Algebra 2

Scope & Sequence

Semester 1 

Semester 2 

Chapter 1: Functions and Systems 

  • 1.1 Functions – key features, domain/range, notation (F.IF.4, 5, 6) 

  • 1.2 Parent functions and transformations (focus on quadratic/absolute value) (F.IF.4, 5; F.BF.3) 

  • 1.3 Graph and write piecewise functions (F.IF.4, 7b) 

  • 1.6 Systems of linear equations (A.CED.2; A.CED.3; A.REI.6) 

 

Chapter 2: Quadratic Functions 

  • 2.1 Vertex form (A.CED.2; F.IF.4; F.BF.3) 

  • 2.2 Standard form: y-intercept and vertex (A.CED.2F.IF.4) 

  • 2.3 Factored form, factoring, and the Zero Product Property (A.SSE.2, 3aA.REI.4bF.IF.8A) 

  • 2.4 Complex numbers and operations (omit dividing) (N.CN.1, 2, 3+, 8+, 9+) 

  • 2.6 Quadratic formula (N.CN.7; A.REI.4, 4a, 4b) 

 

Chapter 3: Polynomial Functions 

  • 3.1 Polynomial vocabulary and features (A.SSE.1a; F.IF.4, 7c; F.BF.3) 

  • 3.2 Add, subtract, multiply polynomials (A.APR.1; F.BF.1b) 

  • 3.4 Divide using long division; use the Factor Theorem (A.SSE.2; A.APR.2, 6) 

  • 3.5 Zeros, multiplicity of zeros, and writing equations from graphs (A.REI.4, 4a, 4b; A.APR.3) 

 

Chapter 4: Rational Functions 

  • 4.1 Parent reciprocal functions and transformations; asymptotes (A.CED.2; F.IF.7d+; F.BF.3) 

  • 4.2 Graphing rational functions (F.IF.C.7d+; F.BF.1b) 

  • 4.3 Multiplying and dividing rational expressions (A.SSE.2; A.APR.6, 7+) 

 

 

Chapter 5: Rational Exponents and Radical Functions 

  • 5.1 Rational exponents (omit radicals of nth root), simplify/solve with radicals (N.RN.1, 2; A.REI.1) 

  • 5.2 Properties of exponents and nth degree radicals – simplify only, omit operations (N.RN.2; A.SSE.1, 2) 

  • 5.3 Graphing square root functions and their transformations (F.IF.4, 5, 7b; F.BF.3) 

  • 5.4 Solving radical equations (one radical per equation only) (A.CED.4; A.REI.2) 

  • 5.5 Composition of functions (omit function operations—interweave elsewhere as needed) (F.BF.1B; F.BF.1c+) 

  • 5.6 Inverse relations (omit domain/restrictions to create inverse functions) (F.BF.4, 4a, 4c+) 

 

Chapter 6: Exponential and Logarithmic Functions 

  • 6.1 Parent exponential functions, transformations, and growth/decay (F.IF.4, 5, 7e, 8b, 9; F.BF.3; F.LE.5) 

  • 6.2 Exponential models (A.SSE.1b; F.LE.1C; F.LE.2) 

  • 6.3 Define/evaluate logarithms, convert b/n exponential and log form, common log (F.BF.4a; F.BF.5+; F.LE.4) 

  • 6.4 Parent log functions and transformations (F.IF.5, 7e, 9; F.BF.3, 4a) 

  • 6.5 Log properties (omit change-of-base) (A.SSE.2; F.LE.4) 

  • 6.6 Solve basic exponential and log equations (A.SSE.2; F.LE.4) 

 

Chapter 7: Trigonometric Functions 

  • 7.1 Trig ratios for right triangles, quotient identity (sin, cos, tan only) (G.SRT.6, 7, 8; F.TF.3+) 

  • 7.2 Angles: standard position, co-terminal, reference, radians and degrees (F.TF.1, 2, 3+) 

  • 7.3 The Unit Circle (for sin, cos) (F.TF.2; F.TF.3+) 

  • 7.4/7.6 Sin, cos parent functions and transformations (F.IF.4, 6, 9; F.BF.3; F.TF.5) 

 

Essential Learnings

Semester 1 

Chapter 1: Functions and Systems 

1.1 

  • Identify key features of functions: domain and range, intercepts, intervals where a function is increasing/decreasing, intervals where a function is positive/negative, maximums and minimums, average rate of change 
  • Interval notation 
  • Interpreting graphs 
  • Function notation 

1.2 

  • Parent Functions: Quadratic and Absolute Value  
  • Review transformations (translations, reflections, dilations) 

1.3 

  • Graph piecewise functions (no step functions) 
  • Write equations for piecewise graphs (no step functions) 

1.4 

  • Arithmetic sequences and series 
  • Writing recursive and explicit equations for arithmetic sequences 
  • Using sigma notation to express an arithmetic series 

1.5 

  • Solving equations and inequalities by graphing (both with the graphing calculator and by hand) 

1.6 

  • Systems of linear equations 
  • Review methods for solving: graphing (using calc), elimination and substitution

 

Chapter 2: Quadratic Functions 

2.1 

  • Vertex form of a quadratic (identifying vertex by translations) 
  • Writing the equation of a quadratic in vertex form from a graph or description 
  • Finding relative maximums and minimums and zeros using the graphing calculator 

2.2 

  • Standard form of a quadratic (identifying y-intercept and vertex) 

2.3 

  • Factored form of a quadratic (identifying roots and vertex) 
  • Zero Product Property 
  • Solving quadratic equations by factoring 

2.4 

  • Complex Numbers 
  • Operations (add, subtract, multiply, divide) with complex numbers 

2.5 

  • Completing the square 
  • Transforming quadratic equations from standard to vertex form by CTS 
  • Solving quadratic equations by CTS  

2.6 

  • The quadratic formula 
  • Solving quadratic equations by the quadratic formula 

2.7 

  • Solving linear-quadratic systems (algebraically and graphically) 

 

Chapter 3: Polynomial Functions 

3.1 

  • Analyzing polynomial functions 
  • Vocabulary: degree, leading coefficient, end behavior, maximums and minimums (relative and absolute)  

3.2 

  • Add, subtract and multiply polynomial expressions 
  • Applications of polynomial functions 
  • Optimization 
  • Using the graphing calculator to identify relative maximums and minimums and zeros 

3.3 

  • Polynomial identities 
  • Sum and difference of squares and cubes 

3.4 

  • Dividing polynomials using long division 
  • Using the Remainder and Factor theorems to identify roots 

3.5 

  • Zeros of polynomial functions 
  • Multiplicity of zeros (single, double, triple roots) 
  • Writing equations of polynomial functions from graphs 

 

Chapter 4: Rational Functions 

4.1 

  • Inverse vs. direct variation 
  • Parent Reciprocal function and transformations 
  • Identifying asymptotes from equations and graphs 

4.2 

  • Graphing rational functions 
  • Using long division to identify transformations 
  • Identifying asymptotes from equations and graphs (given in transf form) 

4.3 

  • Multiplying and dividing rational expressions 

4.4 

  • Adding and subtracting rational expressions 

4.5 

  • Solving rational equations 
  • Applications/mixture problems 

 

Semester 2 

Chapter 5: Rational Exponents and Radical Functions 

5.1 

  • Rational exponents and radicals of the nth root 
  • Simplifying and solving equations that involve radicals or rational exponents 

5.2 

  • Properties of exponents 
  • Properties of nth degree radicals (operations, no abs value when applies even roots – simplify only) 

5.3 

  • Graphing radical functions 
  • Parent Square Root and Cube Root functions and transformations (minimize the number/combo of transf) 

5.4 

  • Solving radical equations (basic level w/one radical only) 

5.5 

  • Function Operations 
  • Compositions of functions 

5.6 

  • Inverse relations and functions (no domain/range restrictions) 

 

Chapter 6: Logarithmic and Exponential Functions 

6.1 

  • Key features of exponential functions 
  • Parent Exponential function and transformations 
  • Exponential growth and decay 

6.2 

  • Exponential models 
  • Solving application problems involving exponents (compounding interest, radioactive decay) 

6.3 

  • Definition of a logarithm 
  • Evaluating logarithms with/without a calculator 
  • Exponential vs. logarithmic form 
  • Common logarithm (base 10) 
  • Natural logarithms (base e

6.4 

  • Parent Logarithmic function and transformations 

6.5 

  • Properties of Logarithms 
  • Change-of-Base formula 

6.6 

  • Solving exponential and logarithmic equations

6.7 

  • Geometric Sequences and Series 
  • Writing recursive and explicit equations for geometric sequences 
  • Finite geometric series 
  • Expressing a geometric series using sigma notation 

 

Chapter 7: Trigonometric Functions 

7.1 

  • Trigonometric ratios of right triangles (sine, cosine, tangent) 
  • Quotient Identity for tangent 

 7.2 

  • Sketching angles on the coordinate plane 
  • Vocabulary: Standard position of an angle, initial and terminal sides, co-terminal angles, reference angles 
  • Radian measurements (converting between radians and degrees) 

7.3 

  • The Unit Circle

7.4 & 7.6 

  • Parent functions of sine and cosine and their transformations 
  • Graphing sine and cosine from equations or story problems 
  • Writing equations of sinusoidal functions from a graph or story problem