Contemplanda
Contemplanda course syllabus
Algebra 2 Honors
A Contemplanda online course.
Algebra 2 Honors is organized around functions. Its first unit treats the parent function families and the features of their graphs; transformations by shifts, reflections, and stretches; piecewise and absolute value functions; even and odd symmetry; and the arithmetic and composition of functions. The rest of the first semester covers inverses with exponential and logarithmic functions; quadratic functions and complex numbers; polynomial functions; rational expressions, equations, and functions; and radicals with rational exponents. The second semester takes up linear systems and matrices, conic sections, sequences and series, and probability and statistics, and each semester ends with a final exam.
Many answers are written in mathematical notation: a domain in interval notation, a piecewise rule entered one piece at a time, a composite function written as an expression, or the solution of an absolute value inequality marked on a number line. Some problems give blank axes on which the graph is sketched. Each skill's practice deals fresh questions at random from shared banks until four answers in a row are correct, and each unit test draws from those same pools. A video accompanies the reading in every teaching lesson.
Course at a glance
- Course title
- Algebra 2 Honors
- Publisher
- Contemplanda
- Structure
- 10 units and 2 semester exams, over two semesters (units 1 to 6 in semester 1; units 7 to 10 in semester 2)
- Lessons
- 74 lessons: 62 teaching lessons, 10 unit tests, and 2 semester exams
- Credit
- Not awarded by Contemplanda
- Enrollment
- Through the student's school
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.
Schools order course seats for their students by writing to info@contemplanda.com, and a student enrolls through their school.
Students enrolled through Contemplanda Direct sign in at direct.contemplanda.com. A student whose school delivers the course signs in on the school's own portal instead.
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
Functions and their transformations
- Function families and the features of their graphs
- Transforming parent graphs: shifts, reflections, and stretches
- Piecewise-defined functions
- Absolute value functions, equations, and inequalities
- Even and odd functions: symmetry by graph, table, and rule
- Combining functions: arithmetic operations and composition
- Unit 1 testUnit test14 questions
Inverses, exponential functions, and logarithms
- Inverse functions across tables, graphs, and equations
- Exponential functions and models
- Nth roots and rational exponents
- Logarithms: undoing an exponential function
- One-to-one functions, restricted domains, and verifying inverses
- Graphs of logarithmic functions, and function families revisited
- Properties of logarithms and the change-of-base identity
- Compounding, the number e, and the natural logarithm
- Solving exponential and logarithmic equations
- Logarithmic scales, models, and inverse functions revisited
- Unit 2 testUnit test22 questions
Quadratic functions and complex numbers
- Quadratic functions: forms, graphs, and models
- Solving quadratics by factoring, square roots, and completing the square
- The quadratic formula and choosing a solving method
- The imaginary unit and complex number arithmetic
- The discriminant and complex solutions of quadratic equations
- The complex plane, conjugates, and division
- Quadratic inequalities and linear-quadratic systems
- Unit 3 testUnit test15 questions
Polynomial functions
- Polynomial arithmetic and factoring higher-degree polynomials
- Dividing polynomials: long division and synthetic division
- The remainder and factor theorems
- Finding every zero: the rational root theorem and the fundamental theorem of algebra
- End behavior and eventual growth
- Graphing polynomials from zeros, multiplicity, and end behavior
- Pascal's triangle and the binomial theorem
- Polynomial inequalities with sign charts
- Unit 4 testUnit test15 questions
Rational expressions, equations, and functions
- Direct, inverse, and joint variation
- Simplifying, multiplying, and dividing rational expressions
- Adding and subtracting rational expressions; complex fractions
- Solving rational equations
- Rational functions: asymptotes, holes, end behavior, and mixed form
- Graphing rational functions and solving rational inequalities
- Unit 5 testUnit test12 questions
Radicals and rational exponents
- Rational-exponent properties and simplest radical form
- Adding, multiplying, and dividing radical expressions
- Square-root and cube-root functions and their graphs
- Solving radical and rational-exponent equations
- Unit 6 testUnit test10 questions
Semester 1 final
- Semester 1 final73 questions
Covers all of semester 1, units 1 to 6.
Semester 2
Linear systems and matrices
- Linear systems in two and three variables
- Systems of inequalities and linear programming
- Matrices: organizing data, adding, scaling, and multiplying
- Solving systems with augmented matrices and row reduction
- Determinants and Cramer's rule
- Inverse matrices and matrix equations
- Unit 7 testUnit test14 questions
Conic sections
- Circles in standard and general form
- Parabolas from a focus and a directrix
- Ellipses: foci, axes, and eccentricity
- Hyperbolas: foci, asymptotes, and eccentricity
- Classifying conics and solving nonlinear systems
- Unit 8 testUnit test12 questions
Sequences and series
- Arithmetic and geometric sequences: explicit and recursive rules
- Arithmetic and geometric means; sigma notation
- Finite arithmetic and geometric series
- Infinite geometric series
- Unit 9 testUnit test11 questions
Probability and statistics
- Counting: the multiplication principle, permutations, and combinations
- Sample spaces, events, and the addition rule
- Conditional probability and independence
- Probability with combinations and binomial distributions
- Normal distributions, the empirical rule, and z-scores
- Sampling, study design, simulation, and margin of error
- Unit 10 testUnit test16 questions
Semester 2 final
- Semester 2 final38 questions
Covers all of semester 2, units 7 to 10.
Assessment
Each teaching lesson includes a graded check.
Each of the ten 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 38 questions on units 7 to 10.
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 or inside a school's own platform
- 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.