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Contemplanda

Core mathematics

Integrated Math 2 Honors

The honors pathway's second year, from quadratics and complex numbers through proof, circles, and probability.

10 units · 83 lessons · 1961 practice items · 280 videos

Integrated Math 2 Honors continues the honors integrated pathway. The first semester is largely algebraic: quadratic functions and the complex numbers their solutions require, piecewise and absolute value functions and their inverses, logarithms alongside exponentials, and an opening unit of formal geometric proof. The second semester turns toward geometry and its measurement, with similarity and right-triangle trigonometry, arcs and angles in circles, circle equations with the unit circle and conic sections, and a closing unit on probability.

The mastery loop from the pathway's first course carries over: each skill deals randomized questions from shared banks until a streak of correct answers closes it, and the unit tests along with both semester finals draw on those same pools. Much of the entry happens in the notation of the subject: a quadratic written in vertex form, a piecewise rule built branch by branch, exact unit-circle values given in radians, proofs assembled step by step, and the counts of a Venn diagram or probability tree filled in on the figure. Short videos sit beside the reading in most lessons.

Syllabus

Every published lesson in this course, by unit.

1Quadratic functions and complex numbers11 lessons
  1. 1Finding roots from vertex form and the symmetry of a parabola
  2. 2Deriving and applying the quadratic formula
  3. 3Choosing the quadratic form that fits the solving job
  4. 4Fluency across solving methods; linear-quadratic systems
  5. 5Solving quadratic and factored-polynomial inequalities
  6. 6Counting x-intercepts with the discriminant
  7. 7Imaginary numbers as solutions of quadratic equations
  8. 8Arithmetic and geometry in the complex plane
  9. 9Conjugates, division, distance, and midpoints of complex numbers
  10. 10Unit 1 review
  11. 11Unit 1 test
2Piecewise, absolute value, and inverse functions9 lessons
  1. 1Reading, writing, and graphing piecewise functions
  2. 2Absolute value functions as two-branch piecewise rules
  3. 3Taking the absolute value of a nonlinear function
  4. 4Inverse functions across tables, graphs, and equations
  5. 5Invertibility, restricted domains, and function composition
  6. 6Inverting an exponential model: the logarithm defined
  7. 7Finding inverses by undoing and verifying by composition
  8. 8Inverse fluency capstone across every representation
  9. 9Unit 2 test
3Logarithmic and exponential functions10 lessons
  1. 1Evaluating, ordering, and bounding logarithmic expressions
  2. 2Graphing logarithmic functions and their transformations
  3. 3Discovering and justifying the properties of logarithms
  4. 4Evaluating with known logs and solving basic log equations
  5. 5Change of base and solving base-10 equations with technology
  6. 6Compounding toward e and the natural exponential function
  7. 7Continuous growth and decay and the natural logarithm
  8. 8Solving exponential and logarithmic equations strategically
  9. 9Mixed equation practice and logarithmic-scale applications
  10. 10Unit 3 test
4Geometric figures and proof8 lessons
  1. 1What makes an argument a proof: triangle angle theorems
  2. 2Special segments and proof-like reasoning from diagrams
  3. 3Flow diagrams and two-column congruence proofs
  4. 4Parallel lines, transversals, and angle theorems by rigid motion
  5. 5Proving and applying parallelogram properties
  6. 6Identifying quadrilaterals from their diagonals
  7. 7Concurrency: medians, bisectors, and triangle centers
  8. 8Unit 4 test
ExamSemester 1 final1 lesson
  1. 1Semester 1 final
5Similarity and right-triangle trigonometry12 lessons
  1. 1Dilations and the proportionality they create
  2. 2Two definitions of similarity and the AA criterion
  3. 3Proportional segments cut by parallel lines
  4. 4Midpoints and ratio partition points on segments
  5. 5Proving the Pythagorean theorem with similar triangles; geometric means
  6. 6How length, area, and volume scale; a first look at trig ratios
  7. 7The six trigonometric ratios from similar right triangles
  8. 8Pythagorean, reciprocal, and quotient identities
  9. 9Verifying trigonometric identities: mastery pass
  10. 10Solving right triangles with trig and inverse trig
  11. 11Modeling with right triangles: elevation, depression, two-triangle problems
  12. 12Unit 5 test
6Circles: arcs, angles, and measurement10 lessons
  1. 1All circles are similar; circle vocabulary and constructions
  2. 2Finding centers with perpendicular bisectors of chords
  3. 3Central, inscribed, and circumscribed angles and their arcs
  4. 4Perimeter and area formulas for regular polygons
  5. 5Special right triangles and composite circle figures
  6. 6Why the circle formulas work: intuitive limit arguments
  7. 7Arc length over radius: the radian
  8. 8Converting between degrees and radians
  9. 9Cylinder and cone volumes connected to sectors and arcs
  10. 10Unit 6 test
7Circle equations, the unit circle, and conic sections11 lessons
  1. 1The equation of a circle from the Pythagorean theorem
  2. 2Completing the square to read center and radius
  3. 3Building the unit circle from special right triangles
  4. 4Sine and cosine as unit-circle coordinates; the other four functions
  5. 5The parabola as equidistant points from focus and directrix
  6. 6Conic form of parabolas, including sideways parabolas
  7. 7The ellipse: constant sum of distances to two foci
  8. 8The hyperbola: constant difference of distances to two foci
  9. 9Classifying conics and building equations from conditions
  10. 10Unit 7 review
  11. 11Unit 7 test
8Probability10 lessons
  1. 1Representing chance: tables, Venn diagrams, and trees
  2. 2Conditional probability across representations
  3. 3Estimating probability from samples; unions, intersections, complements
  4. 4The addition rule and mutually exclusive events
  5. 5Testing independence with two-way tables; sequential probability
  6. 6Independence and the conditional probability formula everywhere
  7. 7The counting principle, permutations, and combinations
  8. 8Probabilities built from combinations
  9. 9Unit 8 review
  10. 10Unit 8 test
ExamSemester 2 final1 lesson
  1. 1Semester 2 final