubes
Factor other binomials
7.5b Factoring Binomials (21)
Factor other binomials
8
F-BF.B.3
F-LE.A.2
F-IF.C.7e
A-SSE.B.3c
F-LE.A.1c
A-APR.B.2
A-APR.D.6
A-APR.B.2
A-APR.D.6
A-SSE.A.1
A-SSE.A.2
A-SSE.A.2
A-SSE.A.1
A-SSE.A.2
A-APR.A.1
A-SSE.A.2
A-SSE.A.1a
A-SSE.A.2
A-APR.A.1
A-SSE.A.2
A-SSE.A.2
7.6a Solving Quadratic Equations (22)
Use the zero factor theorem
Solve quadratic equations by factoring
7.6b Solving Quadratic Equations (22)
Solve equations with degree greater than 2 by factoring
Solve quadratic equations by factoring
Find the x-intercepts of the graph of a quadratic equation in two variables
7.7 Solving Quadratic Equations by Problem Solving (33)
Solve problems that can be modeled by quadratic equations
CHAPTER 8: Rational Express
8.1a Simplifying Rational Expressions (11)
Find the value of a rational expression given a replacement number
Identify values for which a rational expression is undefined
Simplify or write rational expressions in lowest terms
8.1b Simplifying Rational Expressions (22)
Simplify or write rational expressions in lowest terms
Simplify expressions with 4-term polynomials and sums and differences of
cubes
8.2a Multiplying and Dividing Rational Expressions (15)
Multiply rational expressions
Divide rational expressions
Multiply or divide rational expressions
8.2b Multiplying and Dividing Rational Expressions (14)
Multiply or divide rational expressions
8.3 Adding and Subtracting Rational Expressions – Basic (8)
Add and subtract rational expressions with the same denominator
8.5 Equations Containing Rational Expression (30)
Solve equations containing rational expressions
Solve equations containing rational expressions for a specified variable
8.6a Proportions and Problem Solving with Rational Numbers (25)
Solve proportions
Use proportions to solve problems
Solve problems about numbers
Solve problems about work
Solve problems about distance
8.6b Proportions and Problem Solving with Rational Numbers (25)
Use proportions to solve problems
Solve problems about work
Solve problems about distance
A-REI.B.4b
A-SSE.A.1a
A-SSE.A.2
A-SSE.B.3a
A-APR.B.3
A-REI.B.4b
A-CED.A.1
A-REI.B.4b
A-APR.D.6
A-APR.D.6
A-APR.D.7(+)
A-APR.D.7(+)
A-APR.D.7(+)
A-CED.A.1
A-REI.A.2
N-Q.A.1
A-CED.A.1
A-REI.A.3
G-SRT.B.5
A-CED.A.1
A-REI.A.3
G-SRT.B.5
F-IF.B.6
A-CED.A.2
F-BF.A.1a
A-CED.A.1
7.RP.A.2bc
8.7 Variation and Problem Solving (28)
Solve problems involving direct variation
Solve problems involving inverse variation
Other types of direct and inverse variation
Solve applications involving variation
9
8.8a Operations with Complex Numbers (11)
Add or subtract complex numbers
Multiply complex numbers
Reading Assessment Questions for eText section
8.8b Operations with Complex Numbers (11)
Divide complex numbers
Multiply complex numbers
CHAPTER 9: Roots and Radicals
9.1a Radicals and Radical Functions (41)
Evaluate square roots
Evaluate cube roots
Evaluate nth roots
Approximate square roots
Solve application problems
Simplify radicals containing variables
9.1b Radicals and Radical Functions (13)
Find function values of square and cube roots
Graph square and cube root functions
9.2a Simplifying Radicals (27)
Use the product rule to simplify square roots
Use the quotient rule and the product rule to simplify square roots
Simplify radicals containing variables
9.2b Simplifying Radicals (27)
Simplify radicals containing variables
Simplify higher roots
Solve application problems
9.3 Adding and Subtracting Radicals (32)
Add or subtract like radicals
Simplify radical expressions, and then add or subtract any like radicals
9.4 Multiplying and Dividing Radicals (45)
Multiply radicals
Divide radicals
Rationalize denominators
Rationalize denominators using conjugates
Simplify radical expressions
9.5 Solving Equations Containing Radicals (18)
Solve radical equations by using the squaring property of equality once
9.6 Radical Equations and Problem Solving (35)
Use the Pythagorean formula to solve problems
Use the converse of the Pythagorean Theorem
Use the distance formula
Use the midpoint formula
Solve problems using formulas containing radicals
9.7 Radicals, Negative Numbers, and Graphing Complex Numbers (11)
Write square roots of negative numbers in the form bi
Evaluate cube roots
Graph complex numbers on the complex plane
10
N-CN.A.1
N-CN.A.2
N-CN.A.1
N-CN.A.2
N-RN.A.1
N-RN.A.2
F-IF.C.7b
F-IF.A.2
N-RN.A.2
N-RN.A.2
N-RN.A.2
N-RN.A.2
A-CED.A.1
A-REI.A.2
A-CED.A.1
A-CED.A.4
8.G.B.7
8.G.B.8
N-CN.A.1
N-CN.B.4(+)
N-RN.A.2
9.8 Scatterplots (13)
Determine an appropriate function for modeling data
Find a correlation coefficient and/or interpret aspects of a linear relationship
Determine whether linear, quadratic, or exponential curve best fits
scatterplot/data
Define terms related to correlation and regression
Identify factors that contribute to random component of linear regression
model
Calculate the correlation coefficient of data
CHAPTER 10: Quadratic Equations
10.1 Quadratics: Using the Square Root Property (27)
Use the square root property to solve quadratic equations
Solve problems modeled by quadratic equations
10.2 Quadratics: Completing the Square (30)
Write perfect square trinomials
Solve quadratic equations of the form x^2+bx+c=0 by completing the square
Solve quadratic equations of the form ax^2+bx+c=0 by completing the
square
10.3a Quadratics: Using the Quadratic Formula (15)
Use the quadratic formula to solve quadratic equations
10.3b Quadratics: Using the Quadratic Formula (25)
Use the quadratic formula to solve quadratic equations
Approximate solutions to quadratic equations
Determine the number of solutions of a quadratic equation using the
discriminant
Solve quadratic equations by using the quadratic formula
Determine number and type of solutions of quadratic equation using
discriminant
Solve geometric problems modeled by quadratic equations
10.3c Quadratic Formula - Review and Extension (18)
Solve geometric problems modeled by quadratic equations
10.4a Graphing Quadratic Equations (24)
Graph quadratic equations of the form y=ax^2
Use the vertex formula to help graph quadratic equations of the form
y=ax^2+bx+c
10.4b The Parabola and Circle Graphs (15)
Determine an appropriate function for modeling data
Graph quadratic equations of the form y=ax^2
Use the vertex formula to help graph quadratic equations of the form
y=ax^2+bx+c
Graph circles of the form (x-h)^2+(y-k)^2 =r^2
Write the equation of a circle, given its center and radius
10.4c The Parabola and Circle Graphs (11)
Find centers and radii of circles or vertices of parabolas, given the equation
11
S-ID.B.6
A-REI.B.4b
A-SSE.A.2
A-SSE.B.3b
A-REI.B.4
A-REI.B.4b
N-CN.C.7
A-REI.4b
N-CN.C.7
A-CED.A.3
A-REI.B.4b
A-SSE.A.1
N-CN.C.7
A.CED.A.1
A-CED.A.3
F-IF.C.7a
F-BF.B.3
F-IF.C.7a
F-IF.C.8a
S-ID.B.6
G-GPE.A.1
F-IF.C.7a
F-IF.C.8a
G-GPE.A.1
10.5 Linear, Quadratic, and Exponential Models (17)
Determine an appropriate function for modeling data
Solve application exercises involving exponential, linear, and quadratic
models
Solve problems modeled by exponential equations
A.C The Fundamental Counting Principle (12)
Use Fundamental Counting Principle to find number of possible outcomes
Solve Critical Thinking Exercises
A.D Permutations (27)
Use the Fundamental Counting Principle to count permutations
Evaluate factorial expressions
Use the permutations formula
Find the number of permutations of duplicate items
Solve Critical Thinking Exercises
A.E Combinations (26)
Distinguish between permutation and combination problems
Use the combinations formula
Solve problems involving combinations
Solve Critical Thinking Exercises
A.F Arithmetic and Geometric Sequences (28)
Identify arithmetic sequences and their common differences
Identify geometric sequences and their common ratios
Determine if a sequence is arithmetic or geometric
S-ID.B.6
F-IF.A.2
A-CED.A.2
F-BF.A.2
F-LE.A.2
CCSS for Algebra I that are not reflected in MyMathLab course exercises:
CCSS#
Standard Description
Comment
Explain why the sum or product of two rational numbers is rational; Not included in
N-RN.B.3
N-Q.A.2
N-Q.A.3
A-REI.C.5
A-REI.D.11
F-IF.A.3
F-IF.B.4
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.
Define appropriate quantities for the purpose of descriptive
modeling.
Choose a level of accuracy appropriate to limitations on
measurement when reporting quantities.
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.
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.★
the course.
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 ≥ 1.
For a function that models a relationship between two quantities,
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F-IF.C.9
F-LE.A.1a
F-LE.A.3
S-ID.B.5
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.★
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.
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.
Observe using graphs and tables that a quantity increasing
exponentially eventually exceeds a quantity increasing linearly,
quadratically, or (more generally) as a polynomial function.
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.
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