Skill plan for TEKS Resource System - Precalculus
IXL provides skill alignments with recommended IXL skills for each unit. Find the IXL skills that are right for you below!
Unit
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1
Unit 1
Graphs, Attributes, and Applications of Functions
2 - The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
D:  describe symmetry of graphs of even and odd functions
D:  describe symmetry of graphs of even and odd functions
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
Polynomial functions
Rational functions
Exponential and logarithmic functions
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
Polynomial functions
Rational functions
Exponential and logarithmic functions
J:  analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems
J:  analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems
L:  determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities
L:  determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities
M:  describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities
M:  describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities
N:  analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems
N:  analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems
2
Unit 2
Composition and Inverses of Functions
2 - The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
A:  use the composition of two functions to model and solve real-world problems
A:  use the composition of two functions to model and solve real-world problems
B:  demonstrate that function composition is not always commutative
B:  demonstrate that function composition is not always commutative
C:  represent a given function as a composite function of two or more functions
C:  represent a given function as a composite function of two or more functions
E:  determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations
Find values of inverse functions
Find inverse functions
E:  determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations
Find values of inverse functions
Find inverse functions
3
Unit 3
Polynomial and Power Functions, Equations, and Inequalities
2 - The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
G:  graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems
G:  graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
J:  analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems
J:  analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems
N:  analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems
N:  analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems
5 - The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.
J:  solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and real-world problems
Solve equations
Roots of polynomials
Polynomial division
J:  solve polynomial equations with real coefficients by applying a variety of techniques in mathematical and real-world problems
Solve equations
Roots of polynomials
Polynomial division
K:  solve polynomial inequalities with real coefficients by applying a variety of techniques and write the solution set of the polynomial inequality in interval notation in mathematical and real-world problems
K:  solve polynomial inequalities with real coefficients by applying a variety of techniques and write the solution set of the polynomial inequality in interval notation in mathematical and real-world problems
4
Unit 4
Rational Functions, Equations, and Inequalities
2 - The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
G:  graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems
G:  graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
J:  analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems
J:  analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems
K:  analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes
K:  analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes
L:  determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities
L:  determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities
M:  describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities
M:  describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities
N:  analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems
N:  analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems
5 - The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.
L:  solve rational inequalities with real coefficients by applying a variety of techniques and write the solution set of the rational inequality in interval notation in mathematical and real-world problems
L:  solve rational inequalities with real coefficients by applying a variety of techniques and write the solution set of the rational inequality in interval notation in mathematical and real-world problems
5
Unit 5
Exponential and Logarithmic Functions and Equations
2 - The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
E:  determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations
Find values of inverse functions
Find inverse functions
E:  determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations
Find values of inverse functions
Find inverse functions
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
G:  graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems
G:  graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
J:  analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems
J:  analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems
N:  analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems
N:  analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems
5 - The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.
G:  use the properties of logarithms to evaluate or transform logarithmic expressions
Evaluate logarithms
Change of base formula
Properties of logarithms
G:  use the properties of logarithms to evaluate or transform logarithmic expressions
Evaluate logarithms
Change of base formula
Properties of logarithms
H:  generate and solve logarithmic equations in mathematical and real-world problems
H:  generate and solve logarithmic equations in mathematical and real-world problems
I:  generate and solve exponential equations in mathematical and real-world problems
I:  generate and solve exponential equations in mathematical and real-world problems
6
Unit 6
Sequences, Series, and Binomial Expansion
5 - The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.
A:  evaluate finite sums and geometric series, when possible, written in sigma notation
A:  evaluate finite sums and geometric series, when possible, written in sigma notation
B:  represent arithmetic sequences and geometric sequences using recursive formulas
B:  represent arithmetic sequences and geometric sequences using recursive formulas
C:  calculate the nth term and the nth partial sum of an arithmetic series in mathematical and real-world problems
Sums of finite series
Partial sums of infinite series
C:  calculate the nth term and the nth partial sum of an arithmetic series in mathematical and real-world problems
Sums of finite series
Partial sums of infinite series
D:  represent arithmetic series and geometric series using sigma notation
D:  represent arithmetic series and geometric series using sigma notation
E:  calculate the nth term of a geometric series, the nth partial sum of a geometric series, and sum of an infinite geometric series when it exists
Nth terms
Partial sums
Sums and convergence
Repeating decimals
E:  calculate the nth term of a geometric series, the nth partial sum of a geometric series, and sum of an infinite geometric series when it exists
Nth terms
Partial sums
Sums and convergence
Repeating decimals
F:  apply the Binomial Theorem for the expansion of (a + b)n in powers of a and b for a positive integer n, where a and b are any numbers
F:  apply the Binomial Theorem for the expansion of (a + b)n in powers of a and b for a positive integer n, where a and b are any numbers
7
Unit 7
Problem Solving with Trigonometric Ratios
2 - The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
P:  determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems
P:  determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems
4 - The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.
E:  determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical and real-world problems
Find trigonometric ratios
Solve problems involving trigonometric ratios
E:  determine the value of trigonometric ratios of angles and solve problems involving trigonometric ratios in mathematical and real-world problems
Find trigonometric ratios
Solve problems involving trigonometric ratios
F:  use trigonometry in mathematical and real-world problems, including directional bearing
F:  use trigonometry in mathematical and real-world problems, including directional bearing
G:  use the Law of Sines in mathematical and real-world problems
G:  use the Law of Sines in mathematical and real-world problems
H:  use the Law of Cosines in mathematical and real-world problems
H:  use the Law of Cosines in mathematical and real-world problems
8
Unit 8
Trigonometric Functions
2 - The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
E:  determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations
E:  determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
F:  graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions
G:  graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems
G:  graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems
H:  graph arcsin x and arccos x and describe the limitations on the domain
H:  graph arcsin x and arccos x and describe the limitations on the domain
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
I:  determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing
O:  develop and use a sinusoidal function that models a situation in mathematical and real-world problems
Sine functions
Cosine functions
O:  develop and use a sinusoidal function that models a situation in mathematical and real-world problems
Sine functions
Cosine functions
P:  determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems
P:  determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems
4 - The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.
A:  determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical and real-world problems
A:  determine the relationship between the unit circle and the definition of a periodic function to evaluate trigonometric functions in mathematical and real-world problems
B:  describe the relationship between degree and radian measure on the unit circle
B:  describe the relationship between degree and radian measure on the unit circle
C:  represent angles in radians or degrees based on the concept of rotation and find the measure of reference angles and angles in standard position
C:  represent angles in radians or degrees based on the concept of rotation and find the measure of reference angles and angles in standard position
D:  represent angles in radians or degrees based on the concept of rotation in mathematical and real-world problems, including linear and angular velocity
D:  represent angles in radians or degrees based on the concept of rotation in mathematical and real-world problems, including linear and angular velocity
9
Unit 9
Trigonometric Equations and Identities
5 - The student uses process standards in mathematics to evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.
M:  use trigonometric identities such as reciprocal, quotient, Pythagorean, cofunctions, even/odd, and sum and difference identities for cosine and sine to simplify trigonometric expressions
M:  use trigonometric identities such as reciprocal, quotient, Pythagorean, cofunctions, even/odd, and sum and difference identities for cosine and sine to simplify trigonometric expressions
N:  generate and solve trigonometric equations in mathematical and real-world problems
N:  generate and solve trigonometric equations in mathematical and real-world problems
10
Unit 10
Vectors
4 - The student uses process standards in mathematics to apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.
C:  represent angles in radians or degrees based on the concept of rotation and find the measure of reference angles and angles in standard position
C:  represent angles in radians or degrees based on the concept of rotation and find the measure of reference angles and angles in standard position
F:  use trigonometry in mathematical and real-world problems, including directional bearing
F:  use trigonometry in mathematical and real-world problems, including directional bearing
I:  use vectors to model situations involving magnitude and direction
Component form of a vector
Vector sums
Unit vectors
I:  use vectors to model situations involving magnitude and direction
Component form of a vector
Vector sums
Unit vectors
J:  represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically
Vector sums
Scalar multiples
J:  represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically
Vector sums
Scalar multiples
K:  apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems
K:  apply vector addition and multiplication of a vector by a scalar in mathematical and real-world problems
11
Unit 11
Parametric Equations
3 - The student uses the process standards in mathematics to model and make connections between algebraic and geometric relations.
A:  graph a set of parametric equations
A:  graph a set of parametric equations
B:  convert parametric equations into rectangular relations and convert rectangular relations into parametric equations
B:  convert parametric equations into rectangular relations and convert rectangular relations into parametric equations
C:  use parametric equations to model and solve mathematical and real-world problems
C:  use parametric equations to model and solve mathematical and real-world problems
12
Unit 12
Polar Equations
3 - The student uses the process standards in mathematics to model and make connections between algebraic and geometric relations.
D:  graph points in the polar coordinate system and convert between rectangular coordinates and polar coordinates
D:  graph points in the polar coordinate system and convert between rectangular coordinates and polar coordinates
E:  graph polar equations by plotting points and using technology
E:  graph polar equations by plotting points and using technology
13
Unit 13
Conics
3 - The student uses the process standards in mathematics to model and make connections between algebraic and geometric relations.
B:  convert parametric equations into rectangular relations and convert rectangular relations into parametric equations
B:  convert parametric equations into rectangular relations and convert rectangular relations into parametric equations
C:  use parametric equations to model and solve mathematical and real-world problems
C:  use parametric equations to model and solve mathematical and real-world problems
F:  determine the conic section formed when a plane intersects a double-napped cone
F:  determine the conic section formed when a plane intersects a double-napped cone
G:  make connections between the locus definition of conic sections and their equations in rectangular coordinates
G:  make connections between the locus definition of conic sections and their equations in rectangular coordinates
H:  use the characteristics of an ellipse to write the equation of an ellipse with center (h, k)
H:  use the characteristics of an ellipse to write the equation of an ellipse with center (h, k)
I:  use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k)
I:  use the characteristics of a hyperbola to write the equation of a hyperbola with center (h, k)
This document includes the IXL® skill alignments to Texas Curriculum Management Program Cooperative's TEKS Resource System curriculum. IXL provides skill alignments as a service to teachers, students, and parents. The skill alignments are provided by IXL and are not affiliated with, sponsored by, reviewed, approved or endorsed by Texas Curriculum Management Program Cooperative or any other third party. IXL® and IXL Learning® are registered trademarks of IXL Learning, Inc. All other intellectual property rights (e.g., unregistered and registered trademarks and copyrights) are the property of their respective owners.