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IXL Skill Alignment
Precalculus alignment for McGraw Hill Texas Math
Use IXL's interactive skill plan to get up-to-date skill alignments, assign skillsto your students, and track progress.
www.ixl.com/math/skill-plans/mcgraw-hill-texas-math-2016-precalculus
This document includes the IXL® skill alignments to McGraw Hill's McGraw Hill Texas Math 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 McGraw Hill 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.
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Chapter 0Preparing for Precalculus
Textbook section IXL skills
Lesson 0-1: Sets
Lesson 0-2: Operations with Complex Numbers Powers of i1. Powers of i TW8
Operations with complex numbers2. Add and subtract complex numbers GNA
3. Multiply and divide complex numbers RYR
4. Add, subtract, multiply, and divide complexnumbers 2QV
Complex conjugates5. Complex conjugates K5Q
Lesson 0-3: Quadratic Functions and Equations Graph quadratic functions1. Characteristics of quadratic functions GRL
2. Graph a quadratic function DRX
3. Find the maximum or minimum value of aquadratic function KRZ
Solve quadratic functions4. Solve a quadratic equation using the zero
product property TRU
5. Solve a quadratic equation using squareroots 2UF
6. Solve a quadratic equation by factoring MHY
7. Solve a quadratic equation by completing thesquare YMP
8. Solve a quadratic equation using the quadraticformula FYM
Lesson 0-4: nth Roots and Real Exponents Radicals1. Nth roots 6NE
2. Roots of integers 8RV
3. Roots of rational numbers 28Q
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4. Find roots using a calculator 9E4
Rational exponents5. Evaluate rational exponents 26H
6. Operations with rational exponents NQB
Simplify radical expressions7. Simplify radical expressions with variables 9LT
8. Simplify expressions involving rationalexponents 7TC
Lesson 0-5: Systems of Linear Equations andInequalities
System of equation in two variables1. Solve a system of equations by graphing 97U
2. Classify a system of equations TJD
3. Solve a system of equations usingsubstitution ZPV
4. Solve a system of equations usingelimination M8G
Real-world scenario5. Solve a system of equations by graphing: word
problems LXQ
6. Solve a system of equations using substitution:word problems DXU
7. Solve a system of equations using elimination:word problems VFS
System of equations in three variables8. Determine the number of solutions to a system
of equations in three variables ZZQ
System of inequalities9. Is (x, y) a solution to the system of
inequalities? RFY
Lesson 0-6: Matrix Operations Describe and anaylze matrices1. Matrix vocabulary 75N
2. Matrix operation rules SQR
Matrix operations3. Add and subtract matrices 2SM
4. Multiply a matrix by a scalar FJT
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5. Add and subtract scalar multiples ofmatrices 9ME
Lesson 0-7: Probability with Permutations andCombinations
1. Introduction to probability VGH
2. Calculate probabilities of events 74H
3. Combinations and permutations 7ZS
4. Find probabilities using combinations andpermutations PKN
5. Identify independent events PLB
Lesson 0-8: Statistics 1. Mean, median, mode, and range MHB
2. Calculate quartiles and interquartile range 8H9
3. Box plots YE9
4. Interpret bar graphs, line graphs, andhistograms B9A
5. Create bar graphs, line graphs, andhistograms EF6
6. Variance and standard deviation 7L3
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Chapter 1Functions from a Calculus Perspective
Textbook section IXL skills
Lesson 1-1: Functions 1. Identify functions QTA
2. Evaluate functions 6VY
Lesson 1-2: Anaylzing Graphs of Functions andRelations
Evaulate functions1. Find values using function graphs 2AM
2. Complete a table for a function graph L5B
3. Evaluate exponential functions LWE
Quadratic functions4. Match quadratic functions and graphs H59
5. Characteristics of quadratic functions GRL
Polynomial functions6. Find the roots of factored polynomials DTZ
7. Match polynomials and graphs VQK
Domain and range8. Domain and range YEC
9. Domain and range of absolute value functions:graphs Y8C
10. Domain and range of absolute value functions:equations FXV
Lesson 1-3: Continuity, End Behavior, and Limits End behavior1. Identify graphs of continuous functions 24H
2. Determine continuity using graphs Y7R
Continuity3. Determine one-sided continuity using
graphs QMX
4. Find and analyze points of discontinuity usinggraphs S48
5. Determine continuity on an interval usinggraphs E6M
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6. Determine the continuity of a piecewise functionat a point X5C
7. Make a piecewise function continuous VKT
Intermediate value theorem8. Intermediate Value Theorem BDH
Lesson 1-4: Extrema and Average Rates of Change 1. Average rate of change I P8Z
2. Average rate of change II MYZ
Lesson 1-5: Parent Functions and Transformations 1. Function transformation rules DUV
2. Translations of functions XTT
3. Reflections of functions 2S4
4. Dilations of functions 9KX
5. Transformations of functions UAL
6. Describe function transformations JN6
Lesson 1-6: Function Operations and Compositionof Functions
1. Add, subtract, multiply, and divide functions CLF
2. Composition of functions TBH
Lesson 1-7: Inverse Relations and Functions 1. Identify inverse functions 2Y8
2. Find values of inverse functions from tables PBA
3. Find values of inverse functions fromgraphs FDG
4. Find inverse functions and relations DST
5. Check whether two rational functions areinverses KFE
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Chapter 2Power, Polynomial, and Rational Functions
Textbook section IXL skills
Lesson 2-1: Power and Rational Functions 1. Solve radical equations 2G6
2. Domain and range of radical functions VY8
Lesson 2-2: Polynomial Functions Factoring1. Factor out a monomial NMZ
2. Factor sums and differences of cubes 9PW
3. Factor using a quadratic pattern SZN
4. Find the roots of factored polynomials DTZ
Polynomial functions5. Match polynomials and graphs VQK
6. Domain and range of polynomials TZZ
Lesson 2-3: The Remainder and Factor Theorems 1. Divide polynomials using long division 5YS
2. Divide polynomials using synthetic division E6K
3. Evaluate polynomials using syntheticdivision ADF
Lesson 2-4: Zeros of Polynomial Functions Theorems1. Rational root theorem EHC
2. Descartes' Rule of Signs ZFB
3. Fundamental Theorem of Algebra FUF
Write a polynomial4. Write a polynomial from its roots GPB
Solve equations5. Solve equations using a quadratic pattern DSF
6. Solve equations with sums and differences ofcubes 5DG
7. Solve polynomial equations ZCH
Complex roots8. Complex conjugate theorem U5Z
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9. Conjugate root theorems 6MB
Lesson 2-5: Rational Functions Simplify rational expressions1. Simplify rational expressions 37N
2. Multiply and divide rational expressions MG2
3. Add and subtract rational expressions FEX
Solve rational equations4. Solve rational equations 8UN
Rational functions5. Rational functions: asymptotes and excluded
values YSJ
Lesson 2-6: Nonlinear Inequalities 1. Graph solutions to quadratic inequalities RVR
2. Solve quadratic inequalities KL5
3. Graph solutions to higher-degreeinequalities 6PQ
4. Solve higher-degree inequalities RDR
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Chapter 3Exponential and Logarithmic Functions
Textbook section IXL skills
Lesson 3-1: Exponential Functions Graphs of exponential functions1. Exponential functions over unit intervals 8LR
2. Identify linear and exponential functions AUY
3. Match exponential functions and graphs PCX
4. Describe linear and exponential growth anddecay 9QH
Real-world scenarios5. Exponential growth and decay: word
problems 7SH
6. Compound interest: word problems 2WU
7. Continuously compounded interest: wordproblems 5GU
Lesson 3-2: Logarithmic Functions 1. Evaluate logarithms MQM
2. Convert between exponential and logarithmicform SXD
3. Domain and range of exponential andlogarithmic functions GQ9
Lesson 3-3: Properties of Logarithms 1. Change of base formula CUW
2. Product property of logarithms VXL
3. Quotient property of logarithms HMN
4. Power property of logarithms BVY
5. Evaluate logarithms using properties XWK
Lesson 3-4: Exponential and LogarithmicEquations
1. Solve logarithmic equations with onelogarithm GJH
2. Solve logarithmic equations with multiplelogarithms 9CY
3. Solve exponential equations usinglogarithms UWM
4. Solve exponential equations using factoring 5LY
Lesson 3-5: Modeling with Nonlinear Regression
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Chapter 4Trigonometric Functions
Textbook section IXL skills
Lesson 4-1: Right Triangle Trigonometry 1. Find trigonometric ratios using righttriangles L6Y
2. Solve a right triangle ET7
Lesson 4-2: Degrees and Radians 1. Convert between radians and degrees KEV
2. Radians and arc length HVD
3. Coterminal and reference angles PLQ
4. Area of sectors XZQ
Lesson 4-3: Trigonometric Functions on the UnitCircle
1. Find trigonometric ratios using the unitcircle BEM
2. Find trigonometric ratios using referenceangles 9QB
3. Quadrants CTR
4. Find trigonometric ratios of special angles DPR
Lesson 4-4: Graphing Sine and Cosine Functions Sine functions1. Find properties of sine functions NVY
2. Write equations of sine functions fromgraphs TJH
3. Write equations of sine functions usingproperties SMV
4. Graph sine functions HP2
5. Graph translations of sine functions 6PG
Cosine functions6. Find properties of cosine functions JZV
7. Write equations of cosine functions fromgraphs 7MS
8. Write equations of cosine functions usingproperties KVG
9. Graph cosine functions HE5
10. Graph translations of cosine functions RGG
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Mixed practice11. Graph sine and cosine functions C8N
12. Graph translations of sine and cosinefunctions NVC
Lesson 4-5: Graphing Other TrigonometricFunctions
Lesson 4-6: Inverse Trigonometric Functions 1. Inverses of trigonometric functions FUL
Lesson 4-7: The Law of Sines and the Law ofCosines
Solve a triangle1. Law of Sines MXX
2. Law of Cosines 6MW
3. Solve a triangle 8Y3
Area of a triangle4. Area of a triangle: sine formula JU5
5. Area of a triangle: Heron's formula CHZ
Trigonometric ratios6. Trigonometric ratios: find a side length 62D
7. Trigonometric ratios: find an angle measure BFU
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Chapter 5Trigonometric Identies and Equations
Textbook section IXL skills
Lesson 5-1: Trigonometric Identities 1. Trigonometric identities I WHX
2. Trigonometric identities II 8S8
3. Symmetry and periodicity of trigonometricfunctions FSJ
4. Complementary angle identities J5N
Lesson 5-2: Verifying Trigonometric Identities
Lesson 5-3: Solving Trigonometric Equations 1. Solve trigonometric equations DVX
Lesson 5-4: Sum and Difference Identities
Lesson 5-5: Multiple-Angle and Product-to-SumIdentities
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Chapter 6Systems of Equations and Matrices
Textbook section IXL skills
Lesson 6-1: Multivariable Linear Systems and RowOperations
1. Solve a system of equations using augmentedmatrices DL8
2. Solve a system of equations using augmentedmatrices: word problems 4F9
3. Solve a system of equations in three variablesusing substitution RUC
4. Solve a system of equations in three variablesusing elimination S2V
Lesson 6-2: Matrix Multiplication, Inverses, andDeterminants
Matrix operation1. Multiply two matrices 9EF
2. Simplify matrix expressions 8C4
3. Properties of matrices WVY
Matrix inverse4. Is a matrix invertible? 6M6
5. Inverse of a 2 x 2 matrix CLV
6. Inverse of a 3 x 3 matrix XWL
7. Identify inverse matrices 7UH
Determinant8. Determinant of a matrix 7X8
Solve matrix equations9. Solve matrix equations SNU
10. Solve matrix equations using inverses 2UD
Lesson 6-3: Solving Linear Systems Using Inversesand Cramer's Rule
Lesson 6-4: Partial Fractions
Lesson 6-5: Linear Optimization 1. Solve systems of linear inequalities bygraphing KS6
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2. Solve systems of linear and absolute valueinequalities by graphing 6UE
3. Find the vertices of a solution set KSP
4. Linear programming VWA
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Chapter 7Conic Sections and Parametric Equations
Textbook section IXL skills
Lesson 7-1: Parabolas 1. Find properties of parabolas L76
2. Convert equations of parabolas from general tovertex form 39W
3. Write equations of parabolas in vertex form PL2
4. Graph parabolas YPA
Lesson 7-2: Ellipses and Circles Circles1. Find properties of circles QBC
2. Write equations of circles in standard form FE8
3. Graph circles 2WV
Ellipses4. Find properties of ellipses QRV
5. Find the eccentricity of an ellipse W78
6. Write equations of ellipses in standard form 7P6
Lesson 7-3: Hyperbolas 1. Find properties of hyperbolas G2L
2. Find the eccentricity of a hyperbola JMU
3. Write equations of hyperbolas in standardform KBN
4. Convert equations of conic sections from generalto standard form J5G
Lesson 7-4: Rotations of Conic Sections
Lesson 7-5: Parametric Equations
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Chapter 8Vectors
Textbook section IXL skills
Lesson 8-1: Introduction to Vectors Graph a resultant vector1. Graph a resultant vector using the triangle
method LBY
2. Graph a resultant vector using the parallelogrammethod 9E3
Vector scalar multiple3. Multiply a vector by a scalar WNC
4. Find the magnitude of a vector scalarmultiple QM6
5. Determine the direction of a vector scalarmultiple YZ5
Lesson 8-2: Vectors in the Coordinate Plane Unit Vector1. Find a unit vector 74T
Component form of vectors2. Find the component form of a vector XLQ
3. Find the component form of a vector from itsmagnitude and direction angle BSW
Vector operations4. Add vectors KKG
5. Subtract vectors 64N
Magnitude and direction of vectors6. Find the direction angle of a vector RTR
7. Find the magnitude of a vector XV9
8. Find the magnitude and direction of a vectorsum QCS
Linear combinations of vectors9. Linear combinations of vectors JGL
Lesson 8-3: Dot Products and Vector Projections
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Lesson 8-4: Vectors in Three-Dimensional Space 1. Find the magnitude of a three-dimensionalvector NUR
2. Find the component form of a three-dimensionalvector PWR
3. Add and subtract three-dimensional vectors JKR
4. Scalar multiples of three-dimensionalvectors LAA
5. Find a three-dimensional unit vector 2ZV
6. Linear combinations of three-dimensionalvectors TVX
Lesson 8-5: Dot and Cross Products of Vectors inSpace
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Chapter 9Polar Coordinates and Complex Numbers
Textbook section IXL skills
Lesson 9-1: Polar Coordinates
Lesson 9-2: Graphs of Polar Equations 1. Match polar equations and graphs 35P
Lesson 9-3: Polar and Rectangular Forms ofEquations
Lesson 9-4: Polar Forms of Conic Sections
Lesson 9-5: Complex Numbers and DeMoivre'sTheorem
Graph in the complex plane1. Introduction to the complex plane J8S
2. Graph complex numbers ABL
Operations in the complex plane3. Addition in the complex plane VRV
4. Subtraction in the complex plane 2FN
5. Graph complex conjugates CRX
6. Absolute value in the complex plane DUF
Midpoint and distance7. Midpoints in the complex plane 79E
8. Distance in the complex plane MCD
Find the modulus and argument9. Find the modulus and argument of a complex
number 3Y5
Convert complex numbers10. Convert complex numbers from rectangular to
polar form LCP
11. Convert complex numbers from polar torectangular form PVD
12. Convert complex numbers betweenrectangular and polar form JGA
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Chapter 10Sequences and Series
Textbook section IXL skills
Lesson 10-1: Sequences, Series, and SigmaNotation
Find terms of a sequence1. Find terms of a sequence 7W8
2. Find terms of a recursive sequence VSG
Explicit and recursive formula3. Identify a sequence as explicit or recursive DKZ
4. Find a recursive formula FE2
5. Find recursive and explicit formulas FJB
6. Convert an explicit formula to a recursiveformula ZL9
7. Convert between explicit and recursiveformulas PZA
Partial sums8. Introduction to partial sums YQP
Sigma notation9. Introduction to sigma notation FTV
Lesson 10-2: Arithemtic Sequences and Series 1. Find terms of an arithmetic sequence C8R
2. Write a formula for an arithmetic sequence H82
3. Find the sum of an arithmetic series HM5
4. Partial sums of arithmetic series SJ8
Lesson 10-3: Geometric Sequences and Series Geometric sequences1. Find terms of a geometric sequence BHV
2. Write a formula for a geometric sequence Q5V
Geometric series3. Find the sum of a finite geometric series 7HF
4. Convergent and divergent geometric series SVM
5. Find the value of an infinite geometricseries SRN
6. Partial sums of geometric series D2D
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Mixed sequences and series7. Identify arithmetic and geometric series HS9
8. Partial sums: mixed review WUP
Lesson 10-4: Mathematical Induction
Lesson 10-5: The Binomial Theorem 1. Pascal's triangle UMZ
2. Pascal's triangle and the Binomial Theorem 9XR
3. Binomial Theorem I K97
4. Binomial Theorem II 2KV
Lesson 10-6: Functions as Infinite Series
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Chapter 11Inferential Statistics
Textbook section IXL skills
Lesson 11-1: Descriptive Statistics
Lesson 11-2: Probability Distributions Discrete probability1. Identify discrete and continuous random
variables KD7
2. Write a discrete probability distribution MPF
3. Graph a discrete probability distribution E8W
Random variables4. Expected values of random variables YFY
5. Variance of random variables RZU
6. Standard deviation of random variables BHU
Real-world problems7. Write the probability distribution for a game of
chance 42D
8. Expected values for a game of chance QXE
9. Choose the better bet 5MS
Binomial distribution10. Find probabilities using the binomial
distribution 9UZ
11. Mean, variance, and standard deviation ofbinomial distributions E9Y
Lesson 11-3: The Normal Distrubition 1. Find probabilities using the normal distributionI SSW
2. Find probabilities using the normal distributionII QCL
3. Find z-values 9PK
4. Find values of normal variables 87N
Lesson 11-4: The Central Limit Theorem 1. The Central Limit Theorem FC7
2. Use normal distributions to approximatebinomial distributions 8UV
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3. Distributions of sample means 8R5
Lesson 11-5: Confidence Intervals 1. Find confidence intervals for populationmeans 8G2
2. Find confidence intervals for populationproportions XWT
3. Interpret confidence intervals for populationmeans HL7
Lesson 11-6: Hypothesis Testing
Lesson 11-7: Correlation and Linear Regression Outliers1. Outliers in scatter plots CXA
Correlation2. Match correlation coefficients to scatter
plots RVE
3. Calculate correlation coefficients HZ9
Linear Regression4. Find the equation of a regression line 7R9
5. Interpret regression lines AU6
6. Analyze a regression line of a data set HZH
7. Analyze a regression line using statistics of adata set NEV
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Chapter 12Limits and Derivatives
Textbook section IXL skills
Lesson 12-1: Estimating Limits Graphically Estimate limits1. Find limits using graphs BF5
2. Find one-sided limits using graphs L7Q
3. Determine if a limit exists 9YS
4. Find limits at vertical asymptotes usinggraphs VZP
Determine end behavior5. Determine end behavior using graphs VY9
6. Determine end behavior of polynomial andrational functions GVF
Lesson 12-2: Evaluating Limits Algebraically Limit laws1. Find limits using addition, subtraction, and
multiplication laws BTG
2. Find limits using the division law MKT
3. Find limits using power and root laws PJD
4. Find limits using limit laws W8J
Find limits of functions5. Find limits of polynomials and rational
functions 9BY
6. Find limits involving factorization andrationalization GXB
Lesson 12-3: Tangent Lines and Velocity 1. Find instantaneous rates of change XZU
2. Velocity as a rate of change E2W
3. Find the slope of a tangent line using limits F5K
4. Find equations of tangent lines using limits MBX
Lesson 12-4: Derivatives Introduction to derivatives1. Find values of derivatives using limits 9KU
Derivative rules2. Power rule I FMB
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3. Power rule II NML
4. Sum and difference rules LDE
5. Product rule P86
6. Quotient rule D8X
Find derivatives7. Find derivatives of polynomials TL2
8. Find derivatives of rational functions LSM
Lesson 12-5: Area Under a Curve and Integration
Lesson 12-6: The Fundamental Theorem ofCalculus
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