Algebra II

What the course covers

12 units, with exam weights

1. Unit 1

   Linear Equations, Inequalities, and Modeling

   6-8% of examFree
   The linear toolkit the rest of the course assumes, sharpened to SAT speed: solving linear equations and reading their solution count from structure, linear and compound inequalities, absolute value equations and inequalities as distance statements, every form of a linear function, and translating contexts into linear models whose slope and intercept carry meaning. Feeds the SAT Algebra domain.
   5 topics

   1. 1.1Expressions, Equations, and Solving Linear Equations
   2. 1.2Linear Inequalities in One Variable
   3. 1.3Absolute Value Equations and Inequalities
   4. 1.4Linear Functions: Slope, Intercepts, and Forms
   5. 1.5Linear and Inequality Modeling and Interpretation in Context

2. Unit 2

   Functions, Relations, and Transformations

   9-11% of exam
   The grammar of the whole course. Relations and functions, domain and range in three notations, function notation, the library of parent functions, transformations in function notation, symmetry and piecewise definitions, combining and composing functions, and inverses with the domain restrictions they require. Feeds the SAT Advanced Math domain.
   7 topics

   1. 2.1Relations, Functions, Domain and Range
   2. 2.2Function Notation and Evaluation
   3. 2.3Parent Functions and Their Graphs
   4. 2.4Transformations of Functions (Shifts, Stretches, Reflections)
   5. 2.5Even and Odd Functions, Symmetry, and Piecewise Functions
   6. 2.6Operations and Composition of Functions
   7. 2.7Inverse Functions

3. Unit 3

   Systems of Equations and Inequalities

   6-8% of exam
   Two-variable linear systems by graphing, substitution, and elimination; the structure that produces one, zero, or infinitely many solutions; systems of linear inequalities and their solution regions; three-variable systems by elimination and with matrices on technology; and optimization over a feasible region. Feeds the SAT Algebra domain.
   5 topics

   1. 3.1Solving Systems by Graphing, Substitution, and Elimination
   2. 3.2Number of Solutions and Structure
   3. 3.3Systems of Linear Inequalities
   4. 3.4Three-Variable Linear Systems
   5. 3.5Linear Programming and Optimization

4. Unit 4

   Quadratic Functions and Complex Numbers

   11-13% of exam
   Quadratics in vertex, standard, and factored forms and what each reveals; factoring; completing the square; the quadratic formula and the discriminant; complex numbers as the solutions the real line lacks; modeling with quadratics, including writing the function through three points and regression; linear-quadratic systems; and quadratic inequalities. The heaviest unit for the SAT Advanced Math domain.
   7 topics

   1. 4.1Graphing Quadratics: Vertex, Standard, and Factored Forms
   2. 4.2Factoring and Solving by Factoring
   3. 4.3Completing the Square
   4. 4.4The Quadratic Formula and the Discriminant
   5. 4.5Complex Numbers and Operations
   6. 4.6Quadratic Modeling and Quadratic Systems
   7. 4.7Quadratic Inequalities

5. Unit 5

   Polynomial Functions

   9-11% of exam
   Operations on polynomials, factoring degree three and four polynomials (grouping and the sum and difference of cubes), long and synthetic division with the Remainder and Factor Theorems, zeros and multiplicity with the Fundamental Theorem of Algebra, graphing from end behavior and turning points, and modeling with polynomials. Feeds the SAT Advanced Math domain.
   6 topics

   1. 5.1Polynomial Operations and Special Products
   2. 5.2Factoring Higher-Degree Polynomials (GCF, Grouping, Sum and Difference of Cubes)
   3. 5.3Dividing Polynomials; Remainder and Factor Theorems
   4. 5.4Zeros, Multiplicity, and the Fundamental Theorem of Algebra
   5. 5.5Graphing Polynomials: End Behavior and Turning Points
   6. 5.6Modeling with Polynomials

6. Unit 6

   Rational Expressions and Functions

   8-10% of exam
   Simplifying, multiplying, dividing, adding, and subtracting rational expressions with the domain restrictions they carry; complex fractions; solving rational equations and rejecting extraneous solutions; graphing rational functions with vertical and horizontal asymptotes and holes; and modeling with rational equations and inverse variation. Feeds the SAT Advanced Math domain.
   6 topics

   1. 6.1Simplifying Rational Expressions
   2. 6.2Multiplying and Dividing Rational Expressions
   3. 6.3Adding and Subtracting Rational Expressions; Complex Fractions
   4. 6.4Solving Rational Equations (and Extraneous Solutions)
   5. 6.5Graphing Rational Functions: Asymptotes and Holes
   6. 6.6Inverse Variation and Rational Models

7. Unit 7

   Radical Functions and Rational Exponents

   7-9% of exam
   nth roots and rational exponents as two notations for one idea, the exponent laws, simplifying and operating on radical expressions, solving square root, cube root, and rational-exponent equations with extraneous-solution checks, and graphing square root and cube root functions as inverses of power functions. Feeds the SAT Advanced Math domain.
   5 topics

   1. 7.1nth Roots and Rational Exponents
   2. 7.2Properties of Exponents and Simplifying Radicals
   3. 7.3Operations with Radical Expressions
   4. 7.4Solving Radical Equations (and Extraneous Solutions)
   5. 7.5Graphing Radical Functions and Inverses

8. Unit 8

   Exponential and Logarithmic Functions

   10-12% of exam
   Exponential growth and decay, including recursive form and percent change; the number $e$ and continuous growth; logarithms as inverse exponentials; the properties of logarithms; solving exponential and logarithmic equations and checking reasonableness; and modeling with exponential and logarithmic functions, including exponential regression. Feeds the SAT Advanced Math domain.
   6 topics

   1. 8.1Exponential Functions, Growth, and Decay
   2. 8.2The Number e and Continuous Growth
   3. 8.3Logarithms and Logarithmic Functions
   4. 8.4Properties of Logarithms
   5. 8.5Solving Exponential and Logarithmic Equations
   6. 8.6Modeling with Exponential and Logarithmic Functions

9. Unit 9

   Sequences and Series

   5-7% of exam
   Sequences as functions on the positive integers: arithmetic sequences as discrete linear functions and geometric sequences as discrete exponentials, recursive and explicit formulas, finite arithmetic and geometric series, summation notation, and infinite geometric series. Connects to SAT linear and exponential modeling.
   4 topics

   1. 9.1Arithmetic Sequences and Series
   2. 9.2Geometric Sequences and Series
   3. 9.3Recursive and Explicit Formulas
   4. 9.4Infinite Geometric Series and Summation Notation

10. Unit 10

    Conic Sections

    4-6% of exam
    The four conics as cross-sections of a cone and as locus definitions: parabolas from a focus and directrix, circles from a center and radius, ellipses, and hyperbolas, with completing the square as the move that converts a general equation to standard form. Circle equations feed the SAT Geometry and Trigonometry domain.
    4 topics

    1. 10.1Parabolas (as Conics)
    2. 10.2Circles (Review and Equations)
    3. 10.3Ellipses
    4. 10.4Hyperbolas

11. Unit 11

    Trigonometry

    6-8% of exam
    From right-triangle ratios to periodic functions: radian measure and the unit circle, the six trigonometric functions, graphs of sine, cosine, and tangent with amplitude, period, and shifts, the Pythagorean identity and basic trigonometric equations, and the laws of sines and cosines for any triangle. Mirrors Pre-AP Algebra 2 Unit 4T; right-triangle trigonometry feeds the SAT Geometry and Trigonometry domain.
    5 topics

    1. 11.1Angles, Radian Measure, and the Unit Circle
    2. 11.2Trigonometric Functions and Right-Triangle Trigonometry
    3. 11.3Graphs of Sine, Cosine, and Tangent
    4. 11.4Trigonometric Identities and Equations
    5. 11.5Law of Sines and Law of Cosines (Modeling)

12. Unit 12

    Statistics, Data, and Probability

    7-9% of exam
    The data half of SAT Math. Ratios, rates, percentages, and units; one-variable data by center, spread, and shape; two-variable data modeled with linear, quadratic, and exponential regressions and judged by residuals; the normal distribution and z-scores; probability and conditional probability from two-way tables; and sampling, margin of error, and evaluating statistical claims. Feeds the SAT Problem-Solving and Data Analysis domain.
    6 topics

    1. 12.1Ratios, Rates, Proportions, Percentages, and Units
    2. 12.2One-Variable Data: Center, Spread, and Distribution Shape
    3. 12.3Two-Variable Data: Scatterplots, Models, and Regression
    4. 12.4The Normal Distribution and z-Scores
    5. 12.5Probability, Conditional Probability, and Two-Way Tables
    6. 12.6Sampling, Inference, Margin of Error, and Evaluating Claims

The exam, part by part

3 parts, 1 h 55 min in all.

• Section I, Part A: Multiple Choice

  Questions

  30

  Time

  50 min

  Weight

  50%

  Calculator allowed

  Format details

  Four-option, single-answer items. Roughly a third are set in a real-world context, and several come in sets of 2 or 3 items that share one graph, table, or model, the way Pre-AP learning checkpoints and the final exam group items. A graphing calculator or Desmos is available, as on the SAT.

• Section I, Part B: Student-Produced Response

  Questions

  10

  Time

  20 min

  Weight

  20%

  Calculator allowed

  Format details

  Numeric-entry items only (draw from numeric bank items); they stand in for the Pre-AP technology-enhanced items. Answers follow the SAT entry rules: an integer, decimal, or fraction of at most 5 characters for a positive answer and 6 for a negative one (including the sign); a fraction that does not fit is entered as a decimal, a long decimal is truncated or rounded at the fourth digit, a mixed number becomes an improper fraction, and no symbols such as percent, comma, or dollar signs.

• Section II: Open Response

  Questions

  2

  Time

  45 min

  Weight

  30%

  Calculator allowed

  Format details

  Task types: constructed-response, performance-task

  One Constructed Response (about 10 minutes) and one Performance Task (about 35 minutes), scored by the teacher or the AI grader against point-based scoring guidelines, the way the Pre-AP final exam scores its open-response question locally.

Skills the exam scores

• MODApplications and Modeling

  Build and use function models of real situations: choose a linear, quadratic, exponential, or other model that fits the data or description, write it with correct units, use it to predict, and judge whether the model and its answer are reasonable in context.

• ARGMathematical Argumentation

  Justify claims with precise language: explain why a solution is extraneous, why two functions are inverses, why a model is or is not appropriate, or why an equation has no real solutions; find and correct the flaw in someone else's work.

• REPConnections Among Representations

  Move fluently among equations, graphs, tables, and words: read key features from a graph, choose the equivalent form of an expression that reveals a feature, translate a transformation into function notation, and write domain and range in interval, inequality, and set notation.

• TOOLTools, Techniques, and Fluency

  Select and use techniques and tools well: factoring, completing the square, polynomial division, exponent and logarithm laws, exact forms such as radicals and complex numbers, and a graphing calculator or Desmos for intersections, zeros, and regressions when it is the faster route.