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Algebra 2 with Trigonometry Honors

A Contemplanda online course.

Algebra 2 with Trigonometry Honors contains the Algebra 2 Honors sequence and adds two units of trigonometry at the end of the year. After a first unit on function families and their transformations, piecewise and absolute value functions, symmetry, and composition, the first semester treats exponential and logarithmic functions, quadratics and complex numbers, polynomials, rational functions, and radicals. In the second semester, linear systems and matrices, conic sections, sequences and series, and probability and statistics come before the trigonometry: angles, the unit circle, and the laws of sines and cosines, then trigonometric graphs, identities, and equations. A final exam closes each semester.

Expressions, intervals, and piecewise rules are entered in mathematical notation. Other answers are numbers, filled-in tables, points placed on graphs, marks on number lines, or graphs sketched on blank axes, and multiple choice accounts for about a quarter of the questions. Practice questions are dealt at random from shared banks until a student answers four in a row correctly, and the graded checks, unit tests, and semester finals draw from the same pools. A video accompanies the reading in every teaching lesson.

Course at a glance

Course title
Algebra 2 with Trigonometry Honors
Publisher
Contemplanda
Structure
12 units and 2 semester exams, over two semesters (units 1 to 6 in semester 1; units 7 to 12 in semester 2)
Lessons
91 lessons: 77 teaching lessons, 12 unit tests, and 2 semester exams
Credit
Not awarded by Contemplanda
Enrollment
Purchasing is not open yet
Course page
www.contemplanda.com/courses/algebra-2-with-trigonometry-honors

Credit and enrollment

Contemplanda does not award high school credit. A student who wants credit for the course should ask their own school whether it will accept it.

Purchasing is not open yet. Questions about enrolling can go to info@contemplanda.com.

Students who are already enrolled sign in at direct.contemplanda.com.

How the course works

  • Each teaching lesson combines one to two videos, written explanations with typeset mathematics, practice, and a graded check.
  • Practice comes one question at a time and continues until the student answers four in a row correctly. After a wrong answer, the practice keeps drawing questions.
  • Every teaching lesson has a graded check whose questions are drawn for each student from a pool.

Units and lessons

Every published lesson, by semester and unit.

Semester 1

1

Functions and their transformations

  1. Function families and the features of their graphs
  2. Transforming parent graphs: shifts, reflections, and stretches
  3. Piecewise-defined functions
  4. Absolute value functions, equations, and inequalities
  5. Even and odd functions: symmetry by graph, table, and rule
  6. Combining functions: arithmetic operations and composition
  7. Unit 1 testUnit test14 questions
2

Inverses, exponential functions, and logarithms

  1. Inverse functions across tables, graphs, and equations
  2. Exponential functions and models
  3. Nth roots and rational exponents
  4. Logarithms: undoing an exponential function
  5. One-to-one functions, restricted domains, and verifying inverses
  6. Graphs of logarithmic functions, and function families revisited
  7. Properties of logarithms and the change-of-base identity
  8. Compounding, the number e, and the natural logarithm
  9. Solving exponential and logarithmic equations
  10. Logarithmic scales, models, and inverse functions revisited
  11. Unit 2 testUnit test22 questions
3

Quadratic functions and complex numbers

  1. Quadratic functions: forms, graphs, and models
  2. Solving quadratics by factoring, square roots, and completing the square
  3. The quadratic formula and choosing a solving method
  4. The imaginary unit and complex number arithmetic
  5. The discriminant and complex solutions of quadratic equations
  6. The complex plane, conjugates, and division
  7. Quadratic inequalities and linear-quadratic systems
  8. Unit 3 testUnit test15 questions
4

Polynomial functions

  1. Polynomial arithmetic and factoring higher-degree polynomials
  2. Dividing polynomials: long division and synthetic division
  3. The remainder and factor theorems
  4. Finding every zero: the rational root theorem and the fundamental theorem of algebra
  5. End behavior and eventual growth
  6. Graphing polynomials from zeros, multiplicity, and end behavior
  7. Pascal's triangle and the binomial theorem
  8. Polynomial inequalities with sign charts
  9. Unit 4 testUnit test15 questions
5

Rational expressions, equations, and functions

  1. Direct, inverse, and joint variation
  2. Simplifying, multiplying, and dividing rational expressions
  3. Adding and subtracting rational expressions; complex fractions
  4. Solving rational equations
  5. Rational functions: asymptotes, holes, end behavior, and mixed form
  6. Graphing rational functions and solving rational inequalities
  7. Unit 5 testUnit test12 questions
6

Radicals and rational exponents

  1. Rational-exponent properties and simplest radical form
  2. Adding, multiplying, and dividing radical expressions
  3. Square-root and cube-root functions and their graphs
  4. Solving radical and rational-exponent equations
  5. Unit 6 testUnit test10 questions
Exam

Semester 1 final

  1. Semester 1 final73 questions

Covers all of semester 1, units 1 to 6.

Semester 2

7

Linear systems and matrices

  1. Linear systems in two and three variables
  2. Systems of inequalities and linear programming
  3. Matrices: organizing data, adding, scaling, and multiplying
  4. Solving systems with augmented matrices and row reduction
  5. Determinants and Cramer's rule
  6. Inverse matrices and matrix equations
  7. Unit 7 testUnit test14 questions
8

Conic sections

  1. Circles in standard and general form
  2. Parabolas from a focus and a directrix
  3. Ellipses: foci, axes, and eccentricity
  4. Hyperbolas: foci, asymptotes, and eccentricity
  5. Classifying conics and solving nonlinear systems
  6. Unit 8 testUnit test12 questions
9

Sequences and series

  1. Arithmetic and geometric sequences: explicit and recursive rules
  2. Arithmetic and geometric means; sigma notation
  3. Finite arithmetic and geometric series
  4. Infinite geometric series
  5. Unit 9 testUnit test11 questions
10

Probability and statistics

  1. Counting: the multiplication principle, permutations, and combinations
  2. Sample spaces, events, and the addition rule
  3. Conditional probability and independence
  4. Probability with combinations and binomial distributions
  5. Normal distributions, the empirical rule, and z-scores
  6. Sampling, study design, simulation, and margin of error
  7. Unit 10 testUnit test16 questions
11

Trigonometry I: angles, the unit circle, and triangle laws

  1. Right-triangle trigonometry: six ratios and solving triangles
  2. Radian measure, arc length, and sector area
  3. Angles of rotation and the unit circle
  4. Trigonometric functions of any angle
  5. The Law of Sines and the ambiguous case
  6. The Law of Cosines and the area of any triangle
  7. Solving general triangles: bearings and navigation
  8. Unit 11 testUnit test15 questions
12

Trigonometry II: graphs, identities, and equations

  1. Graphs of sine and cosine: amplitude, period, midline, and phase shift
  2. Graphs of tangent and the reciprocal trigonometric functions
  3. Inverse trigonometric functions
  4. Fundamental identities and proving identities
  5. Sum, difference, double-angle, and half-angle identities
  6. Solving trigonometric equations
  7. Modeling periodic phenomena with sinusoids
  8. Complex numbers in polar form and De Moivre's theorem
  9. Unit 12 testUnit test14 questions
Exam

Semester 2 final

  1. Semester 2 final58 questions

Covers all of semester 2, units 7 to 12.

Assessment

Each teaching lesson includes a graded check.

Each of the twelve content units closes with a unit test of 10 to 22 questions.

Each semester closes with a final exam. The semester 1 final has 73 questions on units 1 to 6, and the semester 2 final has 58 questions on units 7 to 12.

Unit tests and semester exams are graded automatically, and all graded work counts toward the student's mastery record, which shows each skill as attempted, familiar, proficient, or mastered.

Contemplanda publishes no grade weighting for this course. A school that decides to grant credit for it also decides how the work counts toward a grade.

Academic integrity

Work in the course must be the student's own.

On the unit tests and semester exams, each question is worked on paper and the answer entered in the course.

Answer keys for graded questions are never sent to the student's device.

Materials and technology

Where the course runs
In a web browser, through Contemplanda Direct
Calculator
Needed for some questions, including some on the unit tests and semester exams. No question in the course calls for a graphing calculator.
Textbook
None required. The course's own lessons are the text.

Published at www.contemplanda.com/courses/algebra-2-with-trigonometry-honors/syllabus

Units, lessons, and counts in this syllabus are generated from the published course.

Questions: info@contemplanda.com

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