Contemplanda
Contemplanda course syllabus
Integrated Math 2 Honors
A Contemplanda online course.
Integrated Math 2 Honors continues the honors integrated pathway. Its first semester is largely algebraic: quadratic functions and the complex numbers their solutions require, piecewise and absolute value functions and their inverses, and logarithms with exponentials, followed by a unit of formal geometric proof. In the second semester the course turns to geometry and measurement, with similarity and right-triangle trigonometry, arcs and angles in circles, and circle equations with the unit circle and conic sections, and it closes with a unit on probability.
Each skill's practice deals fresh questions at random from shared banks until four answers in a row are correct, and the unit tests and both semester finals draw on the same pools. Answers are often written in the notation of the subject, such as a quadratic in vertex form, a piecewise rule built branch by branch, or an exact coordinate on the unit circle for an angle given in radians. Proofs are assembled step by step, and the missing counts or probabilities of a Venn diagram or tree diagram are filled in on the figure. Apart from the tests and finals, every lesson has a video.
Course at a glance
- Course title
- Integrated Math 2 Honors
- Publisher
- Contemplanda
- Structure
- 8 units and 2 semester exams, over two semesters (units 1 to 4 in semester 1; units 5 to 8 in semester 2)
- Lessons
- 83 lessons: 73 teaching lessons, 8 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
- 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.
Units and lessons
Every published lesson, by semester and unit.
Semester 1
Quadratic functions and complex numbers
- Finding roots from vertex form and the symmetry of a parabola
- Deriving and applying the quadratic formula
- Choosing the quadratic form that fits the solving job
- Fluency across solving methods; linear-quadratic systems
- Solving quadratic and factored-polynomial inequalities
- Counting x-intercepts with the discriminant
- Imaginary numbers as solutions of quadratic equations
- Arithmetic and geometry in the complex plane
- Conjugates, division, distance, and midpoints of complex numbers
- Unit 1 review
- Unit 1 testUnit test17 questions
Piecewise, absolute value, and inverse functions
- Reading, writing, and graphing piecewise functions
- Absolute value functions as two-branch piecewise rules
- Taking the absolute value of a nonlinear function
- Inverse functions across tables, graphs, and equations
- Invertibility, restricted domains, and function composition
- Inverting an exponential model: the logarithm defined
- Finding inverses by undoing and verifying by composition
- Inverse fluency capstone across every representation
- Unit 2 testUnit test15 questions
Logarithmic and exponential functions
- Evaluating, ordering, and bounding logarithmic expressions
- Graphing logarithmic functions and their transformations
- Discovering and justifying the properties of logarithms
- Evaluating with known logs and solving basic log equations
- Change of base and solving base-10 equations with technology
- Compounding toward e and the natural exponential function
- Continuous growth and decay and the natural logarithm
- Solving exponential and logarithmic equations strategically
- Mixed equation practice and logarithmic-scale applications
- Unit 3 testUnit test15 questions
Geometric figures and proof
- What makes an argument a proof: triangle angle theorems
- Special segments and proof-like reasoning from diagrams
- Flow diagrams and two-column congruence proofs
- Parallel lines, transversals, and angle theorems by rigid motion
- Proving and applying parallelogram properties
- Identifying quadrilaterals from their diagonals
- Concurrency: medians, bisectors, and triangle centers
- Unit 4 testUnit test14 questions
Semester 1 final
- Semester 1 final62 questions
Semester 2
Similarity and right-triangle trigonometry
- Dilations and the proportionality they create
- Two definitions of similarity and the AA criterion
- Proportional segments cut by parallel lines
- Midpoints and ratio partition points on segments
- Proving the Pythagorean theorem with similar triangles; geometric means
- How length, area, and volume scale; a first look at trig ratios
- The six trigonometric ratios from similar right triangles
- Pythagorean, reciprocal, and quotient identities
- Verifying trigonometric identities: mastery pass
- Solving right triangles with trig and inverse trig
- Modeling with right triangles: elevation, depression, two-triangle problems
- Unit 5 testUnit test15 questions
Circles: arcs, angles, and measurement
- All circles are similar; circle vocabulary and constructions
- Finding centers with perpendicular bisectors of chords
- Central, inscribed, and circumscribed angles and their arcs
- Perimeter and area formulas for regular polygons
- Special right triangles and composite circle figures
- Why the circle formulas work: intuitive limit arguments
- Arc length over radius: the radian
- Converting between degrees and radians
- Cylinder and cone volumes connected to sectors and arcs
- Unit 6 testUnit test15 questions
Circle equations, the unit circle, and conic sections
- The equation of a circle from the Pythagorean theorem
- Completing the square to read center and radius
- Building the unit circle from special right triangles
- Sine and cosine as unit-circle coordinates; the other four functions
- The parabola as equidistant points from focus and directrix
- Conic form of parabolas, including sideways parabolas
- The ellipse: constant sum of distances to two foci
- The hyperbola: constant difference of distances to two foci
- Classifying conics and building equations from conditions
- Unit 7 review
- Unit 7 testUnit test13 questions
Probability
- Representing chance: tables, Venn diagrams, and trees
- Conditional probability across representations
- Estimating probability from samples; unions, intersections, complements
- The addition rule and mutually exclusive events
- Testing independence with two-way tables; sequential probability
- Independence and the conditional probability formula everywhere
- The counting principle, permutations, and combinations
- Probabilities built from combinations
- Unit 8 review
- Unit 8 testUnit test13 questions
Semester 2 final
- Semester 2 final54 questions
Assessment
Each teaching lesson includes a graded check.
Each of the eight content units closes with a unit test of 13 to 17 questions.
Each semester closes with a final exam.
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.
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.